Scientists aim to accomplish two goals with their data. First, they want to organize and describe the data in meaningful ways. Second, they want to use the data to make inferences, or predictions, about a population of interest. To achieve the first goal, scientists rely on descriptive statistics. Descriptive statistics summarize a data set.Descriptive statistics most often involve a measure of central tendency, one value representing the entire set of values. The most commonly used measure of central tendency is the mean, commonly referred to as the average. The mean is calculated by adding all values in a data set and dividing the sum by the total number of values. With a set of five exam scores (67, 72, 72, 91, 77), the mean would be
Normal and Skewed Distributions
To make predictions about a population of interest, scientists use inferential statistics. Inferential statistics generalize conclusions from the sample to a larger population. Different types of inferential statistics serve different purposes. The correlation coefficient measures the relationship between variables. T-tests measure differences between groups. An analysis of variance measures interactions between one or more variables.
Confidence in making inferences is determined by statistical significance, which indicates the probability that an observed result occurred due to chance. As a general rule, a p-value (i.e., calculated probability) of 0.05 is the cutoff for a statistically significant result. A p-value of 0.05 represents 95% confidence the results are not due to error. However, just because a result is statistically significant does not mean it is practically significant. Practical significance indicates whether the result is useful in the real world. A measurement that can help determine practical significance is effect size. Effect size is a measure of the magnitude of a finding. For example, in a study where researchers gave caffeinated coffee to one group before an exam and decaffeinated coffee to another group, they found the caffeinated coffee group scored higher on the exam than the decaffeinated group with a p-value of 0.01. However, upon measuring the effect size, they found that the coffee group scored only 3 points higher on a test out of 100 points. Three additional points will not make a significant difference in people's final letter grade. The effect of caffeine on test scores was statistically significant but small.