Lecture 6

Question 1

classifications for probability distributions

Answer 1

• continuous or discrete
• univariate or multivariate
• central or non central

Question 2

2 ways we can view probability distributions

Answer 2

• density function: can be seen by bell shaped curve
• probability function: can be seen by CUMULATIVE DISTRIBUTION FUNCTION, which in continuous function, involves density function –>

Question 3

what does bell shaped curve indicate?

Answer 3

when we see a bell shaped curve, we are actually looking at the density function

Question 4

why are f distribution and chi square distribution always negatively skewed?

Answer 4

because they can only have a NON NEGATIVE value on the x axis

Question 5

how does a graph with positive skew look like

Answer 5

right tailed
‘facing’ right
most scores are on the left

Question 6

how does a graph with negative skew look like

Answer 6

left tailed
‘facing’ left
most scores are on the right

Question 7

what is mutually exclusive group?

Answer 7

independent groups
you can only belong to 1 group. each group is independent from another.

eg: you can only be in RMHI group or ARMP group.

Question 8

what is mutually paired group?

Answer 8

dependent groups
each score in one group is LINKED to a score in the other group.

eg:

• twins = common dependency
• husband wife on marriage harmony
• different time points (with the same individual)

Question 9

in terms of sample size, what differs mutually paired group to mutually exclusive group?

Answer 9

in mutually paired groups design,
the sample size in all the groups MUST be the same

in mutually exclusive group, you can have unequal sample size

Question 10

assumptions for mean differences in 2 independent groups

Answer 10

1. observations are independent
2. obs scores are normally distributed
3. variances in 2 groups are the same

Question 11

what does balanced design mean

Answer 11

means the size of each group is the same

Question 12

what is the diff between having balanced design and unbalanced design if the groups violate the homosdecasticity assumption

Answer 12

for balanced design, interpretation would still be robust if group variance is not consistent

if it’s unbalanced design, then interpretation would not be robust even if the homosdescaticity is only mild

Question 13

“unstandardised confidence intervals are robust against mild to moderate non normality” true or false?

Answer 13

true

unstandardised confidence interval is ROBUST against these conditions

Question 14

“standardised confidence are robust against mild to moderate non normality” true or false?

Answer 14

false.

standardised confidence interval is NOT ROBUST against these conditions

Question 15

why is bonett functions useful?

Answer 15

it reports both observed and standardised mean differences

Question 16

2 types of standardised mean differences

Answer 16

• hedges’ g (requires NORMALITY and HOMOGENEITY)

- bonett’s d (requires NORMALITY)

Question 17

“we always assume homogeneity of variance unless p value for either test is small” true or false?

Answer 17

true.

if one test <0.05 and the other is >0.05 then we assume heterogeneity of variance.

Question 18

what is the basis of analysis aka what are we calculating when groups are DEPENDENT?

Answer 18

we wanna analyse the DIFFERENCE between the scores (each involving both IV1 and IV2) for each individual

Question 19

Assumptions for mean differences in 2 DEPENDENT groups

Answer 19

1. independent observations
2. normal distribution of observed scores

note:
HOMOGENEITY of variance is NOT relevant because the analysis is undertaken of the difference scores

Question 20

why homogeneity of variance is not a relevant assumption in dependent groups?

Answer 20

because that’s the thing we are analysing

Question 21

in what condition would the bonett test and hedges test result in the SAME standardised estimate value?

Answer 21

standardised estimate value in bonett and hedges test would be the same only if the correlation of the 2 sets of scores is 0.5

Question 22

what is semipartial correlation

Answer 22

It is the correlation between observed scores on the dependent variable and that part of scores on an independent variable that is not accounted for by all other independent variables in the regression analysis.

Question 23

Which of the following descriptions is closest in meaning to the concept of heteroscedasticity of residuals?

Answer 23

Non-constant residual variance for different PREDICTED values of the dependent variable. (NOT OBSERVED VALUES)

Question 24

“we do not need to know how a null hypothesis test would be applied to a semipartial correlation” true or false?

Answer 24

true.

If we did know the standard error for the standardised regression coefficient and we undertook a null hypothesis test, then the obtained P value would be the same as that obtained for a null hypothesis test applied to a semipartial correlation. hence, the foregoing logically follows from knowing the relationship between (i) a semipartial correlation and a standardised regression coefficient and (ii) a confidence interval and a null hypothesis test.

Question 25

Given that an observed R-squared value in a linear regression analysis is much bigger than the adjusted R-squared value, what does it mean?

Answer 25

The value of OBSERVED R-squared estimate is very biased.

Question 26

justification for R-squared being used to measure the overall strength of prediction of linear regression model?

Answer 26

The average size of the squared residuals gets smaller as R-squared gets large

Question 27

what would happen if a regression model in two different samples of the same size results in the same sample R-squared value, but sample A has a greater number of independent variables than sample B

Answer 27

confidence interval for R-squared will be less precise in sample A than in sample B

Question 28

what could we use to identify problems arising from violation of the normality assumption in a multiple regression model

Answer 28

Histogram of residuals; Q-Q plot of the RESIDUALS (not predicted values)

Question 29

If a particular set of scores for one participant that are very influential (OUTLIERS), what can we use to identify that individual when examining regression diagnostics

Answer 29

A large Cook’s D value and a large studentised deleted residual value.

Question 30

Under which conditions will the observed R-squared value be most biased (all other aspects being equal)?

Answer 30

When sample size is small and the number of IVs is large.

Question 31

is probability distribution used in NHST and CI? or just CI? or just NHST?

Answer 31

Probability distributions are used in null hyppthesis significance testing and in the construction of confidence intervals

NHST are derived from probability distributions (and confidence intervals typically use a critical value from a probability distribution in their estimation).

Question 32

What is the most important difference between an independent sample t-test and a dependent samples t-test?

Answer 32

The STANDARD ERROR in a dependent samples t-test takes into account the CORRELATION between scores on the two groups, while the SE in independent test DOES NOT account CORRELATION!!!

a dependent sample t-test is calculated using individual difference scores (same individual but in 2 diff conditions or 2 time slots)

the variability of which is in part determined by the strength of the correlation between the raw scores in the two groups used to calculate the difference scores.

The observed scores for the two groups in an independent samples t-test CANNOT correlate because each person belongs to ONLY ONE of the two groups, and therefore people in the sample do not have a score for each group –>

Question 33

what is the most unwise condition to rely on the variance-assumed confidence interval for mean differences in an independent two-group design?

Answer 33

Unequal group sample sizes (unbalanced); normal distribution of scores; and unequal group variances.

Question 34

what could be used to inspect if there is evidence of homogeniety of group variances?

Answer 34

Boxplot of each group.

Fligner-Killeen test.

Levene’s test.

Question 35

If the population mean for Group 1 equals 10 and the population mean for Group 2 equals 6, what will be the mean of the sampling distribution for the mean difference?

Answer 35

4.

The mean of the sampling distribution of a mean difference will be increasingly equal to the difference between the populations means of the two groups; i.e., 10 - 6 = 4.

Question 36

“Hedges’ g and Bonett’s delta is estimated on the assumption of equal variances.” true or false?

Answer 36

false.

Hedges’ g is estimated on the assumption of equal variances
Bonett’s delta is estimated on the assumption of unequal variances.

Question 37

What of the following is not an assumption of the mean difference between two independent groups?

The design is balanced.

Independence of observations.

Homogeneity of variances.

Normality of scores.

Answer 37

The design is balanced.

the other 3 are important assumptions.

Question 38

How can we best distinguish independent groups from dependent groups?

Answer 38

Participants can only be a member of one of the groups in an independent samples design.