W6: RQ for Group Differences 1

Question 1

What are the 4 most common continuous probability distributions

Answer 1

1. ) Normal
2. ) Chi-Squared
3. ) t
4. ) F

Question 2

Probability distributions are classified by:

Answer 2

1. ) Continuous / Discrete
2. ) Univariate / Multivariate
3. ) Central / Non-Central

Question 3

What are 2 ways of expressing probability distributions. How do they relate to each other

Answer 3

1. ) Density Functions (Bell-shaped Curve)
2. ) Cumulative Distribution functions (p values)

Cumulative distribution function is obtained by integrating Desniity Functions

Question 4

What is the normal density function defined by (parameters)

Answer 4

1. ) The Mean (μ)

2. ) The Standard Deviation (σ)

Question 5

What is the difference between a “normal distribution” and a “standard normal distribution”

Answer 5

Standard Normal Distribution:

Mean (μ) = 0
Standard Deviation (σ) = 1

Question 6

How do we standardize a normal distribution. What is it called

Answer 6

Transform into standardized Z statistic or standard normal variate (not z-score)

Z = (x - μ) / σ

Question 7

What are probability distributions used for

Answer 7

1. ) Constructing confidence intervals

2. ) Calculating P values for null hypothesis tests

Question 8

Correlation coefficients: What are they distributed as

Answer 8

t (df)

Question 9

Cramer’s V: What are they distributed as

Answer 9

χ2 (df)

Question 10

Odds Ratios: What are they distributed as

Answer 10

N (logOR, σ)

Question 11

Regression Coefficients: What are they distributed as

Answer 11

t (df)

Question 12

R-Squared: What are they distributed as

Answer 12

F (df1, df2)

Question 13

How do we calculate confidence intervals from probability distributions. Example: 95% CI in t-Statistic

Answer 13

Use standard error and critical t-value (derived from desired confidence) to calculate the margin of error.

95% CI in a t-distribution, critical t value equals of probability of (1.95/2)=.975 for the given df.

Question 14

What kind of Margin of Error for Confidence Intervals do we normally get when it is derived from t-statistic probability distribution

Answer 14

Symmetric Margin of Error

b^ - ME) <= b^ <= (b^ + ME

Question 15

When we think of a difference, we are interested in groups differing in _______

Answer 15

When we think of a difference, we are interested in whether groups differ in terms of their respective POPULATION MEANS

Question 16

When phrasing RQ in terms of a difference, must we state which group is higher or lower

Answer 16

We can, but its not necessary. We are interested whether there’s a differences

Question 17

When we think of a difference, we are essentially asking whether members of each group are

Answer 17

1. ) Distinct population defined by different means

2. ) Subgroups within the same population and therefore have the same mean

Question 18

How can two groups be formed. Some properties of the groups.

Answer 18

1. ) Mutually-exclusive groups
   - Each score in one group is independent of all scores in the other group
   - Participants can only belong to one group
   - Size of group not necessarily same
2. ) Mutually-paired groups
   - Each score in one group is linked to a score in the other group by either (a) Measured twice in different time (b) Dependency (twins, husbands,etc)
   - Size of groups must be the same

Question 19

Are groups categorical / continous

Answer 19

Categorical

Question 20

How do we initially examine distribution of scores in both groups

Answer 20

Boxplots: Allows us to compare group medians. Also, allows us to examine outliers.

Question 21

After a boxplot to examine distribution of scores, what is nice to use to check out outliers

Answer 21

qqPlot. Check out spread and outliers.

Question 22

If sample distribution is an option in the exam, it is likely the right answer

Answer 22

Just remember.

Question 23

Since there will always be a difference between sample means of 2 groups, what are we actually finding out

Answer 23

Difference is:

(1) Due to random sampling variability when groups from same population
(2) Due to random sampling variability PLUS difference in population means when groups from different compulaions

Question 24

Sampling distribution of Group Mean Differences: What do we try to create

Answer 24

Confidence Interval!

Question 25

Given a sample distribution of group mean difference where M (μ1 - μ1) = 0, what does the confidence interval tell us

Answer 25

The range of plausible values if there is no mean difference
( 0 - crit.tse, 0 + crit. tse)

Question 26

Given a sample distribution of group mean difference where M (μ1 - μ1) = 1.25, what does the confidence interval tell us

Answer 26

The range of plausible values given the mean difference of 1.25
( 1.25 - crit.tse, 1.25 + crit. tse)

Notice how the values are relative to 1.25

Question 27

When investigating differences between 2 independent groups, what are the 3 assumptions

Answer 27

1. ) Observations are independent
2. ) Observed scores on the construct measure are normally distributed
3. ) Homogeneity of variance/Same variance in 2 groups

( No assumption of linearity)

Question 28

When investigating differences between 2 independent groups, how do ensure “Observations are independent” is met

Answer 28

Usually met

Unless duplication / 1 variable affects the other

Question 29

When investigating differences between 2 independent groups, how robust is the confidence interval if “Homogeneity of variance” is violated

Answer 29

Design is BALANCED/NOT BALANCED

Sample size same in each group / not

Question 30

When investigating differences between 2 independent groups, how robust is the confidence interval if the design is balanced

Answer 30

Protects against violation of homogeneity of variance unless variances are VERY different.

Question 31

When investigating differences between 2 independent groups, how robust is the confidence interval if the design is imbalanced

Answer 31

Even mild homogeneity of variance leads to trouble.

Need to calculate confidence intervals using an adjustment separate variance estimates.

Question 32

When investigating differences between 2 independent groups, how do ensure “Homogeneity of variance” is met

Answer 32

Levenetest or Flinger.Test

Question 33

When investigating differences between 2 independent groups, what are unstandardized confidence intervals robust against

Answer 33

Robust against mild-to-moderate non-normality (especially when it’s a balanced design)

Question 34

When investigating differences between 2 independent groups, what are standardized confidence intervals robust against

Answer 34

Not robust against even MILD non-normality.

Question 35

What are 2 types of standardized mean differences. And what do they require?

Answer 35

1. ) Hedges’ g
   - Normality
   - Homogeneity of Variance
2. ) Bonett’s
   - Normality

Question 36

When investigating differences between 2 independent groups, “Homogeneity of variance”: When given a high p value in the levenetest/flinger.test, what does it mean

Answer 36

We can assume homogeneity of variance

Therefore, look at “equal variance assumed”

Question 37

What should we calculate in investigating differences between 2 dependent groups

Answer 37

The basis for the analysis when groups are dependent:

Calculate the mean difference: difference between the pair of scores for each individual.

Question 38

What happens if the population mean difference is 0/non-0

Answer 38

If population mean diff = 0, no difference between 2 dependent groups on construct

If population mean diff /=/ 0, difference between 2 dependent groups on construct

Question 39

When investigating differences between dependent groups, what are the assumptions

Answer 39

1. Observations are independent.
2. Observed scores on the construct measure are normally distributed.

[The homogeneity of variance assumption is not relevant because the analysis is undertaken on the difference scores]
[No Linearity]

Question 40

How robust is the standaridized/unstandardized confidence interval in group differences

Answer 40

Unstandardized confidence intervals are robust against mild-to-moderate nonnormality
in difference scores.

Standardized confidence intervals are not robust against even mild non-normality
in difference scores.