Branding - Raynes Maths · Introduction to questionnaire design and experiments including PPDAC Week 2 Questionnaire, purpose, audience and target population. Week 3 Questionnaire

1 Level 2 Mathematics and Statistics, 2018

Experiment, group,

treatment or intervention, subjects or units,

independent or explanatory variable, dependent or response variable,

nuisance variable, randomisation, replication, causal inference,

sample, sources of variation, symmetry, skewed,

unusual values, standard deviation.

Branding

(6 credits)


Topics School Activities

Week 1 Introduction to questionnaire design and experiments including PPDAC

Week 2 Questionnaire, purpose, audience and target population. Week 3 Questionnaire first draft, desk review, second draft.

Week 4 Questionnaire pilot study and complete questionnaire.

Week 5 Conduct experiments, Problem and Plan

Week 6 Conduct experiments / Data, Analysis

Week 7 Conduct experiments / Data, Analysis

Week 8 Conclusion and Evaluation

Assessment These topics will be assessed by way of a digital assignment over 8 weeks, with regular informal milestones. Milestone 1: Complete “Purpose, Audience and Target Population”. Milestone 2: Complete “First Draft”. Milestone 3: Complete “Desk Review”. Milestone 4: Complete “Second Draft”. Milestone 5: Complete “Pilot Study”. Milestone 6: Complete “Final Questionnaire”. Milestone 7: Complete “Problem and Plan”. Milestone 8: Complete “Experiment”. Milestone 9: Complete “Data”. Milestone 10: Complete “Analysis”. Milestone 11: Complete “Conclusion”. These topics will be assessed against AS91263 Design a Questionnaire worth 3 credits and AS91265 Conduct an experiment to investigate a situation using statistical methods worth 3 credits at level 2 of NCEA. Exemplars can be found here: http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/subjects/mathematics/exemplars/ Taste testing Jess and Avya

http://www.nzqa.govt.nz/ncea/assessment/search.do?query=Mathematics&view=all&level=02

http://www.nzqa.govt.nz/ncea/assessment/search.do?query=Mathematics&view=all&level=02

http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/subjects/mathematics/exemplars/

http://www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/subjects/mathematics/exemplars/

https://www.youtube.com/watch?v=vVjC8dptQvk




Credits: Six Total Time allowed: 8 weeks

Branding

ACHIEVEMENT CRITERIA For Assessor’s use only

Achievement Achievement

with Merit

Achievement

with Excellence

Design a questionnaire Design a questionnaire, with justification

.

Design a questionnaire, with statistical insight.

Overall Level of Performance AS91263

Conduct an experiment to investigate a situation using statistical methods

Conduct an experiment to investigate a situation using statistical method, with justification.

Conduct an experiment to investigate a situation using statistical method, with statistical methods, with statistical insight.

Overall Level of Performance AS91265

Due Date: 22nd May, 2018

NAME:

TEACHER:

Level 2 Mathematics – 2018

AS91263 v3

Design a Questionnaire

AS91265 v3

Conduct an experiment to investigate a situation using statistical methods


AS91263 v3 and AS91265 v3

You must hand this cover page, signed authenticity statement, digital submission and printed assessment to your teacher by the due date.

Statement of Authenticity:

You should work independently to complete ALL WRITE UP aspects of this task.

This assessment task is sat under the conditions outlined by NZQA. Authenticity requirements http://www.nzqa.govt.nz/providers-partners/assessment-and-moderation/assessment-of-standards/generic-resources/authenticity/

I, _____________________________, confirm that the work produced for this assessment is entirely my own work. I understand that if any work submitted is not my own work, a Not Achieved grade will be given.

Signed:_____________________________________________Date____________

Introduction

Product Brands versus Budget Brands. To make change or convince a group of people of something, you need to provide evidence to back up your arguments. Also, if you want to find out what other people want you need to ask them.

Task This assessment activity requires you to design a questionnaire and experiment to collect information (data) which could be presented to a group of your choice who would be interested in your results. The choice of product is up to you. You will plan, write, and review the questions for your questionnaire, and following these results, design, implement and analyse an experiment for evidence to support your argument concerning branding of your product choice.

You may wish to watch Taste testing Jess and Avya

http://www.nzqa.govt.nz/providers-partners/assessment-and-moderation/assessment-of-standards/generic-resources/authenticity/

http://www.nzqa.govt.nz/providers-partners/assessment-and-moderation/assessment-of-standards/generic-resources/authenticity/





Standard Milestone Task – OLE submissions Completed

Qu

estio

nn

aire

Milestone 1 Purpose, Audience and Target Population Dates and teacher signed here

Milestone 2 First Draft

Milestone 3 Desk Review

Milestone 4 Second Draft

Milestone 5 Pilot Study

Milestone 6 Final Questionnaire

Exp

erim

ent

Milestone 7 Problem and Plan – approved by teacher

Milestone 8 Experiment – photographic evidence

Milestone 9 Data

Milestone 10 Analysis

Milestone 11 Conclusion

Questionnaire Design:

This must be created, analysed and completed by each individual student. 1. All steps of design process, linked to experimental ideas required. 2. At least 10 pilot surveys

Experimental Design: Problem, Plan, Execution, and Data Collection to be completed as small groups. Analysis, Conclusion and Evaluation by individual student.

1. Problem and Plan needs teacher signature approval. All students in each group must contribute.

2. Photographic evidence of experiment. 3. Data to be shared among group. 4. Individual A.C.E.


Marking Matrices

AS91263 v3 Questionnaire Section Achieved Merit Excellence

1. Objectives

Identified:

• who the survey is for and what they need to know

• research objectives for the survey which are quantifiable.

Has given a brief overview of what information the questionnaire will provide.

a1

Identified:


• research objectives for the survey which are quantifiable.

