Question 1

When conducting a statistical test,a single outlier can
A)make the test more robust to violations of the assumption of normality.
B)reduce the sample's variance,making significant results easier to achieve.
C)lead to a significant result when the other members of the sample considered without the outlier would not lead to a significant result.
D)improve the reliability of the statistical procedure.

Accepted Answer

A single outlier can have a significant impact on the results of a statistical test. It can produce a significant result when the other members of the sample, considered without the outlier, would not lead to a significant result. Therefore, it is important to address outliers and consider their impact on the results. However, outliers do not necessarily make the test more robust to violations of the assumption of normality, reduce the sample's variance, or improve the reliability of the statistical procedure.

Question 2

In a square-root transformation,
A)high numbers become lower,and low numbers become higher.
B)moderate numbers remain unchanged,but low numbers become slightly higher.
C)low numbers become much lower,but high numbers remain basically unchanged.
D)moderate numbers become only slightly lower,but high numbers become much lower.

Accepted Answer

In a square-root transformation, the transformation reduces the range of data by compressing high values more than low values, making high numbers much lower while moderate numbers become only slightly lower.

Question 3

Which of the following represents the correct scores if 4,25,25,and 100 are transformed using the rank-order method?
A)2,5,5,10
B)1,2.5,2.5,4
C)1,2,3,4
D)1.5,2,3.5,4

Accepted Answer

The rank-order method involves assigning ranks to the scores based on their order from lowest to highest. If there are ties, the average of the ranks that would have been assigned is used. 
4 would be assigned a rank of 1
The two 25s would be assigned a rank of 2.5, which is the average of ranks 2 and 3.
100 would be assigned a rank of 4.

So the transformed scores would be 1, 2.5, 2.5, and 4. Therefore, the best choice is B.

Question 4

Which of the following represents the correct scores if 1,4,25,and 81 are transformed using a square-root transformation?
A)1,2,5,9
B)1,4,25,81
C)4,4,25,25
D)1,2,3,4

Accepted Answer

The square-root transformation involves taking the square root of each number. The square roots of 1, 4, 25, and 81 are 1, 2, 5, and 9, respectively.

Question 5

Assumptions for statistical procedures are about
A)populations.
B)samples.
C)inferences.
D)hypotheses.

Accepted Answer

Statistical procedures often make assumptions about the populations from which samples are drawn, such as normality, homogeneity of variance, or independence.

Question 6

Which of the following represents the correct scores if 4,25,25,and 100 are transformed using a square-root transformation?
A)2,5,5,10
B)1,2.5,2.5,4
C)1,2,3,4
D)1.5,2,3.5,4

Accepted Answer

The square-root transformation of a number is obtained by taking the square root of each number. Thus, the square roots of 4, 25, 25, and 100 are 2, 5, 5, and 10, respectively.

Question 7

A common transformation procedure when scores are positively skewed is the
A)square-root transformation.
B)squared transformation.
C)exponential transformation.
D)sign-reversal transformation.

Accepted Answer

The square-root transformation is the best choice for positively skewed data as it reduces the skewness while preserving the order of the values. Other transformations like squared or exponential may increase the skewness and sign-reversal would not be appropriate for skewed data.

Question 8

In general,the t test and the analysis of variance are
A)dependent on five basic assumptions.
B)free of assumptions.
C)sensitive to violations of assumptions.
D)robust to violations of assumptions.

Accepted Answer

The answer of In general,the t test and the analysis...

Question 9

One indication that a population is not normally distributed is when
A)a small sample drawn from the population is positively skewed.
B)two variables are measured at the same time.
C)a scale or index is used for the measured variable.
D)a ceiling or floor effect is present in a large sample.

Accepted Answer

A ceiling or floor effect in a large sample suggests that many data points are clustered at the high or low end, indicating a lack of normal distribution.

Question 10

Data transformations are legitimate
A)because no information is lost or distorted.
B)when performed post hoc.
C)because the order of scores is not altered.
D)when they favor a researcher's hypothesis.

Accepted Answer

Data transformations are legitimate when they only change the scale of measurement or distribution without altering the order of scores. This type of transformation can help make data more interpretable or easier to work with without losing or distorting information. However, if transformations are made based on a researcher's desired outcome (such as favoring a particular hypothesis) or if they result in the loss or distortion of information, they are not considered legitimate. Transformation should ideally be planned and justified before the data is collected rather than performed post hoc.

Question 11

Which transformation has the strongest influence on a positively skewed distribution?
A)square-root
B)log
C)inverse
D)reflection

Accepted Answer

The answer of Which transformation has the strongest influence on...

Question 12

Which of the following represents the correct scores if 1,4,25,and 81 are transformed using the rank-order method?
A)1,2,5,9
B)1,4,25,81
C)4,4,25,25
D)1,2,3,4

Accepted Answer

The rank-order method assigns ranks to data based on their order, starting with the smallest value. In this case, 1 is the smallest, so it gets a rank of 1; 4 is next, so it gets a rank of 2; 25 follows, with a rank of 3; and 81 is the largest, receiving a rank of 4.

