Lecture 6: Research Questions for Group Differences I

Question 1

What are probability functions?

Answer 1

Continuous probability distributions that are variously called (standard) normal, chi-squared, t, or F. Often classified as continuous/discrete, univariate/multivariate, and central/non-central.

Question 2

How are probability functions expressed?

Answer 2

1. Density function (bell-shaped curve)
2. Cumulative distribution function (p-values)
   - For continuous distributions, integrating (1) produces (2)

Question 3

What is a normal distribution?

Answer 3

Mean = 0, SD = 1

Question 4

What are probability distributions used for?

Answer 4

1. To construct CIs

2. To calculate p-values for NHST

Question 5

What is the formula for df in a simple regression coefficient?

Answer 5

n - 2

Question 6

How do we calculate the margin of error?

Answer 6

ME = critical t-value (.975 probability) x standard error

Question 7

How do we derive the lower and upper bounds?

Answer 7

By adding or subtracting the margin of error to the sample statistic.

Question 8

How do we calculate group differences?

Answer 8

By comparing their population means. We can use distributional plots, boxplots, and qqplots.

Question 9

What are the two ways groups can be formed?

Answer 9

1. Two mutual-exclusive groups (independent scores, where size of groups do not have to be the same)
2. Two mutually-paired groups (each score is linked to another in the other group by either a. being measured twice or b. two people having a common dependency, aid size of group must be equal)

Question 10

What is sampling variability?

Answer 10

There will always be a difference between the sample means of two groups. There can be sampling variability from the same population, or from different populations/

Question 11

What range do the majority of sample mean differences lie in?

Answer 11

Between -1 and +1 SDs.

Question 12

What are the assumptions for mean differences in two independent groups?

Answer 12

1. Independent observations
2. Normally distributed observed scores on the construct measure
3. Homogeneity of variance (variances in the two groups are the same)

Question 13

What protects against violation of homogeneity?

Answer 13

A balanced design.

Question 14

What are the two types of standardised mean differences?

Answer 14

1. Hedges’ g (requires both normality and homogeneity of variance)
2. Bonnet’s (requires only normality)

Question 15

What data do we need to use the CI functions above?

Answer 15

1. Vector of scores on the first group
2. Vector of scores on the second group
3. Confidence level (95%)

Question 16

What p-value shows non-homoegeneity?

Answer 16

p < .5, but if sample sizes are small, then use p < .1

Question 17

Why are boxplots useful initially?

Answer 17

We can use them to compare group medians.

Question 18

What are the assumptions for mean differences in dependent groups?

Answer 18

1. Independent observations
2. Normally distributed observed scores on the construct measure
   - Homogeneity is not relevant because the analysis is undertaken on the difference scores*