Has given a more detailed overview of what information the questionnaire will provide.

m1

Identified:


• research objectives for the survey which are quantifiable and appropriate

Has explained how the questionnaire will provide information that suits the needs of the originators.

e1

2. Population and Sampling

Has identified the target population

a2

Has identified the target population. Has described how sample respondents would be selected

m2

Has identified the target population. Has described in detail how sample respondents would be selected

e2

3. Initial survey questions

Has produced survey questions for an initial questionnaire with relevant variables, measures and a range of question types.

a3

Has produced survey questions for an initial questionnaire with relevant variables, measures and a range of question types. Has explained at least one of the following:

• Why particular questions have been included

• How the questions link together

• How the questions build on one another

• The types of survey questions used

m3

Has produced survey questions for an initial questionnaire with relevant variables, measures and a range of question types. Has explained at least two of the following:

• Why particular questions have been included

• How the questions link together

• How the questions build on one another

• The types of survey questions used

e3

4. Self review

Evidence of a self-review and has made some changes to initial questions

a4

Evidence of a self-review and has made some changes to initial questions. Has explained why some changes have been made.

m4

Evidence of a self-review and has made some changes to initial questions. Has explained why some changes have been made, the significance of the changes or why some changes were not made.

e4

5. Pilot survey

Evidence of a pilot survey and changes made to questionnaire as a result of the pilot survey.

a5

Evidence of a pilot survey and have made and explained changes made to questionnaire as a result of the pilot survey.

m5

Evidence of a pilot survey and have made and explained appropriate changes made to questionnaire as a result of the pilot survey.

e5

6. Final Questionnaire

The final questionnaire contains a variety of valid questions that are suitable for the purpose of the survey.

a6

The final questionnaire contains a variety of valid questions that are suitable for the purpose of the survey. The questionnaire is easy to complete.

m6

The final questionnaire contains a variety of valid and relevant questions that will produce information that clearly meets the purpose of the survey. The questionnaire is easy and logical to complete.

e7

7. Final Summary

Some discussion of how the questionnaire meets the objectives and the needs of the originator(s).

a7

More in-depth discussion of how the questionnaire meets the objectives and the needs of the originator(s) and how it was refined during the design process.

m7

Justification of how the questionnaire meets the objectives and the needs of the originator(s), with statistical and contextual knowledge used to refine the questionnaire.

e7


AS91265 v3 Experiment

Achieved Merit Excellence

The student shows

evidence of using each

component of the

investigation process

The student has:

● PROBLEM: Posed an

investigative question

about the experimental

situation.

● PLAN: Planned the

experiment. The student

has determined

appropriate variables and

measures and also

determined the data

collection and recording

methods.

● DATA: Conducted the

experiment and collected

the data.

● ANALYSIS: Selected

appropriate displays and

measures.

CONCLUSION:

● Discussed the displays

and measures.

For example: The student

has clearly compared the

heart rate of the

participants before and

after caffeine showing the

differences between the

two sets of data and

commented on the

distribution.

● Communicated findings in

a conclusion.

For example: The student has clearly stated their conclusion to the question in context.

The student links components of the

investigation process to the context,

explaining relevant considerations in

the process and supporting the

findings with statements that refer to

evidence gained from the

experiment.

The student has:

● Posed an investigative question

about the experimental situation. The

purpose, hypothesis or question

must link to the situation being

investigated.

● Planned the experiment. The student

has determined appropriate variables

and measures and also determined

the data collection and recording

methods. They have considered

related variables and possible

effects of these.

● Conducted the experiment and

collected the data.

● Selected appropriate displays and

measures.

● Discussed the displays and

measures, using supporting

evidence that is linked to the

context.

For example: The student has clearly

analysed how many heart beats on

average the group has increased by

and commented on the middle 50%

and clusters. Comments must be

justified by supporting evidence.

● Communicated findings in a

conclusion and has linked findings

to the experimental situation. For

example The student has clearly

stated their conclusion to their

question in context and produced

statistical evidence to support their

claim.

The student integrates statistical and contextual

knowledge throughout the investigation process

which may involve reflecting on the process or

considering other variables.

The student has:

● Specified the purpose of the investigation and the

investigative question/hypothesis, and shown how

these are relevant to the situation being

investigated.

● Planned the experiment. The student has

determined appropriate variables and measures and

also determined the data collection and recording

methods. They have considered related variables

and possible effects of these, and have developed

the plan to mitigate against these if possible.

● Conducted the experiment and collected the data.

● Selected appropriate displays and measures.

● Discussed the displays and measures, integrating

statistical and contextual knowledge.

For example: The student has clearly commented on

and analysed any increase in heart rates after

drinking caffeine and stated the numerical value in

context. The student will have commented on the

middle 50% and clusters and commented on the

appropriate statistics for those whose heart rate

increased over a specific threshold.

● Communicated findings in a conclusion and has

linked findings to the experimental situation. They

have reflected on key aspects of the

experimental process, for example they may

have considered possible sources of variability

in the data, considered effects of related

variables, considered other areas to investigate.

For example: The student has clearly stated their

conclusion in context and given statistically

produced evidence to support their findings. The

student has also commented on any unusual values

and what other factors could have affected heart

rates for the experiment and given a possible

extension to the experiment based upon their

findings may be given.

Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the

criteria in the Achievement Standard.


Contents

Questionnaire

Vocabulary List 9

What is a questionnaire 10

Journal milestone 1 - Audience, purpose, target population 13

Journal milestone 2 – First draft 14

Journal milestone 3 – Desk review 31

Journal milestone 4/5 – Second draft and Pilot study 35

Journal milestone 6 – Final questionnaire 36

Experimental Design

What is an experiment? 37

Independent versus comparison 40

Paired comparison 42

Problem 43

Plan 44

Data – NZ Grapher 45

Analysis 48

Conclusion - Evaluation 53


Vocabulary List (E Sneddon, 2018)

Bias Something that causes favouritism.

Cause This is usually the treatment.

Context The real-world story or facts behind an experiment.

Control group The group who does not receive the treatment.

Effect The outcome of applying a treatment, measured by the response variable.

Experiment Process of planning, running, and looking at the results of a test.

Experimental Group Group of experimental units.

Experimental Unit Single person who is being tested upon in an experiment.

Experimenter Person or group of people in charge of running an experiment.

Hypothesis Predication, or expectation. Usually made before an experiment.

