##### Psychology Statistics For Dummies
You may be more interested in studying psychology than in crunching numbers, but knowing psychology statistics is essential if you’re going to make all that research data stack up, and have other people understand it. This Cheat Sheet helps you out with some basic concepts in psychology statistics.

## Determining the role of variables in psychology statistics

In psychology statistics, research studies which involve collecting quantitative data (any data that can be counted or rendered as numbers) usually require you to collect and store data on a data sheet about several variables.

When you conduct your statistical analyses on this data, you need to know what role each variable played in your research design. Generally speaking, you classify variables in psychology statistics as independent variables, dependent variables or covariates.

## Independent variables

Independent variables are sometimes referred to as predictor variables. Strictly speaking, an independent variable is a variable that you manipulate so that you can study how the changes in the independent variable influence changes in other variables.

In some cases, you refer to variables as independent variables even when you’re not directly manipulating them. This type of independent variable is a quasi-independent variable.

## Dependent variables

Dependent variables are sometimes referred to as outcome variables or criterion variables. A dependent variable is usually the variable that you expect to change when you manipulate the independent variable. In other words, the dependent variable is the variable that the independent variable affects. Therefore, the dependent variable is so called because its value depends on the value of the independent variable (at least in theory).

## Covariates

A covariate is a broad term used for a variable in a research design that’s neither an independent nor a dependent variable. In some designs you use a covariate to take account of other factors that might influence the relationship between the independent and dependent variable. A good research design measures these variables so that you can account for their influence. Within this research design, these variables are covariates. Covariates can also exist in research designs where no independent or dependent variables exist.

## Choosing between mode, median, and mean in psychology statistics

When putting together the psychology statistics you need to report when you’re describing a variable, you need to know which of the three measures of central tendency — the mode, median and mean — you should use. Take your cue from the advantages and disadvantages of each measure.

Weighing up the advantages and disadvantages of each measure leads you to the following conclusion: the most appropriate measure of central tendency for a variable depends on the level of measurement of the variable and the nature of the distribution of scores within that variable.

• Level of measurement: You need to distinguish between three levels of measurement (nominal, ordinal, and interval/ratio) when choosing a measure of central tendency.

• Distribution of scores: For the purposes of choosing a measure of central tendency, you need to know whether any extreme scores exist in your data set (often called outliers) or whether the distribution of scores is skewed. When you determine the level of measurement of your variable of interest and whether or not there is skewness and/or extreme scores in your data set then you can determine the most appropriate measure of central tendency, as follows:

• Data measured at the nominal level: Of the three measures of central tendency, the mode is the only appropriate one as the scores cannot be ordered from smallest to largest in a meaningful way.

• Data measured at the ordinal level: The mode and the median are appropriate. The median is usually preferable, because it’s more informative than the mode. The scores can be ordered from smallest to largest and this is meaningful, however they cannot be added up so the mean cannot be calculated.

• Data measured at the interval/ratio level: All three measures of central tendency are appropriate. The mean is usually preferable. However, the mean isn’t appropriate when extreme scores and/or skewness exist in your data set. In this situation the median is usually best.

## Choosing the right measure of dispersion in psychology statistics

The measures of dispersion you use in psychology statistics show you the spread or variability of the variable you are measuring. The three main ones are the range, the interquartile range, and the standard deviation.

## Getting to know the range, interquartile range, and standard deviation

The three most important measures of dispersion are defined as follows:

• The range is the difference between the highest score and the lowest score in a variable. These are the values that have been scored by participants in the study, and not necessarily the highest and lowest possible scores.

• The interquartile range is the difference between the upper quartile and the lower quartile in a set of ordered scores. Quartiles are formed by dividing a set of ordered scores into four equal-sized groups.

• The standard deviation (often abbreviated to Std. Dev. or SD) is the average deviation of scores in your data set from their mean score for a particular variable. The mean score is the average of scores on a variable. The standard deviation indicates the extent to which the scores on a variable deviate from the mean score.

## Working out which measure of dispersion to use

You determine the most appropriate measure of dispersion as follows, depending on the nature of your data:

• Data measured at the nominal level: Because all three measures of dispersion require data to be ranked or summed, none of them are appropriate for data measured at the nominal level.

• Data measured at the ordinal level: The range and interquartile range are appropriate. The interquartile range is usually preferable, as it is more informative than the range.

• Data measured at the interval/ratio level: All three measures of dispersion we have examined are appropriate. The standard deviation is usually preferable. However, the standard deviation (or variance) isn’t appropriate when there are extreme scores and/or skewness in your data set. In this situation the interquartile range is usually preferable.

## Looking at levels of measurement in psychology statistics

When working with psychology statistics you can classify variables according to their measurement properties. When you record variables on a data sheet, you usually record the values on the variables as numbers, because this makes statistical analysis easier. However, the numbers can have different measurement properties and these determine what types of analyses you can do with these numbers. The variable’s level of measurement is a classification system that tells you what measurement properties the values of a variable have.

The measurement properties that the values in a variable can possess are:

• Magnitude: This means that you can order the values in a variable from highest to lowest.

• Equal intervals: This means that a unit difference on the measurement scale is the same regardless of where that unit difference occurs on the scale.

• True absolute zero: The true absolute zero point means that the zero point on the measurement scale is the point where nothing of the variable exists and, therefore, no scores less than zero exist.

These three measurement properties enable you to classify the level of measurement of a variable into one of four types:

• Nominal: This means that a variable has none of the three measurement properties. You measure a variable at the nominal level when you’re using the numbers in the variable only as labels.

• Ordinal: If you measure a variable at the ordinal level then the values on the variable have the measurement property of magnitude only. You measure a variable at the ordinal level when the scores in the variable are ordered ranks.

• Interval: If you measure a variable at the interval level of measurement, it has the measurement properties of magnitude and equal intervals.

• Ratio: if you measure a variable at the ratio level of measurement, it has the measurement properties of magnitude, equal intervals and a true absolute zero.