Question 1

A z-score shows how many standard deviation intervals a value falls above or below the mean.

Accepted Answer

This is the definition of a z-score.

Question 2

When comparing the effect sizes of different studies "stronger" always means "better" or "best," regardless of the nature of the different dependent variables in the different studies.

Accepted Answer

The nature of the dependent variables in the different studies can vary greatly, and therefore, it is not accurate to assume that a stronger effect size always means a better or best result. The strength of an effect size should be evaluated within the context of each individual study and its specific dependent variables.

Question 3

A percentile is the percentage of the normal distribution exceeded by a particular value.

Accepted Answer

This is correct. A percentile can also be thought of as the proportion of the population below a certain value. For example, if a score is at the 70th percentile, it means that 70% of scores in the population are below that score. Percentiles are commonly used in fields such as education and healthcare to compare individuals' performance or measurements to the rest of the population.

Question 4

If the z-score is minus 0.50, the percentile is:
A)69.15
B)30.85
C)50.00
D)25.00

Accepted Answer

A z-score of -0.50 corresponds to a percentile of approximately 30.85%, as found in a standard normal distribution table or calculator.

Question 5

Z-scores enable us to compare outcomes of evaluations that use very different outcome measures.

Accepted Answer

Z-scores standardize scores by converting them to units of standard deviation, allowing for comparisons across different measures.

Question 6

Given the following values, the z-score is: Raw score = 55
Mean = 50
Standard deviation = 5
A)+ 1.0
B)+ 5.0
C)+ .10
D)- 1.0

Accepted Answer

To calculate the z-score, we use the formula:
z = (x - μ) / σ
where x is the raw score, μ is the mean, and σ is the standard deviation.

Plugging in the values given:
z = (55 - 50) / 5
z = 1

Since the z-score is positive (+1.0), the answer is A) +1.0.

Question 7

Given the following values, the percentile is: Raw score = 30
Mean = 30
Standard deviation = 5
A)30
B)50
C)0
D)5

Accepted Answer

To find the percentile, we need to find the z-score first using the formula z = (raw score - mean) / standard deviation. In this case, z = (30 - 30) / 5 = 0. A z-score of 0 corresponds to the 50th percentile, which means that the raw score of 30 is at the 50th percentile.

Question 8

Given the following values for an undesirable outcome variable such as number of incidents of verbal abuse, the Cohen's d effect size is: Experimental group mean = 5
Control group mean = 8
Standard deviation = 2
A)+ 3.0
B)- 3.0
C)+ 1.5
D)- 1.5

Accepted Answer

Cohen's d is calculated as the difference between two means divided by the standard deviation. Here, it is (5 - 8) / 2 = -3 / 2 = -1.5, which is option D, but since only the magnitude is considered for Cohen's d, +1.5 is the correct representation.

Question 9

Given the following values for a desirable outcome variable such as self-esteem, the Cohen's d effect size is: Experimental group mean = 70
Control group mean = 60
Standard deviation = 20
A)+ 10.0
B)- 10.0
C)+ 0.50
D)- 0.50

Accepted Answer

To calculate Cohen's d, we need to subtract the control group mean from the experimental group mean (70-60=10) and then divide by the standard deviation (10/20=0.5). A positive result indicates that the experimental group had higher scores (in this case, higher self-esteem) than the control group, and the effect size is moderate (0.5).

Question 10

If a z score has a minus sign in front of it, then it is undesirable.

Accepted Answer

This statement is false. A z score with a minus sign in front of it simply means that it is below the mean. Whether it is desirable or not depends on the context and the specific problem being analyzed.

Question 11

If the percent of the normal curve between the mean and the z-score is .34, then the percentile is .84.

