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.

Nominal data is best represented by a bar chart. Nominal data can be variables such as religion. This is because there is no inherent rank. No one religion is statistically “better” than the other; therefore, it would be impossible to place one higher up than another in a rank order scheme.

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.

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.

The distance that any point is from the mean is known as the standard deviation. When looking at a normal distribution, the mean is the middle or arithmetic average of the set and the deviation measures the spread of the data points from this central tendency.

Ordinal data is used when variables that have an inherent natural order, such as the collegiate class structure: freshman, sophomore, junior, senior. One must complete every level in order to transcend to the next. Nominal data deals with variables such as religion that do not have an inherent natural order. Interval data deals with things like temperature. Last, ratio data would deal with things like time.

A regression analysis, so long as all but one independent variable at a time can be held fixed, is able to produce a predictive window called a conditional expectation that allows for prediction of dependent variable values given set independent variable levels.

A correlational study looks at the relationship between two or more variables. For example, the relationship between test scores in math and history classes. It does not try to find a cause and effect between the variables, and the researcher does not manipulate the variables. The researcher is simply trying to see if they possess a relationship or correlation.

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.

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.