Statistics week 7 - 12

Question 1

The ANOVA tests for differences between

(A) variances of the groups.
(B) standard deviations of the groups.
(C) means of the groups.
(D) individuals of the groups

Answer 1

Answer is (C). The ANOVA tests for differences between the means of the groups. Two estimates of
the (null) population are obtained – one from the means of the groups(numerator of the F test) and
one from the variances within each group (denominator of the F test).

Question 2

A statistically significant result means that the obtained probability (p) of the test statistic is:

(a) less than .05.
(b) equal to .05.
(c) greater than .05.
(d) greater than 1.

Answer 2

Answer is (A). The level of statistical significance (α) of .05 was adopted by convention in
psychological research. An obtained probability (p) less than this cut-off value of α =
.05 is considered “statistically significant”.

Question 3

If assumptions of the ANOVA are violated, the actual Type I error rate will:

(a) be greater than α.
(b) equal α.
(c) be smaller than α.
(d) be smaller or greater than α

Answer 3

Answer is (D). Violations of assumptions occur to varying degrees and they can cause the Type I error
rate to be smaller or greater than α.

Question 4

A Brain Training software company claims that its 20-week training programme can increase a
person’s IQ by five points. Given that the normative mean of IQ is 100, with a standard deviation
of 15, the magnitude of the claimed effect is:

(a) negligible.
(b) small.
(c) medium.
(d) large.

Answer 4

Answer is (B). According to Cohen’s terminology, small, medium and large effect sizes correspond to
standardized mean differences(Cohen’s d) of .20, .50 and .80. The observed change of five IQ points
in brain training amounts to a standardized mean difference (d) of .33. This would be considered a
small effect or, at best, a “small to medium” effect

Question 5

Upon obtaining a significant F test result in an ANOVA comparing mean weekly gambling
frequency of Catholics, Protestants and Non-Christians, what test(s) would you use to compare
the group means?

(a) the Student t-test.
(b) the Student-Newman-Keuls test.
(c) the Tukey HSD test.
(d) the Tukey-Kramer test

Answer 5

Answer is (B). The SNK test is more powerful than the Tukey alternatives and its family error rate
is no more than α when only three means are involved, whereas several Student t tests would
exceed the family error rate of α

Question 6

The ability to generalise our findings from an experimental design is governed by:

a: A & a cross-sectional design
b: How the variables have been operationalised
c: A & B
d: The sample of participants in the study

Answer 6

A & B
(Note) this seems wrong as A and B are sometimes C or D

Question 7

Internal validity may be improved by:

a: Using a control group
b: Reducing measurement error
c: Using more homogenous samples
d: All of the above

Answer 7

d: All of the above

Question 8

When we ‘test’ participants in an experimental setting, internal validity may be compromised due to

A: B & C
B: Small sample
C: Non-applicability to real-world settings
D: Hathorne effects

Answer 8

Hathorne effects
Response:
Correct! The nature of being observed in a testing environment can change our normal behaviour, mood and thoughts

Question 9

What makes an experiment an experiment

A: Random sampling
B: Random allocation of participants to groups
C: controlled extraneous variables
D: A & C

Answer 9

Random allocation of participants to groups
Response:
Correct!

Question 10

The Solomon group design is useful as it allows for an assessment of:

Difference scores between groups
The effects of post-testing
The effects of pre-testing
A & B

Answer 10

A & B

Response:
CORRECT!