Independent variable

Usually takes only two values, placebo and treatment.

Median The central or middle value of an ordered dataset

Paired Comparison An experiment on a single experimental group, taking a before and after measurement.

Placebo Simply put, a fake treatment.

Random Allocation Process of randomly assigning experimental units to groups using, for example a deck of cards or flipping a coin.

Response variable The measurement that is the main focus of an experiment.

Spread The spread of the data around the median, measured by the interquartile range (IQR) or standard deviation.

Treatment An applied change or influence that should result in a change in the response variable.

Treatment group The group who receives the treatment

Variable A measurement, or characteristic (e.g. weight or gender).


Conducting a Survey with a Questionnaire What is a questionnaire? A questionnaire is set of questions to a person (respondent) who provides information (data) to the researcher. A survey is when we give a questionnaire to a group of people (our target population). A census, is when all people in a population complete a questionnaire. Questionnaires must be:

Simple to administer Easy to complete Must not offend Confidential (encourage truthful answers) Easy to analyse and conclude

What do you think makes a good questionnaire? (Types of questions or responses)

Survey Ethics Speed dating discussion: You have two minutes to get to know someone. What legal and respectful questions would you ask the other person?

• Confidentiality and anonymity conditions important. • Informed consent – who/what is the intentions of the questionnaire for each

respondent. • Survey results reported as accurately as possible.

Notes:

Advantages of a questionnaire:

Information can be obtained about different data in the same questionnaire do. Can indicate future trends about what people may tend to do in the future. The results of your questionnaire will indicate the direction you will take in your experiment.


Defining the Objectives

• A survey objective is often broad. • Who is the survey for? • Survey objectives should be quantifiable, that is have something required to be

measured. • Example “How healthy are students in this school?”

o I wish to find to find out how physically active middle school and senior school students at (state your school)

o I wish to find out typical eating and drinking habits of male and female students at (state your school)

• Write questions that provide measurable/quantifiable data that better define the survey objective.

Defining the Population The target population is the entire group from which you would if possible like to get your data. The population definition must be as precise as possible. For example, all students in year 12, attending a school you wish to name. The survey population is the subgroup you will question for your questionnaire. This may be a different sample to your experimental group. This may be all year 12’s in one ‘house group’ or a mixture of tutor groups. Population: a set which includes all measurements of interest to the researcher Sample: A subset of the population Use the following scenarios to identify populations and samples ( E Sneddon, 2018).

1. A chip company wanted to see if people in the Australia liked their new logo. Which choice best represents a population? A. A selection of logo artists.

B. Every person in the Australia.

C. A selection of shoppers from different states.

D. 3,800 children age 5 - 15


2. A musician wanted to see what people who bought his last album thought about the songs. Which choice best represents a sample? A. Every person who bought the album.

B. A selection of people who didn't want to buy the album.

C. 250 girls who bought the album.

D. A selection of 3,294 people who bought the album.

3. A gaming website wanted to find out which console its visitors owned. Which choice best represents a population? A. Visitors to the 3DS section.

B. All of the website visitors.

C. Visitors to the PS4 section.

D. Visitors who are on the website for more than 5 minutes.

4. Before a nationwide election, a polling place was trying to see who would win. Which choice best represents a sample? A. A selection of voters over age 50.

B. A selection of male voters.

C. A selection of voters of different ages.

D. All voters

Sample Frame The sample frame is the whole list of the possible survey population. From this list, a randomly selected group are chosen. Respondents are the people who respond to the survey.


Journal – Milestone 1 – Audience / Purpose / Target Population

(E Sneddon, 2018)

Throughout the whole design process, you will need to keep a journal to

record decisions, dates, progress and explanations.

Many jobs require a journal or log book to record this information as

part of your job. For example, truck drivers need to record distances

travelled on each day, trip etc.

For the assessment you will have a journal to complete throughout the

process.

Purpose - the reason for which something is done or created; an intention. Audience - the people who want to know the results of the questionnaire.


Journal – Milestone 2 – First Draft

Your first draft questionnaire should have the following items:

● A title,

● A brief description of the purpose,

● An indication of how long it will take someone to complete the questionnaire,

● A statement about the data being anonymous and confidential,

● Short clear instructions on how to fill in the questionnaire,

● A screening question,

● A thank you for their participation at the end of the questionnaire,

● Instructions on what to do when they are finished.

Data Types (E Sneddon, 2018)

Qualitative (groups) variables are characteristics, that cannot be described by numbers e.g. gender, ethnicity, apple variety.

Quantitative (numerical) variables are characteristics described by numbers e.g. height, age, number of apples, weight. Numerical variables are either discrete or continuous.

Discrete variables (whole numbers), values obtained by counting.

Continuous variables (measurement), values obtained by measuring.

Example:

The school council is designing a questionnaire to determine students’ satisfaction with the school canteen.

Draft questions Data type

1. Do you buy your lunch at the school canteen last week?

a. Yes please continue to question 2 Qualitative


b. No thank you for your time, you don’t need to

continue.

2. How much money did you spend at the canteen last week?

a. $0

b. $1 - $5

c. $6 - $10

d. $10 - $15

e. more than $16

Quantitative Continuous

3. Would you have spent more money if different foods were

available?

a. Yes

b. No

Qualitative

4. How satisfied are you with the foods available at the canteen?

not at all very satisfied 0 1 2 3 4 5

Quantitative Discrete

5. How satisfied are you with the drinks available at the canteen?

not at all very satisfied 0 1 2 3 4 5


6. How many days per week did you buy your lunch last week?

a. 1

b. 2

c. 3

d. 4

e. 5


7. Which days did you buy your lunch last week? (Tick all that apply.)

❏ Monday

❏ Tuesday

❏ Wednesday

❏ Thursday

❏ Friday

Qualitative


Survey Methods (E Sneddon, 2018)

Common survey methods include:

● Face to face interview

● Pen and paper

● Internet

● Email

● Telephone

Each of these methods has different advantages and disadvantages. Some of the factors to

consider are:

● Bias

● Accuracy

● Response rate

● Cost

● Time to administer

● Geographical area coverage

● Sensitive questions

● Videos, sound, graphics

● Which method best suits the target population

Bias

Bias is an inclination or prejudice for or against a person or group. We don’t want our data

to be biased. There are several forms of bias that may be present:

Interviewer bias

Accessibility bias

Self-selection bias


Accuracy

We want the answers that respondents give to be

as accurate as possible.

