pel4e_app4

Appendix A Statistical Reasoning in Everyday Life

Describing Data

A-1 How do we describe data using three measures of central tendency, and what is the relative usefulness of the two measures of variation?

Researchers may use descriptive statistics to meaningfully organize the data they’ve gathered.
A measure of central tendency is a single score that represents a whole set of scores. Three such measures are the mode (the most frequently occurring score), the mean (the arithmetic average), and the median (the middle score in a group of data).
Measures of variation tell us how diverse the data are. Two measures of variation are the range (which describes the gap between the highest and lowest scores) and the standard deviation (which states how much scores vary around the mean, or average, score). The standard deviation uses information from each score, so it is especially useful for showing whether scores are packed together or dispersed.
Scores often form a normal (or bell-shaped) curve.

A-2 What does it mean when we say two things are correlated?

When we say two things are correlated, we are saying that they accompany each other in their movements. The strength of their relationship is expressed as a correlation coefficient, which ranges from +1.00 (a perfect positive correlation) through 0 (no correlation) to –1.00 (a perfect negative correlation).
Their relationship may be displayed in a scatterplot, in which each dot represents a value for the two variables.
Correlations predict but cannot explain.

A-3 What is regression toward the mean?

Regression toward the mean is the tendency for extreme or unusual scores to fall back toward their average.

A-4 How do we know whether an observed difference can be generalized to other populations?

Researchers use inferential statistics to help determine the reliability and significance of a study finding.
To feel confident about generalizing an observed difference to other populations, we would want to know that the sample studied was representative of the larger population being studied; that the observations, on average, had low variability; that the sample consisted of more than a few cases; and that the observed difference was statistically significant.

A-5 What are cross-sectional studies and longitudinal studies, and why is it important to know which method was used?

In a cross-sectional study, people of different ages are compared. In a longitudinal study, a group of people is studied periodically over a long period of time.
To draw meaningful conclusions about a study’s results, we need to know whether the study used a representative sample to draw its conclusions. Studies of intelligence and aging, for example, have drawn different conclusions depending on whether a cross-sectional or longitudinal study was used.