(Note) this seems wrong as A and B are sometimes C or D

Question 11

Random allocation to groups helps control for:

a: Participant mortality
b: Individual differences
c: Small effect sizes
d: Experimenter bias

Answer 11

Individual differences
Response:
Correct, and as the sample size increases, so too does the probability that the groups will be more equivalent

Question 12

Multiple t-tests are not recommended because:

A: They increase the Type 1 error rate
B: They inflate the experiment wise error rate
C: They increase the family-wise error rate
D: All of the others

Answer 12

D: All of the others

Question 13

The obtained F value of a study that uses a one-way ANOVA to test for differences between 4 means is 2.30, this means that:

A: The between group variance was greater than the within group variance, but we don’t know if it is significantly greater
B: The groups differ
C: As it is over 1, you would need to conduct post-hoc testing
D: The result is significant

Answer 13

A: The between group variance was greater than the within group variance, but we don’t know if it is significantly greater

Question 14

A one –way ANOVA produces an eta square effect size of .17. This means:

a: The effect size is large
b: The effect is medium strength
c: The effect is likely due to chance
d: The result will be significant as the effect is large

Answer 14

a: The effect size is large

Correct! Yes,
check Cohen’s criterion- .16+ = large effect

Question 15

When conducting a one-way independent ANOVA with three levels on the independent variable, an F-ratio that is large enough to be statistically significant tells us:

A: That the model fitted to the data accounts for less variation than extraneous factors, but it doesn’t tell us where the differences between groups lie.

B: That all of the differences between means are statistically significant.

C: That there is a significant three-way interaction.

D: That one or more of the differences between means is statistically significant but not where the differences between groups lie.

Answer 15

D: That one or more of the differences between means is statistically significant but not where the differences between groups lie.

Yes, this is correct. It is therefore necessary after conducting an ANOVA to carry out further analysis to find out which groups differ

Question 16

The Student Neuman-Keuls test is used in preference to the Tukey when:

A: We have small effect sizes
B: When the Tukey test is too conservative
C: We have 3 group means
D: We have 3 or more group means

Answer 16

C: We have 3 group means

Question 17

The ANOVA testsfor differences between

(A) variances of the groups.
(B) standard deviations of the groups.
(C) means of the groups.
(D) individuals of the groups.

Question 18

Two-way ANOVA differs from One-way ANOVA:

A: Because Two-way ANOVA is for two groups
B: Because you can calculate main effects and an interaction effect
C: Because you can analyse the data two ways
D: Because one uses a F test and the other dies not

Answer 18

B: Because you can calculate main effects and an interaction effect

Question 19

A 4 x 4 ANOVA would be:

a: An example of a sixteen way ANOVA
b: An example of a 4 factor ANOVA
c: An example of a two way ANOVA
d: An example of a 8 factor ANOVA

Answer 19

c: An example of a two way ANOVA

YES! - Two factors, the first with 4 levels and the second also with 4 levels

Question 20

An interaction effect is achieved when:

a: The p value for the F test is significant
b: When the main effects are not significant
c: When the partial eta square is > .14
d: When the plot of the group means shows that the lines crossover

Answer 20

a: The p value for the F test is significant

Question 21

If our 2 x 2 ANOVA shows we have a significant interaction effect:

a: We would want to conduct further analyses to understand how factors impacted upon each other
b: There is no need to do additional analyses to understand the results
c: The homogeneity of the test is questionable
d: We should report the main effects in preference to the interaction effect

Answer 21

a: We would want to conduct further analyses to understand how factors impacted upon each other

Question 22

In a 2 x 8 ANOVA, a simple main effects analysis:

a: Would involve 16 main effects analyses
b: Would involve 10 simple main effects analyses
c: Would involve 2 main effects analyses
d: Is only used when you have more than 2 levels in a factor

Answer 22

b: Would involve 10 simple main effects analyses

Yes, well done! 2 + 8

Question 23

Post-hoc tests of a simple main effects analysis:

A: Are not necessary when you have 3 or more levels in your factor
B: Would be used if you had a non-significant simple main effect
C: Are generally considered redundant
D: Are used after a significant main effect when there are more than 2 levels in the factor

Answer 23

D: Are used after a significant main effect when there are more than 2 levels in the factor

Question 24

In between-subjects ANOVA, the error term is the unexplained variance of the dependent
variable. A second factor when included in a one-way ANOVA, making it a two-way ANOVA, has the effect of:

(A) controlling another source of variance, and increasing the error term.
(B) controlling another source of variance, and decreasing the error term.
(C) adding another source of variance, and increasing the error term.
(D) adding another source of variance, and decreasing the error term.