One way to improve accuracy is to make the

survey anonymous or confidential.

If it is anonymous, people are more likely to give truthful answers.

Response rate

The response rate for your survey is the

percentage of people who respond.

Alternatively, think about it as the number of

people who respond to your survey divided

by the number or people you asked to do

your survey.

You want your response rate to be as high as

possible. Different survey methods give

different typical response rates, as shown from a sample below. (Note: The graph doesn’t

show the response rate for face-to-face interviews, which are typically higher.)

Cost

Depending on your budget, you may choose different methods which have higher or lower costs.

Time to administer

Some survey methods take more time to send out and collect answers from.

Geographical area coverage

Depending on your target population, you may want a wide or small geographical

coverage

For example, if your target population is staff and students at OSC, this is a small

geographical area. Whereas if your target population is teenagers who enjoy

computer games, this is a very wide geographical area to cover.


Other factors

If you want to gather information on sensitive subjects, such as alcohol use, drug use, sexual

health etc, then a face to face interview is more likely to get detailed and honest answers.

Whereas an email questionnaire on sensitive issues is likely to get little to no responses, or

only surface information.

If you have a video or audio message that you want people to watch or listen to, then a

postal survey is not the right method to use. Instead, an online survey - either using email or

the internet allows video and audio to be used.

Depending on the demographics of your target population, it may be that one of the survey

methods is better than others. For example, if your target population includes retired

people, then a postal or phone survey may be better than either email or online surveys, as

retired people are less likely to be regular users of the internet and email.

Example:



Survey method:

As my target population is staff and students at SKC, I will do an online survey as I can easily send out an email to all people at SKC using the mailing list. Below are some of the advantages and disadvantages of choosing this method:

● Bias - all students either have their own device, or are able to access one at school.

This means that the accessibility bias is minimised, which increases the validity of the

answers we will get.

● Response rate - an online survey usually has quite a low response rate, which is a

disadvantage. Ideally it would be best to have as high a response rate as possible, so

that I gather the most information from as many people who use the school canteen,

so that my data represents my target population. I will try to increase the response

rate by asking my friends to fill in the survey for me.

● Accuracy - I am making the survey anonymous, so that it will encourage people to

give truthful answers.

● Cost - an online survey has no actual cost associated with it, other than my time. This

is a definite advantage.

● Time to administer - online surveys are very quick to send out. Google forms also

very quickly collects the answers and displays them, so processing the data takes

almost no time at all.

● Geographical area coverage - I am only wanting to send out the survey to staff and

students at SKC, which is a small geographical area. Therefore, an online survey is

fine for this as I have access to all staff and student emails.

● Sensitive questions - I don’t intend to ask any sensitive questions, so an interview is

not necessary.

● Videos, sound, graphics - if I want to include videos or audio recordings, then online

surveys have a definite advantage here. Using google forms also makes the layout

user friendly and nice to look at.

● Which method best suits the target population - online is a good method for busy

staff and students, as they can do the survey when they have a moment free.


Sampling Methods Deciding who will complete your questionnaire and experiment. In probability sampling, every member of the survey population must have

a. Equal chance of being selected, b. Representative - A sample that bears similar characteristics and proportions

to the population c. Without bias - Relates to the method used to select the sample. Unbiased

methods give all elements of population equal chance of selection Methods of sampling are:

• Simple Random Sampling. Every member of survey population is given a number. Random numbers are generated to select the sample.

• Systematic Sampling. Select every nth member of the survey population until you have the desired sample size.

• Stratified Sampling. Selects members to reflect their proportion in the population. • Cluster Sampling. A whole group is selected to represent the population.

Simple Random Sampling To get a random sample from numbers 1 to 48 inclusive on your calculator:

1. List starting at 1 so input 1+ 2. Push the option button then F6 3. Then push F3 to get the probability 4. Then F4 Ran#x48 5. Truncate (ignore numbers after decimal point)


Systematic Random Sampling Always picking a person at random based on the position of their name on a list. Start with a random number for the first selection point. Divide the total number in the set by the sample size you wish to use in your evaluation. If you want a sample of 30 and you have 180 pieces of data, 180/30 = 6 therefore pick every 6th person in the list Stratified Random Sampling A random stratified sample imitates the characteristic proportions within the population. This can allow for minority groups representation. The population is divided into groups of related items, called strata. Typical strata could be gender, age, location, ethnicity etc. If you wanted to sample year 12 and 13 students in your school and there are 400 year 12’s and 300 year 13’s altogether. 10% of each would total (40 + 30) 70 students. Cluster Sampling In a cluster, a whole group is selected to represent the population. You could choose one year 12 class to represent all year 12 students at your school. Self-Selected Sample These include situations where a person selects to take the questionnaire or experiment. These may include phone-in, online, text or similar. Convenience Sampling

Subjects are selected based on the convenience of availability to the researcher, such as geographic location or personal relationship. This method can be fast and inexpensive, but there is no way to know how a convenience sample relates to the larger population. Quota Sampling In a quota sample the researcher is given an amount of usually a minority group (gender, age, ethnicity, employment status) to ensure relevant groups are included. It has been shown that researchers fill the quotas as quickly as possible and therefore the groups are over-represented.


From the data set provided on the next page (Visitors to New Zealand 2014) as the population, select the following samples of size 30 from the population of 200 using:

1. Simple random sampling

2. Systematic sampling

3. A stratified sample that would ensure that visitors from each region are evenly represented

Comment on:

• how each sample selected appears represent the population. (Does the appear truly random, does each strata appear to represented?)

• how convenient it was to perform Note: in your internal, you are expected to explain in detail how you obtained your sample.


