16.4 APPENDIX REVIEW: Statistics: Understanding Data

KEY POINTS

• Statistics is a branch of mathematics that researchers use to organize and interpret data.

• Descriptive statistics are summaries of data that make the data meaningful and easy to understand. One descriptive statistic is a frequency distribution, which can be presented in the form of a table, a histogram, or a frequency polygon. Some frequency distributions are positively skewed; that is, most of the scores in the distribution pile up at the low end. Distributions that are negatively skewed have mostly high scores. Symmetrical distributions have equal numbers of scores on both sides of the distribution’s midpoint.

• The mode, the median, and the mean are measures of central tendency of a distribution. The mode is the most frequent score. The median is the middle score in the distribution. The mean is the arithmetic average. To calculate the mean, scores are summed and divided by the total number of scores. The mean is usually the best overall representation of central tendency, but it is strongly influenced by extremely high or extremely low scores.

• The range and standard deviation are measures of variability or spread of a distribution. The range is the highest score in the distribution minus the lowest score. The standard deviation is the square root of the average of the squared deviations from the mean.

• A z score expresses a single score’s deviation from the mean of a distribution in standard deviation units.

• The standard normal curve is a symmetrical distribution forming a bell-shaped curve in which the mean, median, and mode are all equal and fall in the exact middle. The percentage of cases that fall between any two points on the normal curve is known. Over 95 percent of the cases fall between two standard deviations above the mean and two standard deviations below the mean.

• Correlation refers to the relationship between two variables. A correlation coefficient is a number that indicates the magnitude and direction of such a relationship. A correlation coefficient may range from -1 to +1. The closer the value is to -1 or +1, the stronger the relationship is. Correlations close to 0 indicate no relationship. A positive correlation coefficient tells us that as one variable increases in size, the second variable also increases. A negative correlation coefficient indicates that as one variable increases in size, the second variable decreases. A correlation relationship may be presented visually in a scatter diagram or scatter plot.

• Correlations enable us to predict the value of one variable from knowledge of another variable’s value. However, a correlational relationship is not necessarily a causal relationship.

• Inferential statistics are used to determine whether the outcomes of a study can be legitimately generalized to a larger population. A population is a complete set of something. A sample is a subset of a population. One technique is a t-test, which is used to compare the means of two groups.

• Inferential statistics provide information about the probability of a particular result if only chance or random factors are operating. If this probability is small, the findings are said to be statistically significant; that is, they are probably due to the researcher’s interventions. Researchers must avoid making decision errors. Erroneously concluding that study results are significant is a Type I error. Failing to find a significant effect that does, in fact, exist is a Type II error.

KEY TERMS