Deck 13: Handling Violations of Assumptions

Question 1

To figure out whether our sample appears to have come from a population exhibiting a normal distribution, which of the following is least useful?

A) Creating a histogram of the data and looking at it carefully.
B) Judging the linearity of values on a quantile plot of the data.
C) Measuring the mean and variance to see if they are equal.
D) Performing a Shapiro-Wilk test on the data.

Answer 1

C

Question 2

A quantile plot for a data set is described by which of the following?

A) A plot of the numerical values versus the t-value expected for a value at that position in the set.
B) A plot of the numerical values versus the Z-value expected for a value at that position in the set.
C) A plot of the numerical values versus their frequency in the set.
D) A plot of the numerical values versus their position in the set.

Answer 2

B

Question 3

Hallmarks of a non-normal population distribution include all of the following except which pattern?

A) A histogram of the sample that has outliers.
B) A histogram of the sample that is skewed heavily to one side.
C) A histogram of the sample that is strongly bimodal.
D) A histogram of the sample that is symmetric around the mean.

Answer 3

D

Question 4

Statistical methods vary in their sensitivity to violations of their assumptions. The methods that are less prone to error when the assumptions are violated are termed which of the following?

A) Reliable
B) Repeatable
C) Resistant
D) Robust

Question 5

The t-test is fairly robust to deviations from normality for large sample sizes, even though this is an assumption of the method. This is because the central limit theorem states that ____.

A) the distribution of population data will be normal.
B) the distribution of population means will be normal.
C) the distribution of sample data will be normal.
D) the distribution of sample means will be normal.

Question 6

When comparing two groups with a t-test, which is the best approach?

A) Either test can be used unless the standard deviations differ by a factor of 3 or more, in which case you can only use a two-sample t-test.
B) Either test can be used unless the standard deviations differ by a factor of 3 or more, in which case you can only use a Welch's t-test.
C) Neither test can be used unless the standard deviations differ by less than a factor of 3, in which case you can use a two-sample t-test.
D) Neither test can be used unless the standard deviations differ by less than a factor of 3, in which case you can use a Welch's t-test.

Question 7

For the data transformation Y' = ln[Y], what is the back transformation?

A) Y = e^Y'
B) Y = 10^Y'
C) Y = Log₁₀[Y']
D) Y = L[Y']

Question 8

Log transformation is most useful for all of the following types of data except which?

A) Highly variable data
B) Left-skewed data
C) Right-skewed data
D) Values that are ratios

Question 9

The square-root transformation is most often used for what types of data?

A) Counts
B) Highly symmetric distributions
C) Proportions
D) Ratios

Question 10

What two values would you get if you apply the square-root transformation with a factor of 1/2 to the numbers 3 and 9?

A) 1.58 and 2.92
B) 1.58 and 3.08
C) 1.87 and 2.92
D) 1.87 and 3.08

Question 11

If we calculate a 95% confidence interval for a square-root transformed (using the 1/2 factor) set of data and get 15.5 < μ' < 22.5, what is the 95% confidence interval in the original values?

A) 225 < μ < 484
B) 225 < μ < 505.75
C) 239.75 < μ < 484
D) 239.75 < μ < 505.75

Question 12

If we calculate a 95% confidence interval for a square-root transformed (using the 1/2 factor) set of data and get 5.33 < μ' < 9.33, what is the 95% confidence interval in the original values?

A) 27.91 < μ < 83.53
B) 27.91 < μ < 86.55
C) 30.86 < μ < 83.53
D) 30.86 < μ < 86.55

Question 13

What assumption does the Wilcoxon signed-rank test make that limits its utility?

A) The distribution must be normal.
B) The distribution must be symmetric.
C) The sample size must be larger than 10.
D) The variance must be equal to the mean.

Question 14

If we have two samples of size 18 and 23 that generate a U-statistic value of 250, what Z-statistic does this approximate to?

A) 0.604
B) 1.130
C) 1.656
D) 2.253

Question 15

If we have two samples of size 27 and 34 that generate a U-statistic value of 273, what Z-statistic does this approximate to?

A) -1.80
B) -2.10
C) -2.40
D) -2.70

Question 16

The Mann-Whitney U-test compares which of the following properties in two groups?

A) The location and shape of their distributions.
B) The location and variance of their distributions.
C) The mean and shape of their distributions.
D) The mean and variance of their distributions.

Question 17

When sample sizes are large and all assumptions are met, a sign test has approximately ____% of the power of the one-sample t-test and the Mann-Whitney U-test has approximately ____% of the power of the two-sample t-test.

A) 65%; 75%.
B) 65%; 95%.
C) 75%; 95%.
D) 95%; 75%.

Question 18

Randomly rearranging the values when we do a permutation test allows us to do which of the following?

A) Estimate the sampling error.
B) Filter out the asymmetry.
C) Model a null hypothesis distribution.
D) Simulate a data set with more precision.

Question 19

Which of the following is not one of the steps in performing a permutation analysis?

A) Calculate the measure of association for the permutated sample.
B) Create a permutated set of data with values of the response variable are randomly reordered.
C) Estimate the P-value of each permutation.
D) Repeat the permutation process many times.

Question 20

When performing a permutation analysis, we remove values from a pool, and they can't be chosen more than once for each new data set. This process is called ___________.

A) sampling with replacement.
B) sampling without replacement.
C) single sampling.
D) unique sampling.

Question 21

Often the best way to check for normality in the population is to just look at the shape of the distribution of sample values.

Question 22

As sample sizes increase, their distributions tend to resemble the population from which they are drawn.

Question 23

The central limit theorem allows the assumption of normality to be ignored for F tests when we use extremely large samples.

Question 24

It is acceptable practice to try multiple transformations and choose the one that makes your data fit the assumptions of the statistical test best.

Question 25

It is acceptable practice to try multiple transformations and choose the one that results in the smallest P-value for your statistical test.

Question 26

Data transformations are only applied to the values that cause a distribution to deviate from normality.

Question 27

The sign test can be performed with highly skewed data sets.

Question 28

The Wilcoxon signed-rank test can be performed with highly skewed data sets.

Question 29

When calculating your U-values to obtain your U-statistic, the two U values will sum up to the product of the two sample sizes.

Question 30

The Mann-Whitney U-test compares the medians in two groups to see if they are significantly different.

Question 31

The Wilcoxon signed rank test can be performed on skewed data sets.

Question 32

An inflated risk of Type I error is the main reason not to use parametric tests when their assumptions are not met.

Question 33

An inflated risk of Type II error is the main reason not to use parametric tests when their assumptions are not met.

Question 34

Permutation tests can be used to compare two means even when the data sets are highly skewed, as long as the skew is similar.

Question 35

Calculate the means and difference in means for the data sets shown. Now, square-root transform (using a factor of 1/2) the data and show the new means and difference in means.
Set 1: 3 9 12 14
Set 2: 14 12 10 2

Question 36

Calculate the means and difference in means for the data sets shown. Now, square-root transform (using a factor of 1/2) the data and show the new means and difference in means.
Set 1: 4 5 7 8
Set 2: 4 4 6 22

Question 37

Draw a flowchart for deciding what test to do when comparing the location of a group to a hypothesized value. Show the options for when the distribution is or is not skewed.

Question 38

Draw a flowchart for deciding what test to do when comparing two groups. Show the options for when the data values are paired, the distributions are or are not skewed, and when the variances are or are not equal.