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128

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84A

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4Eu

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85A

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135

Am

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ca18

5Eu

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86A

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136

Am

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ca18

6Eu

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6O

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r

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87A

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137

Am

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ca18

7Eu

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7O

the

r

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88A

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138

Am

eri

ca18

8Eu

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the

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89A

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139

Am

eri

ca18

9Eu

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r

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90A

sia

140

Am

eri

ca19

0Eu

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the

r

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91A

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141

Am

eri

ca19

1Eu

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the

r

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92A

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142

Am

eri

ca19

2Eu

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93A

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143

Am

eri

ca19

3Eu

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94A

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144

Am

eri

ca19

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95A

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145

Am

eri

ca19

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96A

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146

Am

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ca19

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Am

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ca19

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148

Am

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ca19

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149

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102

Asi

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202

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53A

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103

Asi

a15

3A

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rica

203

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104

Asi

a15

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rica

204

Oth

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5A

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105

Asi

a15

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rica

205

Oth

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6A

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56A

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106

Asi

a15

6A

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rica

206

Oth

er

7A

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107

Asi

a15

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me

rica

207

Oth

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8A

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58A

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108

Asi

a15

8A

me

rica

208

Oth

er

9A

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59A

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109

Asi

a15

9A

me

rica

209

Oth

er

10A

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60A

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110

Asi

a16

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rica

210

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111

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112

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a16

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113

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114

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115

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116

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117

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68A

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118

Asi

a16

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69A

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119

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a16

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e21

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70A

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120

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a17

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121

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72A

sia

122

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a17

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73A

sia

123

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a17

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74A

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124

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a17

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75A

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125

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a17

5Eu

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e22

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76A

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126

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a17

6Eu

rop

e22

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77A

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127

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a17

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rop

e22

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28A

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78A

sia

128

Asi

a17

8Eu

rop

e22

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the

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79A

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129

Asi

a17

9Eu

rop

e22

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the

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30A

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80A

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130

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a18

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81A

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131

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eri

ca18

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r

32A

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82A

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132

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eri

ca18

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rop

e23

2O

the

r

33A

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83A

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133

Am

eri

ca18

3Eu

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e23

3O

the

r

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84A

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134

Am

eri

ca18

4Eu

rop

e23

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the

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85A

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135

Am

eri

ca18

5Eu

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e23

5O

the

r

36A

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86A

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136

Am

eri

ca18

6Eu

rop

e23

6O

the

r

37A

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87A

sia

137

Am

eri

ca18

7Eu

rop

e23

7O

the

r

38A

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88A

sia

138

Am

eri

ca18

8Eu

rop

e23

8O

the

r

39A

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89A

sia

139

Am

eri

ca18

9Eu

rop

e23

9O

the

r

40A

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90A

sia

140

Am

eri

ca19

0Eu

rop

e24

0O

the

r

41A

ust

91A

sia

141

Am

eri

ca19

1Eu

rop

e24

1O

the

r

42A

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92A

sia

142

Am

eri

ca19

2Eu

rop

e24

2O

the

r

43A

ust

93A

sia

143

Am

eri

ca19

3Eu

rop

e24

3O

the

r

44A

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94A

sia

144

Am

eri

ca19

4Eu

rop

e24

4O

the

r

45A

ust

95A

sia

145

Am

eri

ca19

5Eu

rop

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5O

the

r

46A

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96A

sia

146

Am

eri

ca19

6O

the

r24

6O

the

r

47A

ust

97A

sia

147

Am

eri

ca19

7O

the

r24

7O

the

r

48A

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98A

sia

148

Am

eri

ca19

8O

the

r24

8O

the

r

49A

ust

99A

sia

149

Am

eri

ca19

9O

the

r24

9O

the

r

50A

ust

100

Asi

a15

0A

me

rica

200

Oth

er

250

Oth

er


Notes:

Sampling Method

How Advantages Disadvantages

Simple Random

Each member of the population is assigned a random number. Random numbers are drawn

Each member of the population has an equal chance of being chosen. Is representative and unbiased

Can be Time-consuming and expensive when taking a large sample from a large population.

Systematic

The population is listed and then a sample is chosen using a pattern such as choosing every kth member

Quicker and cheaper than random sampling

If there is a repeating pattern in the population the sample may not be representative. The level of sampling errors cannot be determined

Sampling of Volunteers

People ask to be part of the sample

Very quick and cheap Biased and not representative

Give clear instructions and descriptions for your problem and plan.


Question Types Questions – the good, the bad and the ugly.

• What makes a question a good question? • What makes a question a bad question? • What are closed questions? • What are open questions? • Do questions change according to the type of data you wish to collect? If so, how?

link

In your questionnaire, you must have at least 3 different types of questions (this is a

requirement of the Achievement Standard). The different types are:

● Open

● Closed

○ Yes / No

○ Checklist

○ Ranking

○ Rating (scales)

https://www.youtube.com/watch?v=G0ZZJXw4MTA&list=RDG0ZZJXw4MTA#t=74


Question type Advantages Disadvantages

Open

● Question doesn’t lead the

respondent

● Respondent doesn’t have to read

through a long list of responses

● More richer and detailed data as

respondent thinks more deeply

● Harder to analyse results

● Answers can be misinterpreted,

incomplete, etc.

● Takes longer to complete for

respondent, may mean less

people want to start or complete

the questionnaire

Closed

● Numerical data is easier to

analyse

● Easier and quicker to enter data

● Easier and quicker for people to

answer, so they are more likely to

complete the questionnaire.

● Not all possible answers are

available

● Choices available may influence

respondents

● Respondents might not think

deeply about the question

Non-response

This is when a respondent doesn’t answer all the questions. We can minimise this by:

● Keep it simple

○ Short and quick,

○ Simple easy to read questions,

○ Presentation well-spaced,

○ Clear instructions,

○ Anonymity and confidentiality,

○ Thank you at the end.

• How long is a good questionnaire? • What is essential to know, what would be useful to know and what would be

unnecessary? • If the question is not important should it be eliminated?

Link

https://www.youtube.com/watch?v=HfGyiRBwSec


Example: (E Sneddon, 2018)


Research objectives:

● Determine how much students currently spend at the canteen.