Accepted Answer

This statement is true. If the percent of the normal curve between the mean and the z-score is .34, then the area to the left of the z-score is .5 - .34/2 = .08. Using a standard normal table or calculator, we can find that the z-score corresponding to the .08 percentile is approximately -1.05. Adding the standardized value of the mean (0) to this z-score gives us -1.05, which corresponds to the 15.87th percentile. Taking 1 - 0.1587 = 0.8413, or 84.13%, we can see that the statement's claim is true, within rounding error.

Question 12

If the z-score is 1.19, the percent of the area under the normal curve between the mean and the z-score is:
A)38.30
B)36.43
C)47.13
D)36.21

Accepted Answer

The area under the normal curve between the mean and a z-score of 1.19 is 38.30%.

Question 13

Suppose John scores 70 on self-esteem scale A, and Bill scores 50 on self-esteem scale B.Assuming that the higher the score, the more self-esteem, which of the following statements is NOT an appropriate conclusion about comparing the two boys' level of self-esteem.
A)John has more self-esteem
B)We don't know based on this information alone because the two scales are different.
C)We should subtract each scale's mean from each raw score and then divide by each scale's standard deviation.
D)If scale A had a mean of 60 and a standard deviation of 20, and if scale B had a mean of 80 and a standard deviation of 10, then Bill has more self-esteem.

Accepted Answer

Without knowing how the scales compare to each other (e.g., their means, standard deviations, or even if they measure the same construct in the same way), we cannot directly compare raw scores from different scales to conclude who has more self-esteem.

Question 14

After we calculate the absolute value for Cohen's d we insert a plus or minus sign according to whether the difference between the group means represents a desirable or undesirable effect.

Accepted Answer

This statement is true. The sign of Cohen's d indicates the direction of the effect size. If the difference between the groups represents a desirable effect (for example, a treatment that leads to improvement), the sign of Cohen's d is positive. If the difference represents an undesirable effect (for example, a harmful side effect of a medication), the sign of Cohen's d is negative.

Question 15

The Cohen's d effect size formula is simply a z-score formula, except that instead of comparing one case's score to the group mean in the numerator, it compares two group means in the numerator.

Accepted Answer

The statement is correct. The Cohen's d effect size formula compares two group means in the numerator, and the formula is similar to a z-score formula. The numerator is the difference between the means, and the denominator is the standard deviation of the pooled groups.

Quiz 9: Z-Scores, Percentiles and Effect Size

A z-score shows how many standard deviation intervals a value falls above or below the mean.

When comparing the effect sizes of different studies "stronger" always means "better" or "best," regardless of the nature of the different dependent variables in the different studies.

A percentile is the percentage of the normal distribution exceeded by a particular value.

If the z-score is minus 0.50, the percentile is:

Z-scores enable us to compare outcomes of evaluations that use very different outcome measures.

Given the following values, the z-score is: Raw score = 55 Mean = 50 Standard deviation = 5

Given the following values, the percentile is: Raw score = 30 Mean = 30 Standard deviation = 5

Given the following values for an undesirable outcome variable such as number of incidents of verbal abuse, the Cohen's d effect size is: Experimental group mean = 5 Control group mean = 8 Standard deviation = 2

Given the following values for a desirable outcome variable such as self-esteem, the Cohen's d effect size is: Experimental group mean = 70 Control group mean = 60 Standard deviation = 20

If a z score has a minus sign in front of it, then it is undesirable.

If the percent of the normal curve between the mean and the z-score is .34, then the percentile is .84.

If the z-score is 1.19, the percent of the area under the normal curve between the mean and the z-score is:

Suppose John scores 70 on self-esteem scale A, and Bill scores 50 on self-esteem scale B.Assuming that the higher the score, the more self-esteem, which of the following statements is NOT an appropriate conclusion about comparing the two boys' level of self-esteem.

After we calculate the absolute value for Cohen's d we insert a plus or minus sign according to whether the difference between the group means represents a desirable or undesirable effect.

The Cohen's d effect size formula is simply a z-score formula, except that instead of comparing one case's score to the group mean in the numerator, it compares two group means in the numerator.