Chapter 16 Summary

Understand the mean, median, and mode as measures of central tendency.

The mean is the most commonly used measure of central tendency and describes the arithmetic average of the values in a sample data. The median represents the middle value of an ordered set of values. The mode is the most frequently occurring value in a distribution of values. All these measures describe the center of the distribution of a set of values.

Understand the range and standard deviation of a frequency distribution as measures of dispersion.

The range defines the spread of the data. It is the distance between the smallest and largest values of the distribution. The standard deviation describes the average distance of the distribution values from the mean. A large standard deviation indicates a distribution in which the individual values are spread out and are relatively farther away from the mean.

Understand how to graph measures of central tendency.

Distributions of numbers can be illustrated by several different types of graphs. Histograms and bar charts display data in either horizontal or vertical bars. Line charts are good choices for communicating trends in data, while pie charts are well suited for illustrating relative proportions.

Understand the difference between independent and related samples.

In independent samples the respondents come from different populations, so their answers to the survey questions do not affect each other. In related samples, the same respondent answers several questions, so comparing answers to these questions requires the use of a paired-samples t-text. Questions about mean differences in independent samples can be answered by using a student t-test statistic.

Explain hypothesis testing and assess potential error in its use.

A hypothesis is an empirically testable though yet unproven statement about a set of data. Hypotheses allow the researcher to make comparisons between two groups of respondents and to determine whether there are important differences between the groups. Hypothesis tests have two types of error connected with their use. The first type of error (Type I error) is the risk of rejecting the null hypotheses on the basis of your sample data when it is, in fact, true for the population from which the sample data was selected. The second type of error (Type II error) is the risk of not detecting a false null hypothesis. The level of statistical significance (alpha) associated with a statistical test is the probability of making a Type I error.

Understand univariate and bivariate statistical tests.

T statistics are the tests of mean values that should be used when the sample size is small (less than 30) and the standard deviation of the population is unknown; z-tests are statistical tests of mean values best used when sample sizes are above 30 and the standard deviation of the population is known. Both tests involve the use of the sample mean, a t or z value selected from the respective distribution, and the standard deviation of either the sample or population. Tests of the differences between two groups require the use of t-tests for small samples (less than 30) and unknown population standard deviations. For larger samples and known population standard deviations, the z-test is used.

Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods.

ANOVA is used to determine the statistical significance of the difference between two or more means. The ANOVA technique calculates the variance of the values between groups of respondents and compares it to the variance of the responses within the groups. If the between-group variance is significantly greater than the within-group variance as indicated by the F-ration, the means are significantly different. The statistical significance between means in ANOVA is detected through the use of a follow-up test. The test examines the differences between all possible pairs of sample means against a high and low confidence range. If the difference between a pair of means falls outside the confidence interval, then the means can be considered statistically different.