● identify how satisfied students are with the canteen at the present time.

● Estimate how many times per week each student uses the canteen on average.

● Compare how much the canteen is used on different weekdays.

Draft Questions

1. Do you buy your lunch at the school canteen last week?

a. Yes please continue to question 2

b. No thank you for your time, you don’t need to continue.

2. How much money did you spend at the canteen last week?

a. $0

b. $1 - $5

c. $6 - $10

d. $10 - $15

e. more than $16

3. Would you have spent more money if different foods were available?

a. Yes

b. No

4. How satisfied are you with the foods available at the canteen?

not at all very satisfied

0 1 2 3 4 5 5. How satisfied are you with the drinks available at the canteen?

not at all very satisfied

0 1 2 3 4 5

6. How many days per week did you buy your lunch last week?

a. 1

b. 2

c. 3

d. 4

e. 5


7. Which days did you buy your lunch last week? (Tick all that apply.)

❏ I didn’t buy my lunch

❏ Monday

❏ Tuesday

❏ Wednesday

❏ Thursday

❏ Friday

Notes: Use simple language. Write questions everyone will understand in the same way. Start the questionnaire with questions that are likely to be interesting or get the respondents attention. Avoid leading questions and double negatives. Keep the number of questions to a minimum. Keep each question brief yet clear and concise. Question Design Tips (E Sneddon, 2018)

Tip Example

Make sure that you add instructions if the possible responses are not clear tick one box only OR tick all that apply

Checkboxes should be used for responses that are known ie days of the week, times, age categories, etc.

On which weekday are you most likely to socialise with friend (circle answer) Monday Tuesday Wednesday Thursday Friday

Other with comment should be used if additional information may be useful. Other on its own may not be of much use when analysing data.

What is your favourite junk food? pies sweets cakes other If you answered other, what is it? ____________________________

Open questions should be used only when the responses can be quite varied, so the researcher cannot readily identify the expected answers.

Yes/no answers often require follow-up questions

Do you smoke every day? (circle answer) Yes/no


followed by: If you said yes, give an indication of how many cigarettes you smoke a day. A 1 to 5 B 6 to 10 C 11 to 20 D 21 to 30 E more than 30

Skips are useful when not everyone needs to answer all questions

5. Do you smoke? (circle answer) Yes/no

followed by:

If you said no, go to question 8.

Writing questions (E Sneddon, 2018)

We want data that is:

● Accurate,

● Unbiased,

● High response rate,

● Quick for respondents to answer,

● Useful and meets the purpose.

Good questions are:

● Specific,

● Get truthful answers,

● Fair (not misleading),

● Clear and simple language,

● Clear definitions,

● Correct grammar and spelling,

● Keep the questionnaire as short as

possible.

Things to avoid:

Double negatives

Jargon or slang

Double barrelled questions Overlapping response categories


Offensive language

Embarrassing questions

Too many questions


Journal – Milestone 3 – Desk review (E Sneddon, 2018)

Now that you have a first draft of the questions, your next step is to review these, and get someone else to review them. This process is called a desk review.

There is a template available that you can use to do a desk review.

Order of questions

● Screening question first.

● Demographic questions (age, gender, location etc) leave until last, unless they are

needed for screening.

● Group the questions together by topic.


Checklist for desk review

OK? Comment

Introduction

Meaningful Title

Purpose is clear

Indication of how long it will take to complete the questionnaire

Clear instructions of how to complete

Anonymity statement

Questions:

Target Population identified and screened for

Does the question meet the purpose and research objectives?

Question is clear, easy to understand

All possible answers are catered for

At least 3 different types of questions (e.g. multi-choice, open, etc)

Instructions given where appropriate ie tick all that apply or tick one only

Are any questions repeated or unnecessary?

Are there questions missing which would be important for the purpose?

Appropriate language, spelling, grammar, etc

Questions in logical order

Questions will give responses that are easily analysed

Conclusion

Instructions for what to do with completed questionnaire included

Thank you included

How to access results of survey (if respondent wants to see)

Overall presentation of questionnaire

Layout is clear and uncluttered


Exercise:

Identify what is wrong with the following questions and rewrite them.

Question What is wrong? Rewritten question

1 How often do you buy cosmetics? Circle 1 A every week B once a month C every three months D every 6 months or more

2 How much do you spend on cosmetics in a month? A less than $50 B between $50 and $100 C more than $100 D none

3 Do you agree or disagree with the following statement: I felt welcomed by both the staff and students at school.

4 Do you agree or disagree with the following statement: We should not reduce spending on public health services.

5 Is Colgate your favourite toothpaste?

❏ Yes

❏ No


6 How long did you spend in the gym today? ❏ less than 30 minutes

❏ less than 45 minutes

❏ less than 60 minutes

❏ 60 minutes or more

7 Do you agree that single sex schools are better than co-ed schools?

❏ Yes

❏ No

8 How much fizzy drinks do you drink each week?

❏ None

❏ A little

❏ Quite a bit

❏ A lot

9 How much do you like your cellphone? Give a rating from 1 to 5.

10 How many cars does your family have?

❏ 1 car

❏ 2 cars

❏ 3 cars

11 Why are social networking sites harmful?

12 What is your NZQA NSN?


Journal – Milestone 4 – Second Draft

(E Sneddon, 2018)

When your desk review is completed, you can make changes to your questionnaire. For your assessment, you want to have at least 3 changes that you have identified and justified.

Journal – Milestone 5 – Pilot Study (E Sneddon, 2018)

This is where you do a test drive of your questionnaire with a few students.

We do this to get feedback on how we can improve the questionnaire.


Journal – Milestone 6 – Final Questionnaire (E Sneddon, 2018)

The last step is to finalise any changes to your questionnaire after the pilot study. You also want to reflect whether your questionnaire meets the purpose. For this assessment, you would be finished after completing this step (and finishing your journal / log book). For your experiment, you would now continue on, select a sample using a random sampling method. You want a sample size of at least 30.

