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Environmental scientists gather a sample of 2016 chemical spill data from cities in six countries. This table shows information from each sample. Environmental scientists gather a sample of 2016 chemical spill data from cities in six countries. This table shows information from each sample. -In order to properly conduct an ANOVA test, which of the following should be equal across the five countries? A) number of cities in each population B) population average in chemical spills C) sample average in chemical spills D) population variance in chemical spills -In order to properly conduct an ANOVA test, which of the following should be equal across the five countries?


A) number of cities in each population
B) population average in chemical spills
C) sample average in chemical spills
D) population variance in chemical spills

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A researcher calculates eta-squared as being 0.45. Which of the following is the best interpretation of this statistic?


A) We have a 45% chance of rejecting the null hypothesis.
B) The group with the lowest mean value is 45% as large as the group with the highest mean value.
C) Means this different between groups will occur by chance alone 45% of the time.
D) Knowing which group a case belongs to helps reduce errors in prediction by 45%.

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D

What scenario most likely leads to rejecting the null hypothesis in an ANOVA test?


A) high variance within categories, and low variance between categories
B) high variance between categories, and low variance within categories
C) high variance within and between categories
D) low variance within and between categories

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Explain why the F test is always effectively a one-tailed test.

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The only way for the F test statistic to...

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Environmental scientists gather a sample of 2016 chemical spill data from cities in six countries. This table shows information from each sample. Environmental scientists gather a sample of 2016 chemical spill data from cities in six countries. This table shows information from each sample. -What would be the degrees of freedom (within) for an ANOVA test? A) 4 B) 5 C) 56 D) 61 -What would be the degrees of freedom (within) for an ANOVA test?


A) 4
B) 5
C) 56
D) 61

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What is the main difference between the t test and the ANOVA test?


A) The t test is for interval-ratio-dependent variables; ANOVA accommodates dependent variables from all types of measurements.
B) The t test assumes equal population variances across categories; ANOVA makes no such assumption.
C) The t test is for comparing means across two categories; ANOVA accommodates three or more categories.
D) The t test distinguishes between the independent and the dependent variable; ANOVA makes no such distinction.

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Environmental scientists gather a sample of 2016 chemical spill data from cities in six countries. This table shows information from each sample. Environmental scientists gather a sample of 2016 chemical spill data from cities in six countries. This table shows information from each sample. -What would be the degrees of freedom (between) for an ANOVA test? A) 4 B) 5 C) 56 D) 61 -What would be the degrees of freedom (between) for an ANOVA test?


A) 4
B) 5
C) 56
D) 61

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What does SSB quantify?


A) the average difference between any two of the groups selected
B) the amount of total variation explained by group membership
C) the amount of variation in the population
D) the amount of variation between the groups selected

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If the sum of squares total (SST) is 13.5 and the sum of squares within (SSW) is 6.5, what is the sum of squares between (SSB) ?


A) 7
B) 20
C) 26.5
D) 87.75

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A

Suppose we are analyzing the income levels of four ethnic groups and we want to determine how much variance in income can be attributed to ethnic background. What is the statistic that will provide us the answer?


A) eta-squared
B) post hoc test
C) F ratio
D) mean square estimate

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Which of these F (observed) values would most likely be used to reject the null hypothesis in an ANOVA test using reasonably large samples and an alpha value of 0.05?


A) -74
B) -1.3
C) 1.1
D) 3.9

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Suppose we have randomly sampled data from five provinces on work days missed due to illness in the past year. If the null hypothesis is true, what would be true about the data?


A) Mean value of days missed should be roughly equal across the five provinces.
B) Each province should have a markedly different score.
C) The sample standard deviation values from each province would be identical.
D) Each province sample would be exactly the same size.

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How is the test statistic for ANOVA calculated?


A) by dividing mean squares between by mean squares within (MSB/MSW)
B) by summing mean squares between and mean squares within, and dividing by total degrees of freedom ((MSB + MSW) /dft)
C) by looking up the value in an F distribution table with the appropriate degrees of freedom within (dfw) and degrees of freedom between (dfb)
D) by summing all the deviations from the overall mean score How is the test statistic for ANOVA calculated? A) by dividing mean squares between by mean squares within (MSB/MSW) B) by summing mean squares between and mean squares within, and dividing by total degrees of freedom ((MSB + MSW) /dft) C) by looking up the value in an F distribution table with the appropriate degrees of freedom within (dfw) and degrees of freedom between (dfb) D) by summing all the deviations from the overall mean score

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A professor wants to know whether students in his large art history class differ on their exam score depending on which version of the test he gives them, a multiple-choice exam, an essay exam, or a mixed version. A random sample of 5 students is drawn from each exam type. Is there any statistically significant difference in the final exam scores? Use the five-step model and an alpha level of 0.05, and write a sentence or two of interpretation for your results. A professor wants to know whether students in his large art history class differ on their exam score depending on which version of the test he gives them, a multiple-choice exam, an essay exam, or a mixed version. A random sample of 5 students is drawn from each exam type. Is there any statistically significant difference in the final exam scores? Use the five-step model and an alpha level of 0.05, and write a sentence or two of interpretation for your results.

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SST = 2022
SSB = 1086.4
SSW = 935.6
F (o...

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How is the null hypothesis for the ANOVA test generally stated?


A) dfb = dfw
B) How is the null hypothesis for the ANOVA test generally stated? A) dfb = dfw B) C) SST = SSB = SSW D)
C) SST = SSB = SSW
D) How is the null hypothesis for the ANOVA test generally stated? A) dfb = dfw B) C) SST = SSB = SSW D)

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Suppose we want to compare the average number of chronic diseases across three long-term care homes. Below are data from random samples of residents from each long-term care home. Is there a statistically significant mean number across the three groups? Use the five-step model and an alpha of 0.01, and a write a sentence or two to interpret your results. Suppose we want to compare the average number of chronic diseases across three long-term care homes. Below are data from random samples of residents from each long-term care home. Is there a statistically significant mean number across the three groups? Use the five-step model and an alpha of 0.01, and a write a sentence or two to interpret your results.

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SST = 115.94
SSB = 37.74
SSW = 78.20
F (...

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An ANOVA test indicates that there are statistically significant differences for the means of five distinct groups. What do the results of this test fail to tell us?


A) that the differences reveal something meaningful about real-world processes
B) that the differences observed are not likely due to chance fluctuation
C) that the populations representing these groups differ from one another on their mean scores
D) that the F (observed) value exceeds the F (critical) value

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Which of the following is an assumption that must be made in step 1 of the ANOVA test?


A) The random samples are theoretical.
B) The samples are non-random.
C) The random samples are independent.
D) The random samples are dependent.

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For which dependent variables are the ANOVA test most appropriate?


A) continuous and nominal
B) discrete and continuous
C) continuous and interval-ratio
D) discrete and ordinal

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C

A film studies researcher calculated the number of film appearances from randomly sampled Hollywood actors, Bollywood actors, and Chinese industry actors. She calculated an F score of 1.22 after comparing the three samples. What should the researcher do about the null hypothesis?


A) fail to reject it because the differences are not statistically significant
B) reject it because the differences are statistically significant but the effect size is small
C) fail to reject it because the means are significantly different from one another
D) reject it because the differences are no larger than what we would expect by chance

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