In Chapter 1, we introduced the two main branches of statistics—
We informally develop and test hypotheses all the time. I hypothesize that the traffic will be heavy on Western Avenue, so I take a parallel street to work and keep looking down each block to see if my hypothesis is being supported. In a science blog, Tierney-
Let’s put this study in the language of sampling and probability. The sample was comprised of people living in the Park Slope neighborhood of Brooklyn in New York City, an area that Tierney terms “nutritionally correct” because of the abundance of organic food in local stores. The population would include all the residents of Park Slope who could have been part of this study. The driving concern behind this research was the increasing levels of obesity across the United States (something that Tierney explored in a follow-
5.5: Many experiments have an experimental group in which participants receive the treatment or intervention of interest, and a control group in which participants do not receive the treatment or intervention of interest. Aside from the intervention with the experimental group, the two groups are treated identically.
A control group is a level of the independent variable that does not receive the treatment of interest in a study. It is designed to match an experimental group in all ways but the experimental manipulation itself.
An experimental group is a level of the independent variable that receives the treatment or intervention of interest in an experiment.
The group that viewed the photo without the healthy crackers is the control group, a level of the independent variable that does not receive the treatment of interest in a study. It is designed to match the experimental group—a level of the independent variable that receives the treatment or intervention of interest—in all ways but the experimental manipulation itself. In this example, the experimental group would be those viewing the photo that included the healthy crackers.
The null hypothesis is a statement that postulates that there is no difference between populations or that the difference is in a direction opposite of that anticipated by the researcher.
The next step is the development of the hypotheses to be tested. Ideally, this is done before the data from the sample are actually collected; you will see this pattern of developing hypotheses and then collecting data repeated throughout this book. When we calculate inferential statistics, we’re actually comparing two hypotheses. One is the null hypothesis—a statement that postulates that there is no difference between populations or that the difference is in a direction opposite to that anticipated by the researcher. In most circumstances, we can think of the null hypothesis as the boring hypothesis because it proposes that nothing will happen. In the healthy food study, the null hypothesis is that the average (mean) calorie estimate is the same for both populations, which are comprised of all the people in Park Slope who either view or do not view the photo with the healthy crackers.
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The research hypothesis is a statement that postulates that there is a difference between populations or sometimes, more specifically, that there is a difference in a certain direction, positive or negative; also called an alternative hypothesis.
In contrast to the null hypothesis, the research hypothesis is usually the exciting hypothesis. The research hypothesis (also called the alternative hypothesis) is a statement that postulates a difference between populations. Sometimes the research hypothesis is even more exciting (!) because it postulates that the difference between these two populations will be in a specific direction. In the healthy food study, the research hypothesis would be that, on average, the calorie estimate is different for those viewing the photo with the healthy crackers than for those viewing the photo without the healthy crackers. It also could specify a direction—
We formulate the null hypothesis and research hypothesis to set them up against each other. We use statistics to determine the probability that there is a large enough difference between the means of the samples that we can conclude there’s likely a difference between the means of the underlying populations. So, probability plays into the decision we make about the hypotheses.
5.6: Hypothesis testing allows us to examine two competing hypotheses. The first, the null hypothesis, posits that there is no difference between populations or that any difference is in the opposite direction from what is predicted. The second, the research hypothesis, posits that there is a difference between populations (or that the difference between populations is in a predicted direction—
When we make a conclusion at the end of a study, the data lead us to conclude one of two things:
We always begin our reasoning about the outcome of an experiment by reminding ourselves that we are testing the (boring) null hypothesis. In terms of the healthy food study, the null hypothesis is that there is no mean difference between groups. In hypothesis testing, we determine the probability that we would see a difference between the means of the samples, given that there is no actual difference between the underlying population means.
After we analyze the data, we are able to do one of two things:
Let’s take the first possible conclusion, to reject the null hypothesis. If the group that viewed the photo that included the healthy crackers has a mean calorie estimate that is a good deal higher (or lower) than the control group’s mean calorie estimate, then we might be tempted to say that we accept the research hypothesis that there is such a mean difference in the populations—
The second possible conclusion is failing to reject the null hypothesis. There’s a very good reason for thinking about this in terms of failing to reject the null hypothesis rather than accepting the null hypothesis. Let’s say there’s a small mean difference, and we conclude that we cannot reject the null hypothesis (remember, rejecting the null hypothesis is what you want to do!). We determine that it’s just not likely enough—
The way we decide whether to reject the null hypothesis is based directly on probability. We calculate the probability that the data would produce a difference between means this large and in a sample of this size if there was nothing going on.
We will be giving you many more opportunities to get comfortable with the logic of formal hypothesis testing before we start applying numbers to it, but here are three easy rules and a table (Table 5-2) that will help keep you on track.
Hypothesis | Decision | |
---|---|---|
Null hypothesis | No change or difference | Fail to reject the null hypothesis (if research hypothesis is not supported) |
Research hypothesis | Change or difference | Reject the null hypothesis (if research hypothesis is supported) |
Hypothesis testing is exciting when you care about the results. You may wonder what happened in Tierney’s study. Well, people who saw the photo with just the salad and the Pepsi estimated, on average, that the 934-
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Reviewing the Concepts
Clarifying the Concepts
Calculating the Statistics
Applying the Concepts
Solutions to these Check Your Learning questions can be found in Appendix D.