Question 1

Analytical comparisons are calculated ______.
A) when the null hypothesis for the F-ratio is statistically insignificant
B) when the null hypothesis for the F-ratio is rejected
C) when the null hypothesis for the F-ratio is not rejected
D) whenever a research feels like it

Accepted Answer

Analytical comparisons are typically calculated when the null hypothesis for the F-ratio is rejected. This indicates that there are significant differences among group means, warranting further investigation into specific group differences.

Question 2

Which type of analytic comparisons is made in the absence of a specific hypothesis regarding which groups should be included?
A) planned comparisons
B) unplanned comparisons
C) a priori comparisons
D) complex comparisons

Accepted Answer

Unplanned comparisons are made in the absence of a specific hypothesis regarding which groups should be included. The other options, planned comparisons and a priori comparisons, involve making comparisons based on specific hypotheses. Complex comparisons refer to analyses that involve multiple factors or variables.

Question 3

If my value of the F ratio falls between the critical values for α = .05 and α = .01, I will ______ the null hypothesis and conclude ______.
A) not reject; p < .05
B) not reject; p < .01
C) reject; p > .01
D) reject; p < .05

Accepted Answer

If the F ratio falls between the critical values for α = .05 and α = .01, it means the p-value is less than .05 but greater than .01, leading to the rejection of the null hypothesis with a conclusion that p < .05.

Question 4

Imagine the value of an F-ratio is less than the critical value for $\alpha$ = .05 and less than the critical value for α = .01. Which is the most appropriate way to report the level of significance? A) p < .01 B) p > .01 C) p < .05 D) p > .05

Accepted Answer

Since the F-ratio is less than the critical values for both α = .05 and α = .01, it indicates that the observed difference is not statistically significant at these levels. Therefore, the correct way to report the significance level is p > .05, indicating that the probability of observing the data, given that the null hypothesis is true, is greater than 5%.

Question 5

If an F ratio is ______ the critical value, I will ______ the null hypothesis and conclude that ______.
A) less than; not reject; the groups are not all equal to each other
B) greater than; reject; the groups are not all equal to each other
C) less than; reject; the groups do not differ significantly from each other
D) greater than; reject; all of the groups are different from each other

Accepted Answer

When an F ratio is greater than the critical value, it indicates that the variability between groups is greater than the variability within groups. This means that the null hypothesis of no difference between groups can be rejected, and it can be concluded that the groups are not all equal to each other. Therefore, option B is the correct choice.

Question 6

Which type of analytical comparisons is not built into the research design prior to data collection?
A) a priori comparisons
B) planned comparisons
C) unplanned comparisons
D) simple comparisons

Accepted Answer

Unplanned comparisons are not pre-determined and are instead explored after data collection. A priori and planned comparisons are designed before data collection, while simple comparisons refer to basic comparisons between groups or variables.

Question 7

A researcher hypothesizes that people, on average, spend more money a week on gasoline than on food or clothing. She conducts a one-way ANOVA involving Gasoline (M = $51.40), Food (M = $24.57) and Clothing (M = $18.29). If she makes the decision to reject the null hypothesis, what is the MOST specific conclusion she can draw?
A) Money spent varies as a function of type of expense.
B) Money spent on gasoline is greater than food or clothing.
C) The money spent on the three expenses are all different from each other.
D) The analysis supports the research hypothesis.

Accepted Answer

The one-way ANOVA tests if there is a significant difference in means among the groups. Rejecting the null hypothesis indicates that at least one group mean is different, but it doesn't specify which ones. Therefore, the most specific conclusion is that money spent varies as a function of type of expense.

Question 8

Which type of analytic comparisons is made when the researcher has a specific hypothesis regarding which groups should be included?
A) planned comparisons
B) unplanned comparisons
C) simple comparisons
D) post hoc comparisons

Accepted Answer

Planned comparisons are made when a researcher has a specific hypothesis regarding which groups should be included in the analysis. This approach allows for more targeted and focused comparisons, which can increase the statistical power and reduce the risk of making Type I errors. Unplanned comparisons, on the other hand, are exploratory in nature and do not have a specific hypothesis guiding them. Simple comparisons refer to the comparison of two groups, while post hoc comparisons are conducted after the main analysis to explore differences between groups not initially included in the analysis.