Answer 24

Answer is (B).
Including another factor (i.e., independent variable) helps to explain more of the variation in the dependent variable – much like, including another predictor in multiple regression. As such, it would reduce the unexplained variance (error) of the dependent variable.

Question 25

In a two-way ANOVA, the number of possible F ratios is:

(A) 4
(B) 3
(C) 2
(D) 1

Answer 25

Answer is (B).
A two-way ANOVA involves a test for the main effect of A, the main effect of B, and their interaction

Question 26

When a significant F ratio is found for interaction in ANOVA of two factors (A and B) the next step is to test:

(A) main effect of factor A.
(B) main effect of factor B
(C) simple main effects of A and B.
(D) association of A and B.

Answer 26

Answer is (C).
A significant interaction suggests that there may be AGE differences in some level of GENDER, or GENDER differences at some level of AGE, or both.

Question 27

A researcher performed a two-way between-subjects ANOVA - the p value obtained for the first factor (AGE) was .02, the p value obtained for the second factor (GENDER) was .06 and the p value for the interaction (AGE x GENDER) was .04. The most appropriate conclusion to make at this point, without further testing, is:

(A) AGE is statistically significant and GENDER is not statistically significant.
(B) AGE is statistically significant under some level of GENDER.
(C) GENDER is statistically significant under some level of AGE.
(D) (B) or (C), or both

Answer 27

Answer is (D).
A significant interaction means that we should not interpret the main effects of AGE and GENDER because there may be AGE differences in some level of GENDER (e.g., males) but not in another (e.g., females) and, likewise, for GENDER differences at some level of AGE but not in another

Question 28

An ANCOVA is most similar conceptually, to:

a: Stepwise Regression
b: Forward Regression
c: Logistic Regression
d: Hierarchical Regression

Answer 28

d: Hierarchical Regression

Question 29

An appropriate covariate reduces the error in an ANCOVA model and this:

A: Increases the Type 1 error rate
B: Makes finding a significant model more likely
C: Makes finding a significant model less likely
D: Is necessary to satisfy the assumption of normality

Answer 29

B: Makes finding a significant model more likely

Reducing the error increases the ratio of proportion explained to unexplained

Question 30

When using an ANCOVA, the homogeniety of slopes:

a: Is an assumption that needs to be satisfied before proceeding
b: Are assessed using a two-way ANOVA
c: Is not a problem if you do not block the covariate
d: Is less important than heterogeneity of slopes

Answer 30

a: Is an assumption that needs to be satisfied before proceeding

Question 31

A chi square analysis enables:

A: A calculation of partial eta squared
B: A calculation of proportion differences from a two independent groups on one categorical outcome
C: A calculation of the proportion of two independent variables
D: A t test to be conducted

Answer 31

B: A calculation of proportion differences from a two independent groups on one categorical outcome

Question 32

The Chi square test assesses the differences between:

a: The two continuous outcomes
b: The sum of the frequency observed and the frequency expected for each cell
c: The mean for each categorical outcome
d: Null hypothesis and the Ho

Answer 32

b: The sum of the frequency observed and the frequency expected for each cell

Question 33

The Chi square statistic

A: Is a parametric test
B: Is larger when the fe and fo are similar(
C: Is smaller when the fe and fo are similar
D: Is largest when there is heterogeneity in regression slopes

Answer 33

C: Is smaller when the fe and fo are similar

Question 34

Which of the following statements is true about ANCOVA?

(A) ANCOVA is used to compare the means of two or more groups while controlling for a
continuous covariate.

(B) ANCOVA is used to compare the proportions of two or more groups while controlling
for a categorical covariate.

(C) ANCOVA is used to compare the variances of two or more groups while controlling for
a continuous covariate.

(D) ANCOVA is used to compare the medians of two or more groups while controlling for
a categorical covariate.

