# Computing Frequencies and Cross-Tabulation

Describe the procedure for computing frequencies. Frequencies are commonly used for the initial analysis of a data set. Frequencies provide statistics and graphical displays that are useful for describing all different types of variables. The Frequencies procedure can produce such statistics as: frequencies (counts), percentages, cumulative percentages, mean, median, mode, sum, standard deviation, variance, range, minimum and maximum values, standard error of the mean, keenness and kurtosis (both with standard errors), quartiles and percentiles.
It can also produce bar charts, pie charts, and histograms. Basic data analysis provides valuable insights and guides the rest of the data analysis as well as the interpretation of the results. A frequency distribution should be obtained for each variable in the data. The variability of the distribution is described by the range and the variance or standard deviation. The general procedure for hypothesis testing involves eight steps.
Formulate the null and the alternative hypotheses, select an appropriate test statistic, choose the level of significance (a), calculate the value of the test statistic, and determine the probability associated with the test statistic calculated from the sample data under the null hypothesis. Alternatively, determine the critical value associated with the test statistic. Compare the probability associated with the test statistic with the level of significance specified or, alternatively, determine whether the calculated value of the test statistic falls into the ejection or the imperfection region.

Accordingly, make the decision to reject or not reject the null hypothesis, and arrive at a conclusion.
What is the major difference between cross-tabulation and frequency distribution? Cross-tabulation is a statistical technique that describes two or more variables simultaneously and results in tables that reflect the Joint distribution of two or more variables that have a limited number of categories or distinct values.
Frequency distribution is a mathematical distribution with the objective of obtaining a count of he number of responses associated with different values of one variable and to express these counts in percentage terms. The major difference between the two is that a frequency distribution describes one variable at a time, while cross-tabulations describe two or more variables simultaneously.
What is the general rule for computing percentages in cross-tabulation? The general rule is to compute the percentages in the direction of the independent variable, across the dependent variable.

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