Question 9

For the same set of data, the relationship between the t-test and the F-ratio may be characterized as ______. A) t = F B) t² = F C) F² = t D) none of these

Accepted Answer

The t-test and the F-ratio are both used to test hypotheses about the means of two populations. The t-test is used when the variances of the two populations are assumed to be equal, while the F-ratio is used when the variances are assumed to be unequal. The relationship between the t-test and the F-ratio is that the square of the t-statistic is equal to the F-statistic.

Question 10

George calculates the F-ratio for a one-way ANOVA comparing the means of three groups: Group A (M = 4.12), Group B (M = 7.37) and Group C (M = 8.92). If he makes the decision to reject the null hypothesis, what is the most specific and appropriate conclusion he can make?
A) The groups are all different from each other.
B) The groups are not all equal to each other.
C) Group A ≠ Group B ≠ Group C
D) Group A < Group B < Group C

Accepted Answer

Rejecting the null hypothesis in a one-way ANOVA test indicates that at least one group mean is different from the others, but it does not specify which groups are different or the direction of the differences.

Question 11

A study compares the attitudes of 9 Seniors, 9 Juniors, 9 Sophomores, and 9 First-year students and obtains a value of 2.98 for the F-ratio. Which of the following is the correct way to present this analysis?
A) F(4,36) = 2.98, p < .05
B) F(4,36) = 2.98, p > .05
C) F(3,32) = 2.98, p < .05
D) F(3,35) = 2.98, p < .05

Accepted Answer

The study compares the attitudes of students in four different groups, so the degrees of freedom for the numerator should be 3. The degrees of freedom for the denominator should be the total number of participants minus the number of groups being compared, which is 36-4=32. The calculated F-value is 2.98, and according to convention, a p-value of less than .05 is considered statistically significant. Therefore, the correct way to present this analysis is F(3,32) = 2.98, p < .05.

Question 12

A researcher calculates an F-ratio comparing the GPAs of three different SJSU majors: Major A (M = 2.70), Major B (M = 2.87) and Major C (M = 3.01). If she makes the decision to NOT reject the null hypothesis, what is the most specific and appropriate conclusion she can draw?
A) The SAT scores for the three groups are all different from each other.
B) The analysis supports the research hypothesis.
C) The GPAs of the three majors are not significantly different.
D) No conclusion can be determined without conducting further analyses.

Accepted Answer

Since the researcher decided to not reject the null hypothesis, it means that there is not enough evidence to support the claim that the GPAs of the three majors are significantly different. Therefore, the most specific and appropriate conclusion is that the GPAs of the three majors are not significantly different. Answer choice A is not relevant to the analysis conducted, answer choice B is too vague and does not accurately reflect the outcome of the analysis, and answer choice D is incorrect since a conclusion can be drawn based on the researcher's decision to not reject the null hypothesis.

Question 13

A researcher calculates an F-ratio comparing the GPAs of three different SJSU majors: Major A (M = 2.40), Major B (M = 2.16) and Major C (M = 3.05). If she makes the decision to reject the null hypothesis, what is the most specific and appropriate conclusion she can draw?
A) GPAs vary as a function of major.
B) The GPAs for the three majors are not different from each other.
C) The GPAs for the three majors are all different from each other.
D) The analysis supports the research hypothesis.

Accepted Answer

The decision to reject the null hypothesis indicates that there is a significant difference between the GPAs of the three majors. However, it does not provide information on which specific majors have significantly different GPAs. Therefore, the most specific and appropriate conclusion would be that GPAs vary as a function of major.

Question 14

Barry calculates an F-ratio for a one-way ANOVA comparing the incomes of graduates of three different SJSU majors and rejects the null hypothesis. Which of the following is the most appropriate conclusion he could draw?
A) The income levels for the three majors are all different from each other.
B) The income levels for the three majors do not differ from each other.
C) Income levels vary as a function of major.
D) The analysis supports the research hypothesis.

Accepted Answer

When the null hypothesis is rejected in a one-way ANOVA, it means that there is a statistically significant difference in at least one of the group means. Therefore, the appropriate conclusion would be that income levels vary as a function of major. Option A and B are too specific and do not take into account the possibility of some differences between the groups. Option D is also not the best choice because it implies that the analysis definitively proves the researcher's hypothesis, which is not necessarily the case.

Question 15

If an F ratio is ______ the critical value, I will ______ the null hypothesis and conclude that ______.
A) greater than; not reject; the groups are not all equal to each other
B) greater than; reject; all of the groups are different from each other
C) less than; not reject; the groups do not differ significantly from each other
D) less than; reject; the groups are all equal to each other

Accepted Answer

If an F ratio is less than the critical value, it means there is not enough evidence to reject the null hypothesis, suggesting that the groups do not differ significantly from each other.

