Psych stats

• One-way ANOVA


  1. Testing hypothesis about three or more independent groups

  2. Compares means and standard deviations of independent groups

  3. Can be used even if there are only two independent samples, but t-test is more appropriate
• One-way ANOVA


  • Assumptions: If assumptions are not met, alternatives like Kruskal-Wallis test, Jonckheere-Terpstra test, or Friedman test can be used
• Post-hoc analysis


  1. Performed after ANOVA to determine where the differences lie between the groups

  2. Compares all possible pairs of groups to find which ones differ significantly
• Kruskal-Wallis test is the alternative to one-way ANOVA when the data is ranked rather than continuous
• Kruskal-Wallis test


  Tests if independent populations have the same center (median)
• If the data is ranked, Kruskal-Wallis test is more appropriate than one-way ANOVA
• Kruskal-Wallis test is the alternative to one-way ANOVA
• Kruskal-Wallis test


  Tests if independent populations have the same center, using medians of rank data instead of mean and standard deviation
• Kruskal-Wallis test is an extension of the Wilcoxon test and Mann-Whitney U tests
• Kruskal-Wallis test is used when there are more than two independent groups to be tested
• Kruskal-Wallis test is a non-parametric test, meaning it does not require the population to be normally distributed
• Performing Kruskal-Wallis test


  1. Analyze non-parametric tests

  2. Choose independent samples

  3. Select Kruskal-Wallis test

  4. Run the test
• Null hypothesis for Kruskal-Wallis test


  The distribution of sales is the same across categories of shelf height
• The Kruskal-Wallis test rejects the null hypothesis, indicating a difference in sales across shelf height categories
• The minimum rank indicates more sales when ice cream is placed on the waist level
• The p-value of 0.005 from the Kruskal-Wallis test indicates a significant difference in sales across shelf height categories
• The Kruskal-Wallis test is the non-parametric counterpart of the analysis of variance (ANOVA)
• For paired samples research designs, Cohen's d can be used to calculate the effect size instead of eta-squared
• Cohen's d interpretation


  0.2 - small effect, 0.5 - moderate effect, 0.8 - large effect
• The formula for Cohen's d is: (mean of pretest - mean of posttest) / standard deviation
• The final exam for the course will be announced next week
• There are 31 viewers currently and around 60 viewers are expected
• The discussion will continue on hypothesis testing
• The plan is to finish 3 hypothesis tests: repeated measures, Pearson r correlation, and chi-square tests
• The focus for today will be on paired samples t-test
• Paired samples t-test


  A parametric test used to analyze data involving two related groups
• Paired samples t-test


  • Assumes the difference between the before and after measures in the population is normal
  • Sensitive to outliers
• If the data is non-normal and has outliers, non-parametric tests like sign test and Wilcoxon test can be used instead
• Null hypothesis


  States there is no significant difference in the means of the two groups
• Examples of paired samples t-test

  • Pre-test and post-test design
  • Comparing effects of two different conditions (e.g. fertilizers)
  • Matching on specific criteria (e.g. case-control study)
• Steps in the example problem

  1. Measure weights and triglyceride levels of patients before diet

  2. Patients placed on 6-month diet

  3. Measure weights and triglyceride levels again after diet

  4. Compare before and after measurements to test if diet was effective
• The null hypotheses are: 1) No significant difference in patient weights, 2) No significant difference in patient triglyceride levels
• Conducting paired samples t-test in SPSS

  1. Load triglyceride.sav data file

  2. Select Analyze > Compare Means > Paired Samples T Test

  3. Pair the before and after variables for weight and triglyceride
• The SPSS output shows the mean, standard deviation, and standard error for the before and after measurements
• The SPSS output also shows the correlation between the before and after measurements
• To test the hypotheses, we need to look at the Paired Samples T Test results in the SPSS output
• nd one the correlation is 0.649 this is also a high correlation and p-value here is point zero zero seven so sabinate if the p-value is less than point zero five then there is a significant relationship or difference
• in our case correlation on an app not in ah and point zero zero seven is less than point zero five so there is a significant correlation at etunga labas
• what we are looking for is this one our paired samples thetas because we would like to find out if there is a significant difference in the weights of the patients and if there is a significant difference in the triglyceride levels of the patients after they are subjected to the 16 16 days diet okay six months diet program
• Weight before and after

  Mean is 9.438, standard deviation is 9.3331