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, 2 nd Ed, Palgrave Macmillan Dancey, C. & Reidy, J (2007). Statistics without maths for psychology: Using SPSS for windows (4 th ). 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) Wikipedia ( ) Useful for mathematical formulas and descriptions, and other links, but level is often complex: e.g., t-tests -

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 )… -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 (V a > V b 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 )

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 -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)

Target position 1234 Observations Expected Frequency 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 SmokeDon’t smoke Total Drink Don’t drink Total 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

…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 BeforeAfter Score

…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