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 hypothesesResearch 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?

NominalOrdinalIntervalRatio

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

-Nominal - unrelated - 2 test- related - McNemar test

NB. Although chi-square is a test of association, it is classified under differences.

-Ordinal - unrelated - Mann-Whitney test- related - Wilcoxon signed ranks

-Tests for differences between the medians of the 2 groups

-Interval - unrelated - Unrelated t-test- related - 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

-OrdinalIf 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

Frequency250 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: Outputchi square = 11.8, df = 3, p = .008

2x 2 Chi Squared Test

Smoke Don’t smoke

Total

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 – Non-parametric 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 Before After

Score 5

6

2

4

6

7

3

5

5

5

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