Working towards Merit and Excellence In your log book, you should be recording every choice you make and the reasons why you make it, relating each decision to the purpose of the questionnaire and/or the target population and the wider context. When you have completed, evaluate the whole process and the final version of the questionnaire.


Experimental Design Experimental Design notes from E Sneddon, 2018 with the exception of inzight notes.

What is an experiment?

Watch the ghostbusters video, and answer the following questions: 1. What was the experiment testing for? 2. What would Dr. Venkman have been recording (writing down)? 3. What was the treatment or stimulus? 4. Is it possible for the subject to have just guessed the correct answer? 5. The experiment is repeated 80 times for each person. If there are 5 possible answers,

how many out of 80 would you expect them to get right if they just guessed? 6. How many out of 80 would they need to get right to show evidence of Extra Sensory

Perception? 7. Is it a well-designed experiment?


Observational study versus Experimental study

Research the difference between an observational study and an experimental study, then answer the following questions. 1. In which type of study (observational or experimental) does the research apply a

treatment? 2. In which type of study (observational or experimental) does the researcher simply

observe?

Experiments

In this topic we are only concerned with true experiments. What classifies an investigation as an experiment? There must be an intervention. The experimenter must change just one thing between the groups being studied.

Experiment Observational study

A group which does not have to be a random sample

A sample which should be representative of the population

Treatment which is decided by the experimenter (e.g., students are randomly assigned to use their right or left hand)

Samples from two different populations or situations may be compared (e.g. year 9 and year 12 students).

Subjects or units are the individuals which are treated by the experimenter.

Subjects may also be called individuals or values.

Each group needs to be independent. The populations the samples are from may not be independent.

Independent or explanatory variable is changed by the experimenter

Variables are not altered by the investigator.

Dependent or response variable is measured by the experimenter.

Dependent variable is measured by the investigator.


An experiment is a study in which a researcher attempts to understand the effect that a variable (an explanatory or independent variable) may have on some phenomenon (the response or dependent variable) by controlling the conditions of the study. In an experiment the researcher controls the conditions by allocating individuals to groups and allocating the value of the explanatory variable to be received by each group. A value of the explanatory variable is called a treatment. In a well-designed experiment, the allocation of subjects to groups is done using randomisation. Randomisation attempts to make the characteristics of each group very similar so that if each group was given the same treatment, the groups should respond in a similar way, on average. Experiments usually have a control group, a group that receives no treatment or receives an existing or established treatment. This allows any differences in the response, on average, between the control group and the other group(s) to be visible. When the groups are similar in all ways apart from the treatment received, then any observed differences in the response (if large enough) among the groups, on average, is said to be caused by the treatment.


Independent versus Paired Comparison

We are studying experiments which: • make a comparison between a treatment group and a control (2 Independent groups) OR • make a comparison between one treatment and another for the same group (paired

comparison).

Experimental design principles

Issues that need to be considered when planning an experiment. The following issues are the most important: Comparison and control: Most experiments are carried out to see whether a treatment causes an effect on a phenomenon (response). In order to see the effect of a treatment, the treatment group needs to be able to be compared fairly to a group that receives no treatment (control group). If an experiment is designed to test a new treatment then a control group can be a group that receives an existing or established treatment. Consider carefully whether you have maintained controlled conditions for each treatment. Were any individuals able to observe someone else do the experiment before they did it? Ideally, no subject should know anything about the experiment before they do it, as the knowledge might affect how they respond to the treatment. Randomisation: A randomising method should be used to allocate individuals to groups to try to ensure that all groups are similar in all characteristics apart from the treatment received. The larger the group sizes, the better the balancing of the characteristics, through randomisation, is likely to be. Variability: A well-designed experiment attempts to minimise unnecessary variability. The use of random allocation of individuals to groups reduces variability, as does larger group sizes. Keeping experimental conditions as constant as possible also restricts variability. Replication: For some experiments, it may be appropriate to carry out repeated measurements. Taking repeated measurements of the response variable for each selected value of the explanatory variable is good experimental practice because it provides insight into the variability of the response variable.


TWO INDEPENDENT GROUPS

There are two possible situations, two independent roups and paired comparison.

We are going to focus on paired comparison.


PAIRED COMPARISON

With a paired comparison experiment, we need to aware of the fact that we will ask each

experimental unit (usually a person) to do 2 tests, a before and after treatment test. Paired

comparison is where measurements are taken on the same person or object. You cannot do separate dot plots of before and after and discuss as if they were independent.


Problem

Writing an investigation question is the same for both types of experiments. You still need:

• Groups

• Measure

• Population described

You also need to make a prediction about what you think will happen.

Example

If you are interested in doing an experiment to see if senior students can write quicker with their dominant or non-dominant hand, our investigation question might be:

I wonder if writing with your dominant hand causes you to write faster

than writing with your non-dominant hand, for senior students in

12STA at McAuley High School, in 2016.

Our prediction might be:

I think students can write quicker with their dominant hand rather

than their non-dominant hand because the muscles in their dominant

hand are used more, stronger, and therefore will help them to write

quicker.

Some research to support this:

“There was a general trend for the dominant hand to be faster in

manipulating objects than the non-dominant hand in both right- and

left-handed individuals.”

This quote supports the idea that students might be faster writing with their dominant hand, and the quote was taken from: http://hth.sagepub.com/content/8/1/4.abstract.

Experiment 2

Throwing balls into a target is often considered to be more difficult if the target is further away, but is this actually the case? Write an investigation question and a prediction for this experiment.


Plan

The advantage of a paired comparison is that you need less experimental units to collect data from. For example, rather than having 15 students do one test and 15 students do the second test, all 30 students will do both tests, so that your sample size is 30 rather than 15 per group. Increasing the sample size increases the accuracy of the results.

You will need to think carefully about whether the order in which the treatments are given will affect the response variable. To control for order, you can randomly assign students to two groups, which do the two treatments in different order.

If you are doing a before/after experiment, one randomly selected group can be the control group in which no treatment is given, but the response variable is measured before and after a time lapse as for the treatment group.

When you collect the data, you will need an extra column on your table, called “Differences”.

