The “standard deviation” is a measure of variability, or spread of scores. This measure is calculated by subtracting each score from the mean, squaring the result, dividing this result by the total number of scores, and finally taking the square root of the last calculation. The “range” is also a measure of variability but its calculation involves subtracting the highest and lowest scores; therefore, it is not an average. The mean, median, and mode are measures of central tendency. The “mean” is the average of all scores. The “median” is the middle score, or average of the two middle scores. Last, the “mode” is the score that occurs most frequently.

In a negatively skewed distribution, the tail of the distribution falls on the left or negative side of the distribution. The mode is always the highest score, followed by the median, and lastly the mean. The opposite is true for a positively skewed distribution. In a normal distribution, the mean, median, and mode are all equal. 

The exam had a mean of  and a standard deviation of . Karen received a raw score of , which is  points above the mean. In order to calculate her Z-score you must use the Z-score formula:

Karen's Z score is +2. 

You would also be able to guess the correct answer by drawing a picture of a normal curve. You can then see that Karen's score is above the mean, which tells you that her Z-score must be positive.

In order to determine the answer to this question you must have knowledge of T-scores, standard scores, and Z-scores. T-scores always have a mean of 50 and a standard deviation of 10. Carla had a T-score of 65, which is 1.5 standard deviations above the mean, and is equivalent to a Z-score of 1.5. Bob received a Z score of 1.25, which is lower than Carla's Z-score. Standard scores always have a mean of 100 and a standard deviation of 15. Jimmy received a standard score of 85, which is one standard deviation below the mean and equal to a Z-score of -1. Carla had the highest Z-score. 

"Type II error" involves failing to reject a null hypothesis when it is false. This occurs when a researcher says that the findings are not significant, when in fact they are. "Type I error" is the opposite, and involves rejecting the null hypothesis when it is true. "Power" is the likelihood of rejecting the null when it is false, and is desirable in a research study. Last, "clinical significance" is similar to power and is what researchers aim for. It is important to note that "type III error" is not a term used in statistics. 

The mode is the number that occurs most often in the data set. In this case the mode is:

A z-score represents the distance away from the mean for a particular score, expressed in terms of standard deviations. Thus, a z-score of 0 is equal to the mean, and a z-score of 1.4 is equal to 1.4 standard deviations above a given mean.

When calculating the sum of squares (SS) as part of an ANOVA, each individual difference from the mean must be squared before summing. This makes intuitive sense when one realizes that the average of all scores which came together to make a mean in the first place must be that mean!

A two-way analysis of variance is the most appropriate tool for determining simultaneously the effects of two (or more) independent variables on a dependent variable and the strength of the interaction (if any) between the independent variables.

The df for each independent variable or factor is determined by how many different levels of that factor are included in the analysis. This can create a problem for calculating sums of squares and ultimately for calculating post hoc analyses, as the number of levels in a factor can be very large.