RMB, Dependent t-test & Wilcoxon Signed rank, W8

Question 1

Dependent/Paired t-test + conditions for use

Answer 1

• Used for repeated measures design (or related/dependent/paired sample/within groups) > e.g. does recall improve after attending “Hypnotic Memory Training” with Paul McKenna?
• Conditions for Use: Two conditions to be compared, Design must be related + Parametric assumptions must be met + data should be interval or ratio level
• Dependent samples (or “paired”) t-tests typically consist of a sample of matched pairs of similar units, or one group of units that has been tested twice (a “repeated measures” t-test). > usually matched pairs or repeated measures
• Typical example of the repeated measures t-test would be where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are tested again after treatment with a blood-pressure lowering medication.

Question 2

Example of dependent t-test

Answer 2

• A forensic psychologist wants to determine whether physical exercise in a boot camp program has an effect on muscular strength.
• He/she measures the number of pull-ups 25 program participants complete at the beginning of the program and at the end of the program
• Number of Samples: 2 > Nature of Samples: dependent (same subjects at two different points in time)
• Independent Variable: participation in boot camp–exercise > Dependent Variable and its Level of Measurement: number of pull-ups
• To report an independent T-test in APA format you need to know the degrees of freedom, the t value, the p value, mean and SD
• Sig: p-value > Divide by 2 to get one-tailed (directional) p-value (spss gives a 2 tailed p value so non-directional)
• Report in APA: The results of the Dependent t-Test showed that exercise had a significant effect on number of pull-ups attained (t(24) = 5.196, p<0.001). Participants could perform significantly more pull-ups after exercise (M = 4.2, SD = 1.29). than before exercise (M = 3.6, SD = 1.71). > Report as (t(df) = t statistic, p value or p

Question 3

Effect Size

Answer 3

• Effect size is a simple way of quantifying the difference between two groups.
• Effect size emphasises the size of the difference rather than confounding this with sample size. It is easy to calculate, readily understood and can be applied to any measured outcome in Psychology.
• It is particularly valuable for quantifying the effectiveness of a particular intervention, relative to some comparison. It allows us to move beyond the simplistic, ‘Does it work or not?’ to the far more sophisticated, ‘How well does it work in a range of contexts?’ Moreover, by placing the emphasis on the most important aspect of an intervention - the size of the effect - it promotes an alternative to its statistical significance
- Effect size is a measure of the difference between the two sample means > e.g. if two interventions are significant, we can see which has greater effect using effect sizes

Question 4

Types of effect size: Pearson r correlation

Answer 4

• Pearson r correlation: one of the most widely used effect sizes for correlation + non-parametric tests
• Pearson’s r can vary in magnitude from -1 to 1, with -1 indicating a perfect negative relationship, 1 indicating a perfect positive relationship, and 0 indicating no relationship between two variables.
• Cohen (1988, 1992) gives the following guidelines for effect sizes in pearson’s R correlation
• small effect size, r = 0.1; medium, r = 0.3; large, r = 0.5.

Question 5

Types of effect size: Cohen’s d

Answer 5

• Cohen’s d: usually used for t-test and parametric tests effect size.
• d = difference between two means divided by the pooled standard deviation for those means
• Cohen (1992) says: 0.2 is indicative of a small effect, 0.5 a medium and 0.8 a large effect size.
• The pooled standard deviation is a weighted average of standard deviations for two or more groups
• May want to calculate effect size if you are comparing two different things such as two different interventions and see what is more effective
• Effect sizes will also indicate if there will be a significant effect in other places > e.g. if you have a large effect size when look at height between gender, you will likely find an effect size again in similar research

Question 6

Wilcoxon Signed Rank/Matched Pairs test

Answer 6

• Wilcoxon signed-rank test is a non-parametric test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it’s a paired difference test).
• can be used as an alternative to the paired t-test when the population cannot be assumed to be normally distributed or the data is on the ordinal scale

Question 7

Example: Wilcoxon Signed Rank

Answer 7

• A forensic psychologist wants to determine whether physical exercise in a boot camp program has an effect on muscular strength. He/she measures the number of pull-ups 25 program participants complete at the beginning of the program and at the end of the program.
• What is the effect size of the result?
• N = total of all observations (25 total N but we had TWO samples so we have double of N > 2x25=50) > N is not total number of participants but total number of datapoints
• √50 = 7.07 > -3.638/7.07 = -0.5146 > 0.51 is greater than(>) 0.5 which means it is a large effect size
• R = Z score divided by the square root of N > R = Z/√N
• APA Report: To report a Wilcoxon signed rank or matched pairs test in APA format you need to know the Z value and the p value > We also usually report the median values for the two conditions as this is a non-parametric test
• The results of the Wilcoxon signed rank test showed that exercise had a significant effect on number of pull-ups attained (z= 3.638, p<0.001). Participants could perform significantly more pull-ups after exercise (Mdn = 4). than before exercise (Mdn = 3).
• Report as (z=, p= or p