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1

 

Describe the Pearson's r

- Assessing relationships

- Most widely used correleation coefficient

- An effect size, ranges between -1 (perfect negative relationship) to +1 (perfect positive relationship) ((-).1-.3: small effect, (-).3-.5: medium effect, (-).5.-1: large effect)

- Assumptions:

      - Two continuous variables (interval or ratio)

      - Normally distributed data

      - Independent observations

      - Linear relationships

- Non parametric alternatives: Spearman's rho, Kendall's tau, Point Biserial Correlation

2

Describe Spearman's Rho and Kendall's tau

Assessing relationships

- The non-parametric alternatives to Pearson's r

- Can be used when one or both variables are ordinal or when normality assumptions aren't met

- Based on ranks of scores

- Use Kendall's tau if many tied ranks!

3

Describe the Point Biserial Correlation

- Assessing relationships

- Can be used when one variable is binary and the other is continuous

- Calculated using Pearson's r formula

4

Describe the linear regression

- Exploring predictions

- Used to predict the value of a continuous outcome variable using the value of a single (continuous) predictor variable

Assumptions:

      - linear relationships

      - two continuous variables

      - Normal distribution

      - Independent observations

      - Homoscedasticity

5

Describe the independent  t-test

Assessing differences, 2 groups, independent design

- Tests whether means differ for two independent groups that we have collected data for (e.g. average grades of AU and CPH psychology students)

- Assumptions:

       - Outcome variable (DV) must be continuous

       - Grouping variable (IV) must be categorical and binary (2 categories)

       - Normally distributed DV data

       - Groups must be mutually exclusive

       - Homogeneity of varaince (similar spread of scores around the mean)

- Test statistic: t

- Effect size: r or d

- Non-parametric alternative: Mann-Whitney U test

6

Describe the Mann-Whithey U test

Assessing relationships - independent designs

- Non-parametric alternative to an independent t-test!

- Tests whether medians differ for two independent groups that we have collected data for (e.g. average grades of AU and CPH psychology students)

Can be used when you have ordinal data or non-normal continuous data

- Uses medians instead of means

- Test statistic: U statistic 

- Effect size: r

7

Describe the dependent t-test

- Assessing relationships - repeated measures designs

- Tests wheter the means for two conditions differ within a single group (e.g. psychology student's grades in statistics vs work psychology)

Assumptions: 

      - Outcome variable (DV) must be continuous

      - Grouping variable (IV) must be categorical and binary (2 categories)

      - Normally distributed sampling distribution of differences

      - Each participant must be in both conditions!

Test statistic: t

- Non-parametric alternative: Wilcoxon signed-rank

8

Describe the wilcoxon signed rank-test

Assessing relationshipsrepeated measures designs

- Non-parametric alternative to a dependent t-test!

Can be used when you have non-normal continous data or ordinal data

- Converts all raw data into ranks

Uses medians instead of means

- Test statistic: T (sum of positive ranks)

- Effect size: r​

9

 

Describe the independent ANOVA

- Assessing relationships - independent designs

- tests whether means differ for 3+ independent groups that we have collected data for (e.g. average grades of AU, CPH and Odense psychology students) 

- an omnibus test (tells us if there are differences, but doesnt specify which means differ)

- Test statistic: F

- Assumptions:

      - Outcome variable (DV) must be continuous

      - Normal sampling distribution (in each group)

      - 3+ levels of groups variable (IV)

      - Groups must be mutually exclusive

      - Homogeneity of variance

- If significant F: Follow up with post-hoc bonferroni test (t-test comparisons between all groups)

Non-parametric alternative: Krustal-Wallis test

10

Describe the Kruskall-Wallis test

Assessing relationships - independent design

- The non-parametric alternative to an independent ANOVA!

- Can be used to test whether medians differ for 3+ independent groups that we have collected data for (e.g. grades of AU, CPH, Odense psychology students)

- Can be used when you have non-normal continuous data or ordinal data

- Converts all raw data into ranks before analysing them

- Test statistic: H

Significant H-test: follow up with non-parametric post hoc tests (Mann-Whitney U)

11

Describe the dependent (repeated-measures) ANOVA

- Assessing relationships - repeated measures design

- Tests whether means differ between 3+ conditions that we have collected data for (e.g. average mean grades for the same AU students in semester 1, semester 2, semester 3)

- An omnibus test (tells us if there are differences, but doesn't specify which means differ)

Assumptions:

      - Outcome variable (DV) must be continuous

      - Normal sampling distribution

      - 3+ levels of grouping variable (IV)

      - Sphericity

Test statistic: F

- If F is significant: Follow up with post-hoc bonferroni tests

- Non-parametric alternative: Friedman's test

12

Describe the Friedman's test

Assessing relationships - repeated measures design

- The non-parametric alternative to a dependent ANOVA!

- Can be used to test whether medians differ for 3+ conditions that we have collected data for (e.g. grades of the same AU students in 1st, 2nd and 3rd semester)

- Can be used when you have non-normal continuous data or ordinal data

- Converts all raw data into ranks before analysing them

- Test statistic: x2

- Significant x2: follow up with non-parametric post hoc test (Wilcoxon signed rank)

13

Describe the Chi-Square test

- Exploring categorical associations

- Can be used to examine whether, and how, two categorical variables are associated (e.g. what association, if any, exists between political affiliation (democrat/republican) and support for the death penalty (for/against)?)

Non-parametric

- test statistic: χ​2

- DF: (no of rows-1)*(no of coloums-1)

Effect size: Odds ratio for 2x2 (SPSS: Risk), Cramer's V for larger

Assumptions: 

      - 2 categorical variables (non-parametric)

      - Mutually exclusive categories (independence)

      - For 2x2 tables, expected frequencies must not be <5

      - For larger tables, all expected frequencies must be at least 1, with no more than 20% of cells in the contingency table having expeted frequency <5

 

14

What is the non-parametric alternative for an independent t-test?

The Mann-Whitney U test

15

What is the non-parametric alternative for a dependent t-test?

The Wilcoxon-signed rank test

16

What is the non-parametric alternative to an independent ANOVA?

The Krustal-Wallis H test

17

What is the non-parametric alternative to a repeated ANOVA?

The Friedman's test

18

What is What is the non-parametric alternative to a Pearson's correlation?

Spearmans Rho or Kendalls Tau (Tau if small sample, many tied ranks)