Choosing the Right Test: Mathematics & Statistics Help

1. Choosing the right testMathematics & Statistics HelpUniversity of Sheffield

2. Learning outcomes • By the end of this session you should know about: • Some useful approaches to analysing data • By the end of this session you should be able to: • Recognise different data types • Use a flowchart to decide which analysis method to use • Undertake some basic analyses and construct appropriate charts for your data

3. Some initial thoughts

4. Planning a study • What do you want to investigate and why? What are your aims? • How are you going to investigate it? • How will you collect your data? • Who/what is in the sample? • How will you summarise your data? • How will you analyse your data?

5. Steps for choosing the right test (1) • Clearly define your research question • What is your main outcome of interest? There may be more than one. • What data type is it? The data type will determine the type of analysis • Are the observations paired? • Can it be characterised using a known distribution (i.e. parametric vs non-parametric test)? • What may affect the outcome of interest? • What data type is it/are they? • How will your results be summarised? • What charts can you use to display your results?

6. Data types: recap

7. Summary measures: recap

8. Chart types: recap • One variable • Categorical: Pie chart, barchart • Numerical discrete: barchart • Numerical continuous: histogram, boxplots • Two variables • Both categorical: stacked barchart, clustered barchart, multiple pie charts • One categorical / one numerical discrete: boxplots (sometimes!), multiple barcharts • One categorical / one numerical continuous: boxplots, multiple histograms • Both numerical: scatterplot

9. Steps for choosing the right test (2) • Are you interested: • Testing differences between groups. How many groups are there? • Assessing/modelling the relationship between variables • Are the observations paired? • Is the pairing due to having repeated measurements of the same variable for each subject? • Does the test you have chosen make any assumptions? Are the assumptions met? e.g. assumption of normality for t-test

10. Test assumptions Generally assume data or some function of the data follows a known distribution e.g. normal • Parametric tests: • Non-parametric: Nonparametric techniques are usually based on ranks/signs rather than actual data

11. Non-parametric methods are used when: • Dependent variable is ordinal • A plot of the data appears to be very skewed or the data do not seem to follow any particular shape or distribution (e.g. Normal) • Assumptions underlying parametric test not met • There are potentially influential outliers in the dataset • Sample size is small

12. Comparing averages (1) Independent sample t-test Normally distributed Skewed or ordinal 2 Comparing BETWEEN groups Mann-Whitney One way ANOVA 3+ Kruskall-Wallis

13. Paired data (1) • Most commonly, measurements from the same individuals collected on more than one occasion • Can be used to look at differences in mean score: • 2 or more time points e.g. before/after a diet • 2 or more conditions e.g. hearing test at different frequencies Each person listened to a sound until they could no longer hear it at three different frequencies. Would use Repeated measures ANOVA to test for a difference between the frequencies.

14. Comparing averages (1) Independent sample t-test Normally distributed Skewed or ordinal 2 Comparing BETWEEN groups Mann-Whitney One way ANOVA 3+ Kruskall-Wallis Paired t-test 2 Wilcoxon signed rank test Comparing measurements WITHIN the same subject Repeated measures ANOVA Friedman 3+

15. Comparing averages (2)

16. Comparing averages (2)

17. Comparing averages (2)

18. Comparing averages (2)

19. Examples?

20. What to check for normality

21. What to check for normality

22. What to check for normality

23. What to check for normality

24. Example 1: Did gender affect ticket price paid on the Titanic? Steps: • What is the outcome variable? • What is the grouping / explanatory variable? • What methods are available to analyse these data? • Check the assumptions • Conduct the appropriate analysis and report the results What test do you think would be appropriate?

25. Example 1: Did gender affect ticket price paid on the Titanic? Steps: • What is the outcome variable? Ticket price • What is the grouping / explanatory variable? Gender • What methods are available to analyse these data? Comparing ticket price between two groups (male and female). Most appropriate method is independent samples t-test • Check the assumptions. Assumes that the groups are independent, the data in the two groups are normally distributed and the variability in the two groups is similar. • Conduct the appropriate analysis and report the results. If the assumptions for the t-test are not met, use the Mann-Whitney U test

26. Example 1: Did gender affect ticket price paid on the Titanic? • Data were positively skewed • A Mann-Whitney U test was carried out to compare the ticket price for men and women • There was highly significant evidence (U=5.5, p < 0.001) to suggest a difference in the distributions of ticket price for male and females What else would be useful to know when interpreting these results? Medians: women £23 vs men £12

27. Investigating relationships

28. Investigating relationships

29. Investigating relationships

30. Investigating relationships

31. Examples?

32. Example 2: two categorical variables Survival of the pushiest?

33. Example 2: Survival of the pushiest Research question: Was survival on the titanic linked to nationality? Dependent: Survival Independent: Nationality What test do you think you should use? • Chi-squared test http://www.independent.co.uk/news/world/australasia/more-britons-than-americans-died-on-titanic-because-they-queued-1452299.html

34. Example 2: Survival of the pushiest • The data suggests that Americans were more likely to survive as 56% survived compared to 32% of British and 35% of those from other countries • Results from the χ2 test suggest, that there is evidence of a significant relationship between nationality and survival (p < 0.001)

35. Example 2: Further thoughts • Class was one of the most important predictors of survival on the Titanic • 70% of Americans were travelling in 1st class • A more detailed analysis, using logistic regression showed that nationality was NOT a significant predictor of survival after controlling for class In looking at these data is there any other information that would be useful? The numbers for each nationality

36. Learning outcomes • You should now know about: • Some useful approaches to analysing data • By the end of this session you should be able to: • Recognise different data types • Use a flowchart to decide which analysis method to use • Undertake some basic analyses and construct appropriate charts for your data

37. Exercises • Attempt the 4 exercises in SPSS • In each case you need to identify an appropriate analysis based on the dataset provided • Remember to check the assumptions for any analysis you conduct • Add value labels to the data if required • Use the flow charts & table to assist you

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