Question 16

______ are analytical comparisons researchers build into the research design prior to the data collection process.
A) Planned comparisons
B) Unplanned comparisons
C) Simple comparisons
D) Post hoc comparisons

Accepted Answer

Planned comparisons are pre-determined analytical comparisons that researchers build into the research design prior to the data collection process. These comparisons help researchers test specific hypotheses and determine if there are significant differences between groups or conditions. Unplanned comparisons, on the other hand, are not pre-determined, and are made after the data has been collected. Simple comparisons and post hoc comparisons are types of unplanned comparisons.

Question 17

Barry calculates an F-ratio involving the SAT scores of three groups and does NOT reject the null hypothesis. Which of the following is the MOST appropriate conclusion he could draw?
A) The SAT scores for the three groups are all different from each other.
B) The SAT scores for the three groups are all equal to each other.
C) The SAT scores for the three groups are not significantly different.
D) No conclusion can be determined without conducting further analyses.

Accepted Answer

Since Barry did not reject the null hypothesis for the F-ratio, it means that there was not enough evidence to suggest that the SAT scores for the three groups were significantly different. Therefore, the most appropriate conclusion is that the SAT scores for the three groups are not significantly different.

Question 18

When researchers have a plan regarding the comparisons between groups needed to test their research hypotheses, these comparisons are known as ______.
A) planned comparisons
B) unplanned comparisons
C) post hoc comparisons
D) complex comparisons

Accepted Answer

Planned comparisons are pre-determined comparisons between groups that are necessary to test research hypotheses. Unplanned comparisons occur when additional comparisons are made that were not specifically planned in advance. Post hoc comparisons are comparisons made after the data has been collected and analyzed, often in response to unexpected results. Complex comparisons refer to comparisons that involve several independent variables and their interactions.

Question 19

If an F ratio is ______ the critical value, I will ______ the null hypothesis because ______.
A) greater than; not reject; p < .05
B) greater than; reject; p > .05
C) less than; not reject; p > .05
D) less than; reject; p > .05

Accepted Answer

If an F ratio is less than the critical value, it indicates that the observed variance between groups is not significantly greater than the variance within groups, leading to a p-value greater than .05. This means there is not enough evidence to reject the null hypothesis, so we do not reject it.

Question 20

A study compares the attitudes of 6 Democrats, 6 Republicans, and 6 Independents and obtains a value of 3.80 for the F-ratio. Which of the following is the correct way to present this analysis?
A) F(2,15) = 3.80, p < .05
B) F(2,15) = 3.80, p > .05
C) F(2,18) = 3.80, p < .05
D) F(3,18) = 3.80, p < .05

Accepted Answer

The correct way to present the analysis is F(2,15) = 3.80, p < .05. The degrees of freedom for the numerator is the number of groups minus one (3 groups - 1 = 2), and for the denominator, it's the total number of subjects minus the number of groups (18 subjects - 3 groups = 15). The p-value indicates whether the result is statistically significant, with p < .05 typically considered significant.

Quiz 11: One-Way Analysis of Variance Anova

Analytical comparisons are calculated ______.

Which type of analytic comparisons is made in the absence of a specific hypothesis regarding which groups should be included?

If my value of the F ratio falls between the critical values for α = .05 and α = .01, I will the null hypothesis and conclude .

Imagine the value of an F-ratio is less than the critical value for $\alpha$ = .05 and less than the critical value for α = .01. Which is the most appropriate way to report the level of significance?

If an F ratio is the critical value, I will the null hypothesis and conclude that __.

Which type of analytical comparisons is not built into the research design prior to data collection?

Which type of analytic comparisons is made when the researcher has a specific hypothesis regarding which groups should be included?

For the same set of data, the relationship between the t-test and the F-ratio may be characterized as ______.

George calculates the F-ratio for a one-way ANOVA comparing the means of three groups: Group A (M = 4.12) , Group B (M = 7.37) and Group C (M = 8.92) . If he makes the decision to reject the null hypothesis, what is the most specific and appropriate conclusion he can make?

A study compares the attitudes of 9 Seniors, 9 Juniors, 9 Sophomores, and 9 First-year students and obtains a value of 2.98 for the F-ratio. Which of the following is the correct way to present this analysis?

