MSc Applied Psychology
PYM403 Research
Methods
Quantitative Methods I
Quantitative Methods I:
T-tests, chi squared, other nonparametric methods
Aims of this session to consider:



Levels of measurement
Parametric / nonparametric data
Choosing an appropriate statistical test

chi squared

other nonparametric tests of difference
(Mann Whitney / Wilcoxon signed ranks)

t-tests (independent / related samples)
Quantitative Methods I:
Indicative Reading
Books on conducting statistical analyses, e.g.,
Clark-Carter, D. (1997). Doing Quantitative Psychological Research:
From Design to Report. Brighton: Psychology Press.
…with SPSS
Field, A (2008) Discovering Statistics Using SPSS for Windows: Advanced
Techniques for beginners, Sage Publications
Brace, N, Kemp, R & Snelgar, R (2003) SPSS for Psychologists: A Guide
to Data Analysis using SPSS for Windows, 2nd Ed, Palgrave Macmillan
Dancey, C. & Reidy, J (2007). Statistics without maths for psychology:
Using SPSS for windows (4th). London: Pearson. (Chapters 6, 8 & 15)
Quantitative Methods I:
Useful websites
Useful websites, e.g.,
Website on how to choose the right statistical test, with SPSS (but based
on old DOS-based version, but still useful for interpreting output)
http://www.ats.ucla.edu/stat/mult_pkg/whatstat/default.htm
Wikipedia ( http://en.wikipedia.org/wiki/Main_Page ) Useful for
mathematical formulas and descriptions, and other links, but level is often
complex:
e.g., t-tests - http://en.wikipedia.org/wiki/T-test
How to choose an appropriate
quantitative analysis technique
Refer to your research hypotheses
Research hypotheses should be specific and should be
expressed in terms of the independent and dependent
variables.
Does the hypothesis predict a difference or a relationship?
- Is there a difference between 2 or more groups or
conditions?
- Is there a relationship between 2 or more variables?
- Will the value of one variable predict the value of another
variable?
How to choose an appropriate
quantitative analysis technique
-At what level of measurement is the data collected?
Nominal
Ordinal
Interval
Ratio
E.g., See Fife-Schaw ‘Levels of Measurement’ (in Breakwell
et al., 1995, pp. 38-49)…
-Discrete vs. continuous variables (p. 43)
Choices over levels of measurement (p. 46)
How to choose an appropriate
quantitative analysis technique
-Do the data collected meet the assumptions required for
parametric tests?
- Homogeneity of variance (Va > Vb x 3)
- At least interval level of measurement
-- (often with minimum range of scores > 20)
- Population from which samples are drawn must be normally
distributed (consider skew & kurtosis)
For parametric vs. nonparametric tests, see
“Choosing a statistical test” - See Fife-Schaw ‘Bivariate
Statistical Analayses’ (in Breakwell et al., 1995, pp. 353-359)
How to choose an appropriate
quantitative analysis technique
-If the hypothesis predicts a difference
How many IV’s and DV’s are there?
How many levels of each IV are there?
Is the design related or unrelated or mixed?
-If the hypothesis predicts a relationship
How many IV’s (predictors) and DV’s (criteria) are there?
Choosing an appropriate
analysis technique - differences
unrelated
- 2 test
related
- McNemar test
NB. Although chi-square is a test of association, it is
classified under differences.
-Nominal
-Ordinal
-
unrelated
related
- Mann-Whitney test
- Wilcoxon signed ranks
-Tests for differences between the medians of the 2 groups
-Interval
-
unrelated
related
- Unrelated t-test
- Related t-test
-Tests for differences between the means of the 2 groups
Choosing an appropriate
analysis tests - relationships
-Nominal
-If 1 dichotomous variable
- Point biserial correlation
-If 2 dichotomous variables - Phi coefficient
-If >2 levels of nominal
- Chi-square test
-NB. Chi-square test indicates an association but not strength
-Ordinal
If at least ordinal
- Spearman’s rho correlation
- Interval
-If both interval
- Pearson’s Product-Moment
Before Inferential Analysis…
Before actually carrying out the chosen inferential
analysis:

Get to know your data
 Produce some descriptive statistics - check that there
are no silly answers e.g., maximum or minimum values
beyond possible range, plausible means/SDs, non-restricted
range, etc

Produce some graphical representations - how are the
data distributed e.g. frequency histograms, stem and leaf plots

Summarise and describe what you have deduced
Chi Squared
Different types:
- One-variable chi squared (goodness of fit test) One variable
- Chi squared test for independence: 2 x 2 variables
- Chi squared test for independence: r x 2 variables
Dancey, C. & Reidy, J (2004). Statistics without maths for psychology:
Using SPSS for windows (3rd). London: Pearson.
CHAPTER 8 – Measures of Association
One –sample Chi Squared
(Goodness of fit test)
One –sample Chi Squared
(Goodness of fit test)
Target
position
1
2
3
4
Observations
290
260
224
226
Expected
Frequency
250
250
250
250
One-sample chi square
- Input data
- One column for observations
- One column for category
Select Data… select Weight Cases…
select Weight cases by… insert Frequency variable
…Select Nonparametric Tests… select Chi-Square…
…insert Frequency variable in Test Variable List…
…select OK
One-sample Chi-Square: Output
chi square = 11.8, df = 3, p = .008
2x 2 Chi Squared Test
Smoke Don’t Total
smoke
Drink
35
20
55
Don’t drink
15
30
45
Total
50
50
…input Frequencies
…in Variable View…Label category variables …
…Weight Cases by frequency variable…
…select Descriptive Statistics… select Crosstabs
…move row variable (Drink) to Row(s)…
…move column variable (Smoke) to Column(s)…
…select Statistics… select Chi Square…
…select Cells… select Observed and Expected…
2 x 2 Chi Square Output:
Chi Square = 9.1, df = 1, p = .003
Other Nonparametric Tests for
Differences
- Independent groups (between subjects)
Mann-Whitney U Test (or Welch’s t for heterogeneous data)
- Use when t- test not possible (small sample, etc)
- Ranks data
- Dependent groups (repeated measures)
Wilcoxon Signed Rank Test for Matched Pairs
Dancey, C. & Reidy, J (2004). Statistics without maths for psychology:
Using SPSS for windows (3rd). London: Pearson. CHAPTER 15 – Nonparametric Statistics
Mann- Whitney U Test
Mood
Bad
Mood
Good
Mood
Score
7
15
14
3
17
4
6
11
7
9
4
7
…select Analyze… select Nonparametric Tests…
select 2 Independent Samples…
…insert Score into Test Variable List…
insert Condition into Grouping Variable and Define Groups
Mann-Whitney U Test:
U = 10.0, N = 12, p = .219
Wilcoxon Signed Ranks Test
Mood
Score
Before
5
6
2
4
6
7
3
5
5
5
After
7
6
3
8
7
6
7
8
5
8
…select Analyze… select Nonparametric Tests…
select 2 Related Samples…
…insert both variables into Test Pairs List…
select Options… select Descriptives… select Quartiles
Wilcoxon Signed Rank Test for matched pairs:
T = -2.26, N = 10, p = .024
Parametric Tests for
Differences
- Must fulfil parametric test assumptions (but robust)
- Independent groups (between subjects)
Independent Groups t-test
- Dependent groups (within subjects / repeated measures)
Paired t-test
Dancey, C. & Reidy, J (2004). Statistics without maths for psychology:
Using SPSS for windows (3rd). London: Pearson.
CHAPTER 6 – Analysis of Difference Between Two Conditions: the t-test
Parametric Tests for
Differences
-Independent groups (between subjects)
Independent Groups t-test
- Create Data
- Define conditions
- Analyse – Compare Means – Independent Samples t-test
- Insert Test Variable – Define Grouping Variable
- Consider Descriptive Statistics
- Report Inferential Statistics
Parametric Tests for
Differences
- Dependent groups (between subjects)
Paired t-test
- Create Data (before / after scores in separate columns)
- Analyse – Compare Means – Paired Samples t-test
- Insert Variable Pairs
- Consider Descriptive Statistics
- Report Inferential Statistics