Question 13

Prior to using a procedure that is "distribution-free," the sample scores would probably be transformed using the
A)reflection method.
B)antilog method.
C)rank-order method.
D)inverse method.

Accepted Answer

The rank-order method is often used for distribution-free procedures because it does not rely on assumptions about the shape or parameters of the population distribution. The other methods listed (reflection, antilog, and inverse) are specific mathematical transformations that may be used for certain types of data distributions or statistical analyses, but they are not necessarily appropriate or necessary for all situations.

Question 14

When the assumption of a normal curve is seriously violated,the ordinary t test
A)resembles an analysis of variance.
B)is conducted using √t instead of t.
C)gives an incorrect result.
D)is robust.

Accepted Answer

When the assumption of a normal curve is seriously violated, the ordinary t test may give incorrect results. This is because the t test relies on the assumption of normality for the sampling distribution of the means, and if this assumption is not met, the t distribution may not accurately reflect the true distribution of the sample means. Therefore, it is important to use alternative non-parametric tests or to transform the data if the normality assumption is seriously violated.

Question 15

When a distribution is negatively skewed,which of the following transformations should be performed first?
A)square-root
B)log
C)inverse
D)reflection

Accepted Answer

Reflection is typically performed first to convert a negatively skewed distribution into a positively skewed one, making it easier to apply other transformations like log or square-root.

Question 16

A widely used procedure when the sample's scores do not appear to come from a normal population is to
A)duplicate scores which will make the sample more normal.
B)sample only members of the population who will make the sample normal.
C)transform the sample scores.
D)delete the scores that make the distribution nonnormal if the results are not significant.

Accepted Answer

Transforming the sample scores can make the distribution more normal, allowing for the use of parametric statistical tests that assume normality. Duplicating scores or limiting the sample to only those who fit normality assumptions is not a valid method for addressing non-normality. Deleting scores that make the distribution non-normal is generally not recommended, as it can lead to biased or misleading results.

Question 17

A sample drawn from a normally distributed population
A)might have more members than the population.
B)is sometimes approximately normally distributed.
C)is always approximately normally distributed.
D)is never approximately normally distributed.

Accepted Answer

The sample drawn from a normally distributed population is sometimes approximately normally distributed. This is because the central limit theorem states that the distribution of sample means approaches a normal distribution regardless of the shape of the population distribution, as long as the sample size is sufficiently large (typically at least 30). Therefore, even if the population distribution is not normally distributed, the sample means can still be normally distributed, making the sample approximately normally distributed. However, this is not always the case and depends on the sample size and the underlying population distribution.

Question 18

Having discovered an extreme score in a sample of scores,the first thing to do is to
A)discard the score.
B)make sure the score was not recorded in error.
C)perform a log transformation.
D)perform an inverse transformation.

Accepted Answer

Before discarding the extreme score, it is necessary to verify whether it was recorded in error or not. It is possible that the score was a result of a mistake in recording or entering the data. Therefore, conducting a check on the extreme score is important to ensure it is not a data entry error or mistake.

Question 19

A distribution of rank-ordered scores will always be
A)a normal curve.
B)bimodal.
C)rectangular.
D)skewed.

Accepted Answer

The answer of A distribution of rank-ordered scores will always...

Question 20

The first step in considering a data transformation is to
A)examine the transformed sample distribution.
B)apply the most appropriate transformation.
C)examine the sample data to determine the shape of the distribution.
D)conduct Cochran's Test for Nonnormality.

Accepted Answer

Before applying any transformation, it is important to examine the sample data to determine the shape of the distribution. This will help in selecting the appropriate transformation.

Quiz 14: Strategies When Population Distributions Are Not Normal: Data Transformations and Rank-Order Tests

When conducting a statistical test,a single outlier can

In a square-root transformation,

Which of the following represents the correct scores if 4,25,25,and 100 are transformed using the rank-order method?

Which of the following represents the correct scores if 1,4,25,and 81 are transformed using a square-root transformation?

Assumptions for statistical procedures are about

Which of the following represents the correct scores if 4,25,25,and 100 are transformed using a square-root transformation?

A common transformation procedure when scores are positively skewed is the

In general,the t test and the analysis of variance are

One indication that a population is not normally distributed is when

Data transformations are legitimate

Which transformation has the strongest influence on a positively skewed distribution?

Which of the following represents the correct scores if 1,4,25,and 81 are transformed using the rank-order method?

Prior to using a procedure that is "distribution-free," the sample scores would probably be transformed using the

When the assumption of a normal curve is seriously violated,the ordinary t test

When a distribution is negatively skewed,which of the following transformations should be performed first?

A widely used procedure when the sample's scores do not appear to come from a normal population is to

A sample drawn from a normally distributed population

Having discovered an extreme score in a sample of scores,the first thing to do is to

A distribution of rank-ordered scores will always be

The first step in considering a data transformation is to