Example

Here is an example of what the data for the dominant versus non-dominant hand experiment looks like. Notice the third column of differences.

Experiment 2

Plan Write a set of instructions on how to carry out your experiment (including the sample size, random allocation, and how to record the data).


Data

INZIGHT will not give arrows plots, therefore if doing a paired comparison NZ grapher will give all the plots.

NZ Grapher

The next step is to open NZGrapher and Paste Table (all three columns) in.

We now choose a different graph type: Paired Experiment.

Next select the two variables. In this case I want to calculate the Difference = Non-dominant hand – Dominant hand, So I need to put the Dominant hand as Variable 1, and the Non-dominant hand as Variable 2.


You then get the following graph appear:

Then tick the following options:

• Summaries

• Box Plots

• Informal C-I

• C-I Limits

Give the graph a Title.

Copy and paste this graph into your experiment document. This is a graph of the differences, which we will come back to analysing.


The first graph we want to analyse, is the Arrows graph.

When you select the Arrows graph, the following graph will appear. (We will look at how to interpret these graphs in the Analysis section).

Copy and paste this graph into your experiment document. Experiment 2 Data Roles: Presenter: Materials manager: Data recorder: Observation recorder: Data: Now it’s time to carry out the experiment with the class, following the instructions you created previously, and record your data on the Google Sheet. Observations:

Next, you need to copy and paste your data into NZ Grapher or INZIGHT, and get the graphs and statistics that you need.


Analysis The analysis that you do is different. Because the two groups that you are comparing (before and after) are NOT independent, we calculate the differences, and then draw two types of graphs – a graph of the differences, and an arrows graph. Additionally, you analyse the shape, center and spread of the DIFFERENCES (treating it as a single sample).

Analysis 1: Arrows graph

Before Intervention (or control, or treatment one)

After Intervention (or treatment, or treatment two)

You need to describe what you see only in terms of the direction of the arrows (i.e., the differences).

Example

Notice the arrows going from the dominant hand data values, to the non-dominant hand values. Each arrow represents how much faster or slower each person writes with their dominant or non-dominant hand.


Questions

1. How is the difference between the writing speeds represented on this graph?

2. What does an arrow going in this direction mean?

3. What does an arrow going in this direction mean?

4. What does it mean if lots of arrows are going in both directions? E.g.


5. What direction are most of the arrows on the graph going in? What does this mean?

6. What would the analysis for this experiment be from the arrows graph?


Analysis 2 – Differences graphs

And make a dot plot of the differences (there may be positive and negative differences).

You need to describe what you see (centre, spread, unusual features). Compare the centre and spread of the distributions.

Example


Questions

1. What does each data value represent?

2. All of the values are positive, what does this mean?

3. If all the values were negative, what would that mean?

4. If the values were both positive and negative, what would that mean?

5. Describe the features of the Differences graph (shape, center, spread).

Shape: The shape of the differences between the time it takes 12 STA students in this experiment to write with their dominant and non-dominant hand, is right skewed, because there is a long tail on the right hand side, and the data on the left hand side is closely packed. Center: I notice that the median difference between the time it takes 12STA students in this experiment to write with their dominant and non-dominant hand is 59.5 seconds. Because this difference is positive, this shows that it takes students a median of around 59.5 seconds longer to write a paragraph with their non-dominant hand, compared to their dominant hand. Spread: IQR (Difference) = 82 – 41.5 = 40.5 seconds The spread of the differences between the time it takes students to write with their dominant hand and non-dominant hand has a spread in the middle 50% of 40.5 seconds. That shows that there is a reasonable spread in the time differences. Confidence Interval: I can estimate that the median difference in time that 12STA students in tis experiment take to write a paragraph with their dominant hand is around 59 seconds shorter than with their dominant hand. I am not completely certain in this estimate, but I am more confident saying that it is likely that the students take between 48 seconds and 71 seconds longer to write with their non-dominant hand than their dominant hand.


Experiment 2

Describe and justify the features of your data:Co

Conclusion - Evaluation

Making the call.

If the confidence interval includes zero, it suggests that there is not sufficient evidence to claim that the explanatory variable caused a change in the response

variable for this group.

Example

Here is data looking at different blends of concrete, and measuring how hard the concrete is to see which Blend might be better.

Notice down the left-hand side are the comparisons they are making for the differences in hardness of concrete. Notice on the graph, that some confidence intervals of differences are positive, some are negative, and some include the value of zero in the confidence interval.


Questions:

1. What does it mean if the confidence interval includes zero?

2. What does it mean if the confidence interval is all positive?

3. What does it mean if the confidence interval is all negative?

Example

Discuss the results in context. As the confidence interval does not contain zero, this means we have enough evidence to prove that the treatment ‘tends to cause’ a difference for this experiment on this group. Because the confidence interval is all positive, this shows that writing with the dominant hand tends to be quicker than writing with the non-dominant hand. I have enough evidence to show that writing with the dominant hand tends to cause students to write faster than writing with their non-dominant hand, for students in 12STA in this experiment at McAuley High School, in 2016. Experiment 2

Discuss the results in context.


Journal – Questionnaire

You will: • Define the objectives - State the purpose of the questionnaire and your responding

experimental plan. Who will use it. List the variables • Produce an initial survey - Pose survey questions including variables and measures

that will give you information to help you when planning your experiment. • How will you select a sample to ask? What/who is your target population? • Know how every question will be analysed and be prepared to handle missing data.

Know what kind of data you need to collect. What are the variables? Are they numerical? Categorical? Opinion?

• Conduct a self-check of the initial survey. • Refine the initial survey. • Conduct a pilot survey. • Refine the survey. • Produce the final questionnaire. • Produce a report detailing how the questionnaire meets the objectives - Document

the process in a journal discussing decisions.

Experiment

You will:

• Define your experiment using the results of your questionnaire. • Follow through with the PPDAC cycle.

Documents

Branding - Raynes Maths · Introduction to questionnaire design and experiments including PPDAC Week 2 Questionnaire, purpose, audience and target population. Week 3 Questionnaire