Question 1

When interpreting F??, ??? = 8.80, p < .05, what is the within-groups df?&#10;A) 30&#10;B) 27&#10;C) 3&#10;D) 2

Accepted Answer

When interpreting F, we need to look at the degrees of freedom (df) in the output. The degrees of freedom for the numerator (between-groups) are typically listed first, followed by the degrees of freedom for the denominator (within-groups). In this case, the output only provides the F-value and the significance level, but we know that p < .05, which means that the F-value is statistically significant. This suggests that we reject the null hypothesis of no group differences and conclude that there are differences between the groups on the dependent variable.

To determine the within-groups df, we need to have information about the total sample size and the number of groups. Since this information is not given in the question, we cannot calculate the exact value of the within-groups df. However, we can use some logical reasoning to narrow down the possibilities.

The within-groups df is calculated as the total sample size minus the number of groups. We know that the F-value is statistically significant, which means that the sample size must be large enough to provide enough power to detect group differences. Therefore, we can assume that the total sample size is relatively large, which suggests that the within-groups df is likely to be small.

Based on this reasoning, we can eliminate choices A and C, which both suggest relatively large within-groups df values. This leaves us with choices B and D. Since we don't have any additional information about the number of groups or the sample size, we cannot rule out either of these options based on logic alone. However, we can infer that the within-groups df is likely to be no more than 30 (the total sample size), which makes choice B the best option.

Question 2

When interpreting F??, ??? = 8.80, p < .05, what is the total sample size examined?&#10;A) 30&#10;B) 29&#10;C) 3&#10;D) 2

Accepted Answer

The total sample size cannot be determined from the given information, as it only provides the F-value and the p-value.

Question 3

If you wanted to examine whether the level of parental involvement differs based on students' grade in school (i.e., 1st, 2nd, 3rd, etc.), what is the dependent variable of interest?&#10;A) Grade level&#10;B) Students&#10;C) Parents&#10;D) Level of parent involvement

Accepted Answer

The dependent variable of interest is the level of parent involvement, as it is the variable being examined to see if it differs based on students' grade in school. The independent variable is the grade level, and the other two options (students and parents) are not the focus of the research question.

Question 4

When your research question calls for you to examine the differences in group means among three or more groups, which of the following would be the appropriate procedure?&#10;A) Pearson correlation&#10;B) t test for dependent samples&#10;C) t test for independent samples&#10;D) Analysis of variance

Accepted Answer

Analysis of variance (ANOVA) is the appropriate analysis when examining the differences in group means among three or more groups. ANOVA allows for the comparison of means between multiple groups to determine if there are statistically significant differences present. This analysis calculates an F-statistic which compares the between-group variability to the within-group variability.

Question 5

Which of the following would be an example of a design that examines the effects of gender and socioeconomic status (i.e., high, medium, and low) on a test of student achievement?&#10;A) Simple ANOVA&#10;B) One-way ANOVA&#10;C) 2 &#215; 3 ANOVA&#10;D) 3 &#215; 3 ANOVA

Accepted Answer

The 2 × 3 ANOVA would be the best choice as it allows the examination of both gender (male vs. female) and socioeconomic status (high, medium, low) on the test of student achievement. This design allows for the examination of the main effects of gender and socioeconomic status, as well as the interaction between the two factors.

Question 6

When interpreting F??, ??? = 8.80, p < .05, how many groups were examined?&#10;A) 30&#10;B) 27&#10;C) 3&#10;D) 2

Accepted Answer

The notation F with a subscript (in this case, "??") typically indicates the degrees of freedom associated with an F-test in statistics, which is used in ANOVA (Analysis of Variance) tests. The degrees of freedom for an F-test are denoted as df1 and df2, where df1 corresponds to the number of groups minus one. Therefore, if "?? = 8.80" represents the F statistic value and not the degrees of freedom, the actual number of groups cannot be directly inferred from this value. However, given the options and common usage, "???" in the context of an F-test often refers to the degrees of freedom for the numerator (df1), which reflects the number of groups or conditions being compared minus one. Since there is no direct information given in the question about "???" being the degrees of freedom or relating directly to the number of groups, and assuming a typical interpretation mistake where "???" might be thought to represent the number of groups directly from the F statistic (which it does not), the correct interpretation based on standard statistical notation and the most common scenario in which an F-test is used (comparing more than two groups, hence ANOVA) would lead to the conclusion that there were more than two groups involved. However, without clear information on what "???" stands for, directly inferring the exact number of groups just from "F??, ??? = 8.80, p < .05" is not straightforward. The correct answer should be based on understanding that an F-test is used for comparing three or more groups, hence option C (3) is chosen assuming a misunderstanding in the question's presentation regarding how statistical notation is typically interpreted.

Question 7

What is the variability between groups due to?&#10;A) Chance&#10;B) The grouping factor&#10;C) The F ratio&#10;D) The levels of the dependent variable

Accepted Answer

The variability between groups is due to the grouping factor, which is the factor being manipulated in an experiment or study.

