Psychology 2812 - Statistics for Psychology II - Final Exam
1.Week 6!: One Way ANOVA and the GLM.
2.Characterize a t test.: - 2 groups.
- Used to compare means of two independent samples (groups).
3.What are H0 and H1 in an ANOVA/the omnibus f test?
Additionally, what is the p value?: - H0:
- Groups sampled from populations with the same mean.
- H1:
- Groups not sampled from populations with the same mean.
- P-value:
- What is the probability of observing differences between groups as
large as the ones observed, if H0 is true?
4.What is an ANOVA?: A statistical test that compares the means of two
or more groups.
5.Characterize a one-way between-subjects ANOVA.: - Has only one
indepen- dent variable.
- Since it is between subjects, each participant contributes an
observation in only one group.
6.ANOVA computes an "omnibus" (overall) F-statistic, which is a ratio of
two variances.
The numerator is the variance, the denominator is the
variance.: between groups variance; within groups variance.
Conceptually, this is the ratio of treatment to error variance,
7.What is the rationale behind ANOVA?: If the variance between
experimental conditions is markedly greater than the variance within
the conditions, it suggests the independent variable is causing the
difference.
8.Omnibus F-statistic is a metric of the "overall" question...: "Are the
means of the groups the same? (or not the same)?"
9.What does an f ratio far above 1.0 mean?
Relatedly, what does an f ratio far below 1.0 mean?: - F-ratio far above 1.0:
- Between groups variance is larger than within-groups variance.
,- F-ratio below 1.0:
- Between groups variance is smaller than within groups variance.
10.Under the null hypothesis we expect the F-statistic to be close to 1.0
most of the time.
But due to random sampling, under the null hypothesis, sometimes it will be
.: larger.
11.In ANOVA, an omnibus F statistic can take on values:
- A. Between -1.0 and 1.0.
- B. Between 0.0 and 1.0.
- C. Between 0.0 and infinity.
- D. Between -infinity and infinity.: - C. Between 0.0 and infinity.
- The F-statistic in an ANOVA is always positive!! It can not be negative!!
12.In what case do we not perform a follow up test after running an
omnibus f test?: If the f test is not significant!
13.What are SSb and SSw?
What is the equation for each one?: - SSb:
- Sum of squares between.
- Each group mean minus the grand mean of all the groups.
- SSw:
- Sum of squares within.
- Each observation minus the group mean to which it belongs.
14.The ANOVA omnibus f test examines whether the differences
between group means are real or due to random chance.
What does Gribble mean by "real" in this case?: By "real", he means faithfu
representation of the differences between the means of the underlying
population(s) from which each sample was drawn.
15.What is the equation for the omnibus f test? What does it tell us?:
- MSbetween ÷ Mswithin.
- Gives an overall measure of the difference between all group
means together, relative to the variability within each group.
16.What are the assumptions of ANOVA?: - 1. Normality of the residuals.
- 2. Homogeneity of variance across groups.
- 3. Independence of observations.
,17.True or false?
If the normality assumption is violated, we can not use ANOVA.: False!
If the normality assumption is violated, we can still use ANOVA, but we
should use a non-parametric test!
18. When
normality is violated for ANOVA, we use the test that
works on ranks of data and not the data itself.: Kruskal Wallis.
19.What test do we use for homogeneity of variance?: Levene's test!
20.True or false?
If the homogeneity of variance assumption is violated, we can still use
ANOVA, and we would use the Welch one way test instead of the regular
ANOVA f test.: True!
21.What would an example of a clear violation of the independence of
obser- vations assumption be?: Repeated measures within each group.
22.ANOVA is a model of your data just like regression / multiple-
regres- sion.: linear.
23.What are the consequences of estimating for 3 parameters instead of 1?:
- We "pay" by moving 2 degrees of freedom for the MSw term to the
MSb term.
- This makes it harder to reject the null hypothesis/find a statistically
significant difference.
- We need to make sure the increase in SSb is worth it!
- It's a tradeoff.
24.Week 9!: One Way ANOVA: Follow Up Tests & Statistical Power.
25.Statistical significance tells you how likely it is that a result is due to
chance rather than a real effect, and it is given be the .: p
value.
26.Define effect size.: Effect size gives us a measure of the size of the
difference between groups.
An effect is a primary measurement that you use to test your hypothesis
and the effect size is the magnitude of that effect.
27.What is eta squared (·2)?What is the equation?: - A statistic used
ANOVA to measure the proportion of variance in a dependent variable
explained by an independent variable.
, - ·2 =SSb ÷ SStot.