A researcher calculates an F-ratio comparing the GPAs of three different SJSU majors: Major A (M = 2.70) , Major B (M = 2.87) and Major C (M = 3.01) . If she makes the decision to NOT reject the null hypothesis, what is the most specific and appropriate conclusion she can draw?

A researcher calculates an F-ratio comparing the GPAs of three different SJSU majors: Major A (M = 2.40) , Major B (M = 2.16) and Major C (M = 3.05) . If she makes the decision to reject the null hypothesis, what is the most specific and appropriate conclusion she can draw?

Barry calculates an F-ratio for a one-way ANOVA comparing the incomes of graduates of three different SJSU majors and rejects the null hypothesis. Which of the following is the most appropriate conclusion he could draw?

If an F ratio is the critical value, I will the null hypothesis and conclude that __.

______ are analytical comparisons researchers build into the research design prior to the data collection process.

Barry calculates an F-ratio involving the SAT scores of three groups and does NOT reject the null hypothesis. Which of the following is the MOST appropriate conclusion he could draw?

When researchers have a plan regarding the comparisons between groups needed to test their research hypotheses, these comparisons are known as ______.

If an F ratio is the critical value, I will the null hypothesis because __.

A study compares the attitudes of 6 Democrats, 6 Republicans, and 6 Independents and obtains a value of 3.80 for the F-ratio. Which of the following is the correct way to present this analysis?

Quiz 11: One-Way Analysis of Variance Anova

Analytical comparisons are calculated ______.

Which type of analytic comparisons is made in the absence of a specific hypothesis regarding which groups should be included?

If my value of the F ratio falls between the critical values for α = .05 and α = .01, I will ______ the null hypothesis and conclude ______.

Imagine the value of an F-ratio is less than the critical value for α\alphaα = .05 and less than the critical value for α = .01. Which is the most appropriate way to report the level of significance?

If an F ratio is ______ the critical value, I will ______ the null hypothesis and conclude that ______.

Which type of analytical comparisons is not built into the research design prior to data collection?

Which type of analytic comparisons is made when the researcher has a specific hypothesis regarding which groups should be included?

For the same set of data, the relationship between the t-test and the F-ratio may be characterized as ______.

George calculates the F-ratio for a one-way ANOVA comparing the means of three groups: Group A (M = 4.12) , Group B (M = 7.37) and Group C (M = 8.92) . If he makes the decision to reject the null hypothesis, what is the most specific and appropriate conclusion he can make?

A study compares the attitudes of 9 Seniors, 9 Juniors, 9 Sophomores, and 9 First-year students and obtains a value of 2.98 for the F-ratio. Which of the following is the correct way to present this analysis?

A researcher calculates an F-ratio comparing the GPAs of three different SJSU majors: Major A (M = 2.70) , Major B (M = 2.87) and Major C (M = 3.01) . If she makes the decision to NOT reject the null hypothesis, what is the most specific and appropriate conclusion she can draw?

A researcher calculates an F-ratio comparing the GPAs of three different SJSU majors: Major A (M = 2.40) , Major B (M = 2.16) and Major C (M = 3.05) . If she makes the decision to reject the null hypothesis, what is the most specific and appropriate conclusion she can draw?

Barry calculates an F-ratio for a one-way ANOVA comparing the incomes of graduates of three different SJSU majors and rejects the null hypothesis. Which of the following is the most appropriate conclusion he could draw?

If an F ratio is ______ the critical value, I will ______ the null hypothesis and conclude that ______.

______ are analytical comparisons researchers build into the research design prior to the data collection process.

Barry calculates an F-ratio involving the SAT scores of three groups and does NOT reject the null hypothesis. Which of the following is the MOST appropriate conclusion he could draw?

When researchers have a plan regarding the comparisons between groups needed to test their research hypotheses, these comparisons are known as ______.

If an F ratio is ______ the critical value, I will ______ the null hypothesis because ______.

A study compares the attitudes of 6 Democrats, 6 Republicans, and 6 Independents and obtains a value of 3.80 for the F-ratio. Which of the following is the correct way to present this analysis?

If my value of the F ratio falls between the critical values for α = .05 and α = .01, I will the null hypothesis and conclude .

Imagine the value of an F-ratio is less than the critical value for $\alpha$ = .05 and less than the critical value for α = .01. Which is the most appropriate way to report the level of significance?

If an F ratio is the critical value, I will the null hypothesis and conclude that __.

If an F ratio is the critical value, I will the null hypothesis and conclude that __.

If an F ratio is the critical value, I will the null hypothesis because __.