Question 8

What is the first step in the computation of the F statistic?&#10;A) Setting the level of risk&#10;B) Selection of the appropriate test&#10;C) Computing the obtained value&#10;D) Stating the null and research hypotheses

Accepted Answer

The first step in the computation of the F statistic, as in any statistical test, involves stating the null and research hypotheses. This step sets the foundation for the analysis by defining what is being tested.

Question 9

When interpreting F??, ??? = 8.80, p < .05, what is the between-groups df?&#10;A) 30&#10;B) 27&#10;C) 3&#10;D) 2

Accepted Answer

The answer of When interpreting F??, ??? = 8.80, p...

Question 10

Who is responsible for the invention of the F statistic?&#10;A) Pearson Fisher&#10;B) Karl Pearson&#10;C) R. A. Fisher&#10;D) R. A. Pearson

Accepted Answer

R.A. Fisher is widely credited as the inventor of the F statistic, also known as the Fisher-Snedecor distribution. Options A and B reference Pearson, who made significant contributions to statistics but did not invent the F statistic. Option D combines the names of two statisticians and is therefore incorrect.

Question 11

What is the variability within groups due to?&#10;A) Chance&#10;B) The grouping factor&#10;C) The F ratio&#10;D) The levels of the dependent variable

Accepted Answer

The answer of What is the variability within groups due...

Question 12

Which of the following is the same as t&#178; when examining the difference between two groups?&#10;A) F&#10;B) t&#10;C) Cohen's d&#10;D) F&#178;

Accepted Answer

The answer of Which of the following is the same...

Question 13

When you compute the sum of the differences between each individual score and the group mean, you have calculated which of the following:&#10;A) MS within&#10;B) SS within&#10;C) SS between&#10;D) MS between

Accepted Answer

The answer of When you compute the sum of the...

Question 14

In order to increase the F value, which of the following must occur?&#10;A) MS within > MS between&#10;B) MS within = MS within&#10;C) MS between > MS within&#10;D) Ratio = 1

Accepted Answer

The answer of In order to increase the F value,...

Question 15

Which of the following is the formula for computing the F statistic?&#10;A) F = MS between/MS within&#10;B) F = SS between/SS within&#10;C) F = SS within/SS between&#10;D) F = MS within/MS between

Accepted Answer

The answer of Which of the following is the formula...

Question 16

When computing the degrees of freedom for ANOVA, how is the within-group estimate calculated?&#10;A) n - 1&#10;B) k - 1&#10;C) N - k&#10;D) n/k

Accepted Answer

The answer of When computing the degrees of freedom for...

Question 17

If you wanted to examine whether the level of parental involvement differs based on students' grade in school (i.e., 1st, 2nd, 3rd, etc.), what is the independent variable of interest?&#10;A) Grade level&#10;B) Students&#10;C) Parents&#10;D) Level of parent involvement

Accepted Answer

The answer of If you wanted to examine whether the...

Question 18

Computing the between-group variance first calls for summing the difference between the grand mean and the group means. What is this known as?&#10;A) MS within&#10;B) SS within&#10;C) SS between&#10;D) MS between

Accepted Answer

The answer of Computing the between-group variance first calls for...

Question 19

When computing the degrees of freedom for ANOVA, how is the between-group estimate calculated?&#10;A) n - 1&#10;B) k - 1&#10;C) N - k&#10;D) n/k

Accepted Answer

The answer of When computing the degrees of freedom for...

Question 20

What type of ANOVA is used when there is only one type of treatment or grouping factor with more than two levels?&#10;A) One-way&#10;B) Two-way&#10;C) Three-way&#10;D) Four-way

Accepted Answer

The answer of What type of ANOVA is used when...

Question 21

When is analysis of variance the appropriate statistical procedure to use?

Accepted Answer

The answer of When is analysis of variance the appropriate...

Question 22

What is the MS within value?

Accepted Answer

The answer of What is the MS within value?...

Question 23

What is the formula for computing the F statistic?

Accepted Answer

The answer of What is the formula for computing the...

Question 24

If the total sample size was 50 and three groups were examined, what is the within-groups degrees of freedom?

Accepted Answer

The answer of If the total sample size was 50...

Question 25

What is the sum of squares total?

Accepted Answer

The answer of What is the sum of squares total?...

Question 26

What is the F value?

Accepted Answer

The answer of What is the F value?...

Question 27

How are the F statistic and t statistic related?

Accepted Answer

The answer of How are the F statistic and t...

Question 28

What are the three different ANOVA options within the Analysis Toolpak?

Accepted Answer

The answer of What are the three different ANOVA options...

Question 29

If the total sample size was 50 and three groups were examined, what is the between-groups degrees of freedom?

Accepted Answer

The answer of If the total sample size was 50...

Question 30

What is the MS between value?

Accepted Answer

The answer of What is the MS between value?...

Deck 13: Two Groups Too Many? Try Analysis of Variance