APPENDIX II
Statistics in Psychological Research

1. DESCRIBING DATA
   1. The Frequency Histogram
      Frequency histograms, graphic descriptions of data, are useful for visualizing and better understanding the "shape" of research data.
   2. Descriptive Statistics
      The numbers that summarize a pool of data are called descriptive statistics. The four basic categories measure the number of observations, summarize the typical value of the data set, summarize the variability of the data set, and express the correlations.
      1. N. The easiest statistic to compute is N, the number of observations in the data set.
      2. Measures of Central Tendency. Three statistical measures describe the typical value of a data set. The mode is the score that occurs most often in the data set. The median is the halfway point in the data set: half of the scores fall above the median, and half fall below it. The mean is the arithmetic average of all the scores in the data set.
      3. Measures of Variability. There are two statistical measures that indicate the dispersion of scores in a data set, or that measure variability. The range describes the distance between the highest score and the lowest score. The standard deviation measures the average difference between each score and the mean of the data set.
      4. The Normal Distribution. When most of the scores in a data set fall in the middle of a distribution that has few extreme scores, the data resemble a bell-shaped curve called the normal distribution. In this case, the mean, median, and mode all have the same value. The normal distribution is the basis for percentiles and standard scores. A percentile indicates the percentage of subjects or observations that fall below a given score. A standard score expresses distance in standard deviations from the mean.
      5. Correlation. The relationship between two variables is described by a correlation. The statistical measures that represent this relationship are called correlation coefficients.
2. INFERENTIAL STATISTICS
   Inferential statistics provide a measure of confidence or probability that conducting the same experiment again would yield similar results.
   1. Differences Between Means: The t Test
      The t test, a type of inferential statistic, assesses whether differences between two means occurred because of chance or because of the effect of an independent variable. Results that show a low probability of chance effects are statistically significant. Performing a t test requires using (a) the difference between the means, (b) the standard deviation, and (c) the number of observations or subjects. The researcher also takes the degrees of freedom and p value into account.
   2. Beyond the t Test
      Other statistical tests are used to analyze data from experiments that are more complex than comparisons between two groups. An analysis of variance analyzes the effects of more than one variable on a dependent variable.