Answer 34

(A) ANCOVA is used to compare the means of two or more groups while controlling for a
continuous covariate

Question 35

Which of the following is NOT a key assumption of ANCOVA?

(A) Each cell contains at least 5 cases

(B) Homogeneity of regression slopes

(C) Independence of observations

(D) Normality of residuals

Answer 35

(A) Each cell contains at least 5 cases

Question 36

Which of the following is a potential benefit of using ANCOVA in statistical analysis?

(A) ANCOVA can increase statistical power by reducing error variance.

(B) ANCOVA can decrease statistical power by introducing additional sources of variation.

(C) ANCOVA can only be used with single covariates, limiting its usefulness in many
research studies.

(D) ANCOVA can only be used with small sample sizes, making it less useful for studies
with large populations

Answer 36

Answer: A A) ANCOVA can increase statistical power by reducing error variance. (For stem B, actually if done correctly hierarchical regression and ANCOVA will produce
identical outcomes)

Question 37

Which of the following statements is true about chi-square?

(A) Chi-square is a parametric test used to compare the means of two or more groups.

(B) Chi-square is a non-parametric test used to compare the means of two or more
groups.

(C) Chi-square is a parametric test used to test the independence of two categorical
variables.

(D) Chi-square is a non-parametric test used to test the normality of a sample

Answer 37

(B) Chi-square is a non-parametric test used to compare the means of two or more groups

Question 38

A researcher wants to examine the relationship between sex at birth (male vs. female) and voting preference (Republican vs. Democrat) in a sample of 500 individuals. After collecting the data, the researcher runs a chi-square test and calculates a phi coefficient of 0.3. What does this phi coefficient indicate about the relationship between gender and voting preference?

(A) There is a weak relationship between sex at birth and voting preference.

(B) There is a strong relationship between sex at birth and voting preference.

(C) There is a moderate relationship between sex at birth and voting preference.

(D) There is no significant relationship between sex at birth and voting preference

Answer 38

(C) There is a moderate relationship between sex at birth and voting preference.

Question 39

Which of the following statements accurately describes the Reliable Change Index (RC )?

1. The RCI is a method for calculating the standard deviation of a data set.
2. The RCI is a statistical measure used to determine the magnitude of change in a variable over time(
3. The RCI is a qualitative assessment tool used to evaluate subjective experiences.
4. The RCI is a psychological assessment technique used to measure intelligence.

Answer 39

2. The RCI is a statistical measure used to determine the magnitude of change in a variable over time

Question 40

Which of the following statements accurately describes the impact of Cronbachs alpha on the Reliable Change Index (RC )?

1. Cronbach’s alpha is used to calculate the RCI, and lower alpha values result in more accurate estimates of significant change.
2. Higher values of Cronbach’s alpha indicate greater test-retest reliability, which can increase the reliability of the RCI estimates.
3. Cronbach’s alpha has no impact on the RCI, as they are independent statistical measures assessing different aspects of data
4. Cronbach’s alpha is used to calculate the RCI, but its impact on the reliability of the index depends on the sample size and measurement scale.

Answer 40

2. Higher values of Cronbach’s alpha indicate greater test-retest reliability, which can increase the reliability of the RCI estimates.

Question 41

Which of the following statements accurately describes the impact of one versus two-tailed criterion values on the Reliable Change Index (RCI)?

1 - One-tailed criterion values are typically used in the RCI calculation to provide a more conservative estimate of significant change.

2: The choice between one or two-tailed criterion values has no impact on the RCI, as it solely depends on the specific statistical test used

3: The decision to use one or two-tailed criterion values in the RCI calculation depends on the specific research question and the desired level of statistical significance.

4: two-tailed criterion values are generally preferred in the RCI calculation as they offer a more sensitive estimate of significant change.

Answer 41

3: The decision to use one or two-tailed criterion values in the RCI calculation depends on the specific research question and the desired level of statistical significance.