After studying Chapter 12, you should know and understand the following key points:

1. The Analysis Story

   When data analysis is completed, we must construct a coherent narrative that explains our findings, counters opposing interpretations, and justifies our conclusions.

2. Computer-Assisted Data Analysis

   Researchers typically use computers to carry out the statistical analysis of data. Carrying out statistical analyses using computer software requires that the researcher must have a good knowledge of research design and statistics.

3. Illustration: Data Analysis for an Experiment Comparing Means

   1. Stage 1: Getting to Know the Data

      We begin data analysis by examining the general features of the data and edit or "clean" the data as necessary. It is important to check carefully for errors such as missing or impossible values (e.g., numbers outside the range of a given scale), as well as outliers.

      A stem-and-leaf display is particularly useful for visualizing the general features of a data set and for detecting outliers.

      Data can be effectively summarized numerically, pictorially, or verbally; good descriptions of data frequently use all three modes.

   2. Stage 2: Summarizing the Data

      Measures of central tendency include the mean, median, and mode.

      Important measures of dispersion or variability are the range and standard deviation.

      The standard error of the mean is the standard deviation of the theoretical sampling distribution of means and is a measure of how well we have estimated the population mean.

      Effect size measures are important because they provide information about the strength of the relationship between the independent variable and the dependent variable that is independent of sample size.

      An important effect size measure when comparing two means is Cohen's d.

      An important effect size measure when comparing more than two means is eta squared.

   3. Stage 3: Using Confidence Intervals to Confirm What the Data Tell Us

      An important approach to confirming what the data are telling us is to construct confidence intervals for the population parameter, such as a mean or difference between two means.

4. ILLUSTRATION: DATA ANALYSIS FOR A CORRELATIONAL STUDY

   A correlation exists when two different measures of the same people, events, or things vary together - that is, when scores on one variable covary with scores on another variable.

   1. Stage 2: Summarizing the Data

      The major descriptive techniques for correlational data are the construction of a scatterplot and the calculation of a correlation coefficient.

      The magnitude or degree of correlation is seen in a scatterplot by determining how well the points correspond to a straight line; stronger correlations more clearly resemble a straight line (linear trend) of points.

      The magnitude of a correlation coefficient ranges from -1.0 (a perfect negative relationship) to +1.0 (a perfect positive relationship); a correlation coefficient of 0.0 indicates no relationship.

      When two variables are related (correlated), we can make predictions for the variables; however, we may not make causal statements regarding the relationship solely on the basis of correlational evidence.

      When a relationship between two variables can be explained by a third variable, the relationship is said to be spurious.

   2. Stage 3: Constructing a Confidence Interval for a Correlation

      We can obtain a confidence interval estimate of the population correlation, c, just as we did for the population mean, m.