Chapter 1 DATA AND PROBLEM SOLVING. Section 1.1 GETTING STARTED

Chapter 1 DATA AND PROBLEM SOLVING

Section 1.1 GETTING STARTED

Vocabulary

Statistics – The science of gathering, describing and analyzing data or the actual numerical descriptions of sample data.

Population – The particular group of interest.

Data – Information prepared for a study

Census – When data is obtained from every member of the population.

Parameter – A numerical description of a particular population characteristic.

Sample – A subset of the population from which data is collected.

Sample Statistic – The actual numerical description of a particular sample characteristic.

Two Types of Statistics

Descriptive Statistics –

Inferential Statistics -

Example 3

Descriptive

Example 4

Inferential

Section 1.2 LEVEL OF MEASUREMENT

Qualitative vs. Quantitative

Labels or descriptions of traits of the sample Categorical

Examples

Foods

Places

Colors

Identification Numbers

Counts and measurements Numerical

Examples

Test scores

Average rainfall

Median heights

Continuous vs. Discrete

Data that can take any value within an interval Cannot be counted

Examples

Measurements

Time

Temperature

Data that refers to individual data that is countable Can be counted

Examples

Number of pets

Levels of Measurement

Example 1

Qualitative

Neither

Nominal

Example 2

Quantitative

Continuous

Ratio

Section 1.3 THE PROCESS OF A STATISTICAL STUDY

Ways to Collect Data

Sampling Methods

RandomEvery member of the population has an equal chance of being selected.

Example:

Drawing names from a hat.

Stratified The population is divided into groups based on a characteristic, then members from each group are chosen randomly.

Example:

Separating students by class, then randomly choosing 5 from each class.

Cluster The population is divided into groups that are similar to the population, then groups are chosen at random to sample.

Example:

Dividing students so there are 10 of each class in a group, then choosing 2 groups to sample.

Sampling Methods cont.

SystematicThe population is aligned in no specific order then every nth member is chosen.

Example:

Choosing every 5th person.

ConvenienceChoosing a sample the is “convenient” to the researcher.

Example:

Teacher surveying students from one of their classes to represent the population.

Types of Studies

Single-blind vs. Double-blind

Additional Vocabulary

Section 1.4 THE REALITY OF CONDUCTING A STUDY

Institutional Review Board

A group of people who review the design of a study to make sure that it is appropriate and the no unnecessary harm will come to the subjects involved.

Ethical and Practical Concerns

Informed ConsentCompletely disclosing to participants the goals and procedures involved in a study and obtaining their agreement to participate.

Biased A study tends to favor certain results

Researcher BiasWhen the researcher influences the results of the study to favor a certain outcome.

Sampling ErrorsErrors resulting from the way the sample is chosen

DropoutA participant who begins the experiment but then fails to complete it.

Participation BiasWhen there is a problem with either the participation – or lack thereof – of those chosen for the study.

Non-sampling ErrorsOccur from sources other than the construction of the sample.

Processing Errors A type of non-sampling error that occurs in the reporting, could be a typo in the data set.

Non-adheresSubjects who stray from the directions they were given, but remain in the sample to the end.

Confounding VariablesVariables that the researcher did not account for.