Chapter 5: Testing Hypotheses About Two Independent Means

The previous chapters have addressed several issues about samples, means, and standard errors, with the intent to explain the data. The implication was that they are all useful but quite different from each other. In fact, you may get different answers if you use different samples. This chapter will explore these differences because the real question is, How much will they differ ? How can you decide whether a difference in sample means can be attributed to their natural variability or to a real difference between groups in the population?

OVERVIEW

At this point in the book, you can look at specific data and describe a sample. That is all you can do if you cannot understand the relationships between samples and populations. However, now you are ready to do more. You can look in the sample at the percentage of a response and relate that information back to the population. You know that you have one of many possible samples and that the chances are slim that the value calculated from the sample is identical to the population value. You can also calculate the standard error and use that number to calculate a 95% confidence or any other confidence you desire . Even though this calculation is possible, you never know if the particular interval you calculated contains the population value (it either does or it does not). However, you do know that the interval will include the population value 95 times out of 100 (or whatever the confidence).

If the confidence is narrow, that is a good indication because you want to pinpoint the population value as closely as possible. You do not know where within a confidence interval the population value might be. It is much more useful, then, to know that the 95% confidence interval is between a set of limits rather than outside of either side of the set. When you conduct a survey or experiment, look at both the mean and its confidence interval. If the interval is wide, you have only a very rough estimate of the population mean.