- Ranges between 0 and 1, just like R2 in regression.
1.Week 6!: One Way ANOVA and the GLM.
2.Characterize a t test.: - 2 groups.
- Used to compare means of two independent samples (groups).
3.What are H0 and H1 in an ANOVA/the omnibus f test?
Additionally, what is the p value?: - H0:
- Groups sampled from populations with the same mean.
- H1:
- Groups not sampled from populations with the same mean.
- P-value:
- What is the probability of observing differences between groups as
large as the ones observed, if H0 is true?
4.What is an ANOVA?: A statistical test that compares the means of two
or more groups.
5.Characterize a one-way between-subjects ANOVA.: - Has only one
indepen- dent variable.
- Since it is between subjects, each participant contributes an
observation in only one group.
6.ANOVA computes an "omnibus" (overall) F-statistic, which is a ratio of
two variances.
The numerator is the variance, the denominator is the
variance.: between groups variance; within groups variance.
Conceptually, this is the ratio of treatment to error variance,
7.What is the rationale behind ANOVA?: If the variance between
experimental conditions is markedly greater than the variance within
the conditions, it suggests the independent variable is causing the
difference.
8.Omnibus F-statistic is a metric of the "overall" question...: "Are the
means of the groups the same? (or not the same)?"
9.What does an f ratio far above 1.0 mean?
Relatedly, what does an f ratio far below 1.0 mean?: - F-ratio far above 1.0:
- Between groups variance is larger than within-groups variance.
,- F-ratio below 1.0:
- Between groups variance is smaller than within groups variance.
10.Under the null hypothesis we expect the F-statistic to be close to 1.0
most of the time.
But due to random sampling, under the null hypothesis, sometimes it will be
.: larger.
11.In ANOVA, an omnibus F statistic can take on values:
- A. Between -1.0 and 1.0.
- B. Between 0.0 and 1.0.
- C. Between 0.0 and infinity.
- D. Between -infinity and infinity.: - C. Between 0.0 and infinity.
- The F-statistic in an ANOVA is always positive!! It can not be negative!!
12.In what case do we not perform a follow up test after running an
omnibus f test?: If the f test is not significant!
13.What are SSb and SSw?
What is the equation for each one?: - SSb:
- Sum of squares between.
- Each group mean minus the grand mean of all the groups.
- SSw:
- Sum of squares within.
- Each observation minus the group mean to which it belongs.
14.The ANOVA omnibus f test examines whether the differences
between group means are real or due to random chance.
What does Gribble mean by "real" in this case?: By "real", he means faithfu
representation of the differences between the means of the underlying
population(s) from which each sample was drawn.
15.What is the equation for the omnibus f test? What does it tell us?:
- MSbetween ÷ Mswithin.
- Gives an overall measure of the difference between all group
means together, relative to the variability within each group.
16.What are the assumptions of ANOVA?: - 1. Normality of the residuals.
- 2. Homogeneity of variance across groups.
- 3. Independence of observations.
,17.True or false?
If the normality assumption is violated, we can not use ANOVA.: False!
If the normality assumption is violated, we can still use ANOVA, but we
should use a non-parametric test!
18. When
normality is violated for ANOVA, we use the test that
works on ranks of data and not the data itself.: Kruskal Wallis.
19.What test do we use for homogeneity of variance?: Levene's test!
20.True or false?
If the homogeneity of variance assumption is violated, we can still use
ANOVA, and we would use the Welch one way test instead of the regular
ANOVA f test.: True!
21.What would an example of a clear violation of the independence of
obser- vations assumption be?: Repeated measures within each group.
22.ANOVA is a model of your data just like regression / multiple-
regres- sion.: linear.
23.What are the consequences of estimating for 3 parameters instead of 1?:
- We "pay" by moving 2 degrees of freedom for the MSw term to the
MSb term.
- This makes it harder to reject the null hypothesis/find a statistically
significant difference.
- We need to make sure the increase in SSb is worth it!
- It's a tradeoff.
24.Week 9!: One Way ANOVA: Follow Up Tests & Statistical Power.
25.Statistical significance tells you how likely it is that a result is due to
chance rather than a real effect, and it is given be the .: p
value.
26.Define effect size.: Effect size gives us a measure of the size of the
difference between groups.
An effect is a primary measurement that you use to test your hypothesis
and the effect size is the magnitude of that effect.
27.What is eta squared (·2)?What is the equation?: - A statistic used
ANOVA to measure the proportion of variance in a dependent variable
explained by an independent variable.
, - ·2 =SSb ÷ SStot.
- Ranges between 0 and 1, just like R2 in regression.
