Practice Quiz Chapter 08

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. In an ANOVA test how is the total variation in the sample divided?

a) The variation between the groups and the variation within groups correct incorrect

b) The means of the groups and the variation within groups correct incorrect

c) The means of the groups and standard error correct incorrect

d) Cohen's d and t-tests correct incorrect

e) T-distribution and the means of the group correct incorrect

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. With one-way ANOVA tests, the total variation captures what?

a) The variation between the groups correct incorrect

b) How far the cases in the sample are spread out around the sample mean, regardless of group membership correct incorrect

c) The variation within the groups correct incorrect

d) The variation between the groups subtracted from the variation within the groups correct incorrect

e) The variation within the groups subtracted from the variation between the groups correct incorrect

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. What is the formula for the total sum of squares?

a) The between group sum of squares plus the within group sum of squares correct incorrect

b) The between group sum of squares minus the within group sum of squares correct incorrect

c) The within group sum of squares subtracted from the between group sum of squares correct incorrect

d) Cohen's d subtracted from the ANOVA test statistic correct incorrect

e) The difference between the group means subtracted from the ANOVA test statistic correct incorrect

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. Which of the following is not part of the formula for calculating the sum of squares within a group?

a) A value for an individual case correct incorrect

b) The mean of the group the case belongs to correct incorrect

c) Squaring the deviations from the mean for each case in a group correct incorrect

d) Dividing the total by the standard deviation of the sample correct incorrect

e) Summing the differences between the cases and the group mean correct incorrect

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. Which of the following is not part of the formula for calculating the sum of squares within a group?

a) Calculate the overall and group means correct incorrect

b) Find the difference between each group mean and the overall mean and square it correct incorrect

c) Multiply the squared result for each group by the number of cases in each group correct incorrect

d) Divide the rows by the standard deviation for the sample correct incorrect

e) Sum the rows correct incorrect

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. What does an F-statistic and F-distribution tell us?

a) How much bigger between group variation is compared to within group variation to suggest there is a difference in population means correct incorrect

b) How much bigger within group variation is compared to between group variation to suggest there is a difference in population means correct incorrect

c) The degrees of freedom correct incorrect

d) How much bigger one group's mean is compared to another's correct incorrect

e) The sum of the squares significance correct incorrect

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. The F-statistic is also known as what?

a) F-select correct incorrect

b) F-ratio correct incorrect

c) The degrees of freedom calculator correct incorrect

d) F-ration correct incorrect

e) A measure of association correct incorrect

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. Which of the following is not true of calculating the F-statistic?

a) The numerator captures information about the between group variation correct incorrect

b) The denominator captures information about the between group variation correct incorrect

c) The denominator captures information about the within group variation correct incorrect

d) The between group variation is captured by dividing the between group sum of squares by the between group degrees of freedom correct incorrect

e) The denominator shows the amount of "unexplained variation" or the amount of variation not attributable to group membership correct incorrect

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. If the sum of squares between groups is 918.8 and the degrees of freedom for between groups is 2, then what is the F-statistic when the sum of squares within group is equal to 1094 with degrees of freedom within the group of 8?

a) 0.036 correct incorrect

b) 3.6 correct incorrect

c) 3.36 correct incorrect

d) 0.36 correct incorrect

e) 0.0036 correct incorrect

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. Using a critical value of 4.46, interpret your answer from the previous question: What does it mean?

a) We need more information to suggest a state of the population correct incorrect

b) The critical value is too small—no further calculation is possible correct incorrect

c) Reject the null hypothesis correct incorrect

d) The ratio is large enough to suggest that there is a relationship in the population correct incorrect

e) The ratio isn't large enough to suggest that there is a relationship in the population correct incorrect

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. What does the p-value with each F-statistic show?

a) That the group means are equal in the population if they are approximately equal in the samples selected correct incorrect

b) The probability of selecting a sample with the observed relationship (or a relationship of greater magnitude) if the null hypothesis is rejected correct incorrect

c) The probability of selecting a sample with the observed relationship (or a relationship of greater magnitude) if the alternative hypothesis is true in the population correct incorrect

d) The probability of selecting a sample with the observed relationship (or a relationship of greater magnitude) if the null hypothesis is true in the population correct incorrect

e) The probability of selecting a sample with the observed relationship (or a relationship of greater magnitude) if the null hypothesis is false in the population correct incorrect

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. When the F-statistic for a hypothetical example is lower than the critical value, what does this mean?

a) We can assert a relationship found between two or more variables in the sample exists in the population correct incorrect

b) We cannot assert a relationship found between two or more variables in the sample exists in the population correct incorrect

c) We can assert a relationship found between three or more variables in the sample exists in the population correct incorrect

d) We can assert a relationship found between four or more variables in the sample exists in the population correct incorrect

e) We can assert a relationship found between five or more variables in the sample exists in the population correct incorrect

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. If the sum of squares between groups is 27,107 and the degrees of freedom for between groups is 2, then what is the F-statistic when the sum of squares within groups is equal to 2,242,076 with degrees of freedom within the group of 19,199?

a) 1.6 correct incorrect

b) 116 correct incorrect

c) 0.116 correct incorrect

d) 0.016 correct incorrect

e) 11.6 correct incorrect

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. Using a critical value of 3, interpret your answer from the previous question: What does it mean?

a) We need more information to suggest a state of the population correct incorrect

b) The critical value is too small—no further calculation is possible correct incorrect

c) Reject the null hypothesis, there is likely a relationship in the population correct incorrect

d) Accept the null hypothesis, there is no relationship in the population correct incorrect

e) The ratio isn't large enough to suggest that there is a relationship in the population correct incorrect

