Quantitative data analysis

In plain English

Need to know

• Information collected in study called “data”

• Numerical data are called “quantitative”

• Levels of data– Nominal– Ordinal– Interval– Ratio

Mnemonic technique (acronym) to remember these: NOIR

Levels of data: Nominal

• Data goes into categories.• Can only be used as frequencies.• Example: Which newspaper paper do you

read regularly?

Levels of Data: Ordinal

• Data can be put in order… highest to lowest

Example: RacesExample: What grade did you get for each of your gcse’s?

Finish line

Levels of data: Interval• Data are measured using units of equal measure

Example:How anxious are you?

1 2 3 4 5 6 7 8 9 10

Levels of data: Ratio•Must have all properties of interval data•There is also a true zero point

Reaction times: We can measure and compare the exact time because there is an absolute zero point (0 seconds).

Example: How quick is your reaction time?

Measures of central tendency

o Mean – average (add up all the values and divide by the total number of values)o Median – middle valueo Mode – value that is most common

Tell us about a ‘typical’ response for a data set

Mean-Cannot be used with nominal data sets- Not good if too many extreme values-Uses all the values

Median-Not as affected by extreme scores-Not as ‘sensitive’ as the mean

Mode-Useful with nominal data-Not useful if there are several modes

Measures of dispersion

Describes how spread out the data is

o Range – lowest to highest

3, 5, 8, 8, 9, 10, 12, 12, 13, 15 Range = 12 (3-15)Mean = 9.5

1, 5, 8, 8, 9, 10, 12, 12, 13, 17 Range = 16 (1-17)Mean = 9.5

Measures of dispersion

o Standard deviation – shows amount of deviation in a set; describes data around the mean.

Visual Displays: Tables

• Numbers you collect, untreated “raw data”

• Can be summarized using mean, median, mode

3, 5, 8, 8, 9, 10, 12, 12, 13, 15 1, 5, 8, 8, 9, 10, 12, 12, 13, 17

Visual Displays: Bar Chart

• Shows frequency• Can be used with nominal data (categories) or numbers

Visual Displays: Line Graph

• Y-axis shows frequency• X-axis Cannot use with nominal data (categories)

Visual Displays: Scattergram

• Graph used with correlational analysis (we’ll look at this later!!)

Practice!Fakedata and Fraud (2004) carried out an investigation to decide what colour to paint the walls of their Psychology department. They assigned each possible colour to a number (white=1, green=2, brown=3, red=4 etc.) and then carried out a survey to see which colour the staff and students would prefer. Once they had asked everyone their preference, they decided on the final colour by calculating the mean of all the colour values to find an average colour that everyone would like. The mean came out at 3.1, so the researchers painted the department brown. Everyone hated it.

1. Explain where Fakedata and Fraud went wrong, referring to their choice of measure of central tendency in your answer.

More practiceTake a look at each of the following data sets. For each one, state which measure of central tendency you would choose to summarise it, and explain why your choice is appropriate.

(a)1, 3, 4, 4, 7, 9, 10, 10, 12

(b) yes, yes, no, yes, no, no, yes, no, yes, yes, yes, no, no, no, no

(c) 13, 17, 19, 20, 24, 25, 26, 31, 36, 37, 56

(d) 0, 0, 0, 0, 0, 0, 0, 12, 14, 17, 20

(e) 3, 21, 25, 26, 30, 32, 32, 35, 36, 45, 47, 50

Into groups

Group A:Question 2: Why is it better to know about the mean and range of a data set rather than just the mean?Also Data Set 1 (Question 1)

Group B:Question 3: Explain why it might be better to know the standard deviation of a data set rather than the range.

Also Data Set 2 (Question 1)

Group C:Question 4: Look at the following data sets. Which one do you think would have the smaller standard deviation?2 2 3 4 5 9 11 14 18 20 21 22 252 5 8 9 9 10 11 12 14 15 16 20 25

Also Data Set 3 (Question 1)

Group D:There are three graphs on page 81.a.What can you conclude from graph C?b.Write a title that would be suitable for all three graphs.c.Describe the y axis of all three graphs.Also Data Set 4 (Question 1)