Using SAS to Analyze the Summary Data

Most of the time, we have the raw data to conduct the necessary statistical analysis in SAS®. However, when there is only summary data available, some additional SAS coding is necessary in order to perform the hypothesis test. SAS procedures, as well as simplified macros (%SUM_TTEST, %SUM_ANOVA, %P_ANOVA, %SUM_CHI) with examples, will be discussed in this paper for chi-square test, two sample t-test, and analysis of variance with summary data as input. INTRODUCTION Before initiating a new study, there is often extensive literature review to retrieve background information, compare existent findings, and support the significance of the study. Since most of the papers only present the summary statistics (sample sizes, means, standard deviations, percentages, etc.), it is very helpful if we have the right tools to generate other statistics in a quick and convenient way. For example, if means and standard deviations are known for two independent groups, it is always interesting to know whether there is statistical significant difference in the mean between the two groups. Similarly, if the number of events and sample size are known for two groups, the relative risk, odds ratio, or risk difference between those groups, could also be calculated. This paper discusses the concept of statistical analysis using the summary data and introduces a series of simplified macros for such analysis. ANALYSIS OF SUMMARY CONTINUOUS DATA The continuous variable is usually reported as sample size ( n ), mean (Y ) and standard deviation ( s ). If there are two or more groups of data, additional hypothesis tests of the existence of differences among groups are sometimes very helpful in understanding the background of the research field. The t and F statistics as well as their degree of freedom can be calculated from the sufficient summary statistics Y n, and s (Table 1 and 2); therefore always as to construct the hypothesis tests without the original individual level data. Table 1. Test Statistic for Independent Two Samples T-TEST Assumption t Statistic DF Equal Variance , 1 1