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. If a categorical variable in an LSD test is divided into three groups, then how many pairs of relationships must be tested?

a) 3.3 correct incorrect

b) 33 correct incorrect

c) 13 correct incorrect

d) 1 correct incorrect

e) 3 correct incorrect

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. If the sum of squares between groups is 32,714 and the degrees of freedom for between groups is 4, then what is the F-statistic when the sum of squares within group is equal to 2,655,448 with degrees of freedom within the group of 22,846?

a) 74 correct incorrect

b) 0.0074 correct incorrect

c) 7.4 correct incorrect

d) 0.740 correct incorrect

e) 70.4 correct incorrect

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. If the sum of squares between groups is 44,816 and the degrees of freedom for between groups is 8, then what is the F-statistic when the sum of squares within group is equal to 1,788,220 with degrees of freedom within the group of 15,555?

a) 48.3 correct incorrect

b) 4.83 correct incorrect

c) 0.483 correct incorrect

d) 0.0483 correct incorrect

e) 483 correct incorrect

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. Which of the following statements about t-tests of independent means and one-way ANOVA tests is not true?

a) Both tests are run under the assumption that the data they rely on are from a randomly selected, unbiased sample of a population correct incorrect

b) Both tests assume that the dependent variable is approximately normally distributed, with limited kurtosis and skew correct incorrect

c) Both tests are run under the assumption that the data they rely on are not from a randomly selected, unbiased sample of a population correct incorrect

d) Both tests are somewhat forgiving when normality is breached correct incorrect

e) Both tests assume the groups are independent of each other and that cases are not linked or paired in anyway correct incorrect

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. When should t-tests and ANOVA not be used?

a) When the mean is a poor measure of the centre of a variable's distribution while the standard deviation is modified and is now a good measure of its spread correct incorrect

b) When the mean is a poor measure of the centre of a variable's distribution and the standard deviation is a poor measure of its spread correct incorrect

c) When the mean is a good measure of the centre of a variable's distribution and the standard deviation is a poor measure of its spread correct incorrect

d) When the mean is a poor measure of the centre of a variable's distribution and the standard deviation is a good measure of its spread correct incorrect

e) When the mean has been modified and is now a good measure of the centre of a variable's distribution while the standard deviation is still a poor measure of its spread correct incorrect

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. If the sum of squares between groups is 4,344 and the degrees of freedom for between groups is 2, then what is the F-statistic when the sum of squares within groups is equal to 17,880 with degrees of freedom within the group of 255?

a) 31 correct incorrect

b) 3.1 correct incorrect

c) 0.031 correct incorrect

d) 0.31 correct incorrect

e) 0.331 correct incorrect

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. When a categorical independent variable has more than two attributes researchers must utilize an ANOVA table.

a) True correct incorrect

b) False correct incorrect

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. With one-way ANOVA tests, the variation between the groups captures how far the cases in each group are spread out around their group mean, whereas the variation within the groups captures the distance between the group means.

a) True correct incorrect

b) False correct incorrect

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. The ANOVA test statistic is a ratio that compares the between group variation to the within group variation.

a) True correct incorrect

b) False correct incorrect

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. One-way ANOVA tests rely on assessing the amount of variation within a sample.

a) True correct incorrect

b) False correct incorrect

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. The calculation of the between group sum of squares relies on a different logic than the calculation for the within group sum of squares.

a) True correct incorrect

b) False correct incorrect

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. The calculation of the total sum of squares is almost identical to the calculation of the within group sum of squares with the difference being the researcher finds the deviation of each case from the overall mean, instead of the group mean.

a) True correct incorrect

b) False correct incorrect

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. The F-statistic accounts for the number of groups being compared and for the sample size by dividing each sum of squares by its degrees of freedom.

a) True correct incorrect

b) False correct incorrect

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. The degrees of freedom of the within group sum of squares does not account for the sample size.

a) True correct incorrect

b) False correct incorrect

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. The F-statistic shows whether the between group variation is larger or smaller than the within group variation, after accounting for the sample size and the number of groups.

a) True correct incorrect

b) False correct incorrect

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. The F-statistic is interpreted in relation to a t-distribution.

a) True correct incorrect

b) False correct incorrect

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. It is not possible to obtain a negative F-statistic because it's not possible to have negative variation.

a) True correct incorrect

b) False correct incorrect

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. The area under the curve beyond the F-statistic on an F-distribution shows the probability of randomly selecting a sample with the observed ratio of between group variation to within group variation if the group means are equal in the population.

a) True correct incorrect

b) False correct incorrect

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. Only the between group sum of squares and the within group sum of squares are needed to calculate the F-statistic.

a) True correct incorrect

b) False correct incorrect

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. ANOVA tests do not rely on pooling together the within group variation and all the between group variation.

a) True correct incorrect

b) False correct incorrect

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. One of the most common post-hoc tests that researchers can use in conjunction with the ANOVA test is the least significant differences (LSD) test.

a) True correct incorrect

b) False correct incorrect

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. A limitation of the LSD post-hoc test is that it uses a version of the t-test of independent means, which assumes the group variances are equal in the population.

a) True correct incorrect

b) False correct incorrect

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. All post-hoc tests assume that the group variances are equal in the population.

a) True correct incorrect

b) False correct incorrect

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. Error-bar graphs help contextualize the results of one-way ANOVA and post-hoc tests.

a) True correct incorrect

b) False correct incorrect

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. Two-way ANOVA tests account for how the two independent variables might combine or interact to influence the independent variable.

a) True correct incorrect

b) False correct incorrect

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. T-tests of independent means and one-way ANOVA tests are both used to assess the reliability of a relationship between a categorical independent variable and a ratio-level dependent variable.

a) True correct incorrect

b) False correct incorrect