A Detailed Look at Each of the Six Steps
Step 1: The Null Hypothesis
When engaged in hypothesis testing, a researcher begins by stating a null hypothesis.
If there is just one population involved in the study, the null hypothesis is a pinpoint statement as to the unknown quantitative value of the parameter in the population of interest. To illustrate what this kind of null hypothesis might look like, suppose that (1) we conduct a study in which our population contains all full-time students enrolled in a particular university, (2) our variable of interest is intelligence, and (3) our statistical focus is the mean IQ score. Given this situation, we could set up a null hypothesis to say that 100. This statement deals with a population parameter, it is pinpoint in nature, and we made it.
The symbol for null hypothesis is , and is usually followed by (1) a colon, (2) the parameter symbol that indicates the researcher’s statistical focus, (3) an equal sign, and (4) the pinpoint numerical value that the researcher has selected.
Accordingly, we specify the null hypothesis for our imaginary study by stating H0:
100.
If our study’s statistical focus involves something other than the mean, we must change the parameter’s symbol to make consistent with the study’s focus.
For example, if our imaginary study is concerned with the variance among students’
heights, the null hypothesis must contain the symbol rather than the symbol . Or, if we are concerned with the product–moment correlation between the students’
heights and weights, the symbol must appear in r H0.
m s2
H0 m
H0 m
With respect to the pinpoint numerical value that appears in the null hypoth-esis, researchers have the freedom to select any value that they wish to test. Thus, in our example dealing with the mean IQ of university students, the null hypothe-sis could be set up to say that , , , or any specific value of our choosing. Likewise, if our study focuses on the variance, we could set up , the null hypothesis, to say that 10 or that any other positive number of our choosing. And in a study having Pearson’s product–moment correla-tion coefficient as its statistical focus, the null hypothesis could be set up to say that or that or that or that any specific number be-tween and
The only statistical restrictions on the numerical value that appears in are that it (1) must lie somewhere on the continuum of possible values that correspond to the parameter and (2) cannot be fixed at the upper or lower limit of that contin-uum, presuming that the parameter has a lowest or highest possible value. These re-strictions rule out the following null hypotheses:
because the variance has a lower limit of 0 whereas Pearson’s product–moment cor-relation coefficient has limits of 1.00.
Excerpts 7.1 and 7.2 show how researchers sometimes talk about their null hypotheses. In the first of these excerpts, the statistical focus of the null hypothesis is the mean, as is made clear by the inclusion of the symbol . As you can see, there are two s in this null hypothesis, because there are two populations involved in this study, boys and girls. The symbol m,of course, corresponds to the mean score
m
EXCERPTS 7.1–7.2
• The Null Hypothesis
the null hypothesis [is] that the population mean of boys is equal to the population mean of the girls on valuing of reading.
Source: Sturtevant, E. G., & Kim, G. S. (2010). Literacy motivation and school/non-school literacies among students enrolled in a middle-school ESOL program. Literacy Research and Instruction, 49(1), 68–85.
To compare whether there is a significant correlation between age and the anthro-pometric dimensions of the Malaysian elderly, [we set up] the null-hypothesis (H0:
0). . . .
Source: Rosnah, M. Y., Mohd Rizal, H., & Sharifah-Norazizan, S. A. R. (2009). Anthropometry dimensions of older Malaysians: Comparison of age, gender and ethnicity. Asian Social Science, 5(6), 133–140.
r
H0:m1 - m2 = 0,
on some variable of interest. As indicated in the excerpt, the researchers wanted to compare the two groups in terms of how much they valued reading.
Previously, I indicated that every null hypothesis must contain a pinpoint nu-merical value. From what is stated in Excerpt 7.1, it is clear that the pinpoint num-ber in this excerpt’s is zero. This pinpoint number would still be in the null hypothesis (but slightly hidden from view) if the researchers had said . If two things are equal, there is no difference between them, and the notion of no difference is equivalent to saying that a zero difference exists.
Although researchers have the freedom to select any pinpoint number they wish for , a zero is often selected when the samples from two populations are being compared. When this is done, the null hypothesis becomes a statement that there is no difference between the populations. Because of the popularity of this kind of null hypothesis, people sometimes begin to think that a null hypothesis must be set up as a “no difference” statement. This is both unfortunate and wrong. When two populations are compared, the null hypothesis can be set up with any pinpoint value the researcher wishes to use. (For example, in comparing the mean height of men and women, we could set up a legitimate null hypothesis that stated inches.) When the hypothesis testing procedure is used with a single population, the notion of “no difference,” applied to parameters, simply does not make sense. How could there be a difference, zero or otherwise, when there is only one (or only one , or only one , etc.)?
Excerpt 7.2 contains a null hypothesis that involves a correlation. The symbol in this represents the Pearson product–moment correlation in the study’s pop-ulation. As you can see, is set equal to zero in this null hypothesis. Theoretically, the value of in could have been set equal to any pinpoint number, such as .20,
.55, or any other value between 1.00 and 1.00. However, it is almost always the case that researchers set equal to 0.00 in when using the hypothesis test-ing procedure in a correlational study.
In Excerpts 7.3 and 7.4, we see two additional null hypotheses. In the first of these excerpts, the null hypothesis stated that two percentages were equal.1Because of the wording in this excerpt, you might think that this stipulates that the percent-age of intangible outputs from the 10 members of the T work group is identical to
H0
1In Chapter 17, we consider in depth statistical tests that focus on percentages.
EXCERPTS 7.3–7.4
• Two Additional Null Hypotheses
This research utilized a set of subjects, 19 in total (ten from T-work group and nine from the WT-work group). . . . H0: Pwto Pto, this means the percentage of “intangible”
outputs by WT-work is equal to the percentage of “intangible” outputs by T-work.
Source: Waters, N. M., & Beruvides, M. G. (2009). An empirical study analyzing traditional work schemes versus work teams. Engineering Management Journal, 21(4), 36–43.
the percentage of such outputs from the 9 members of the WT work group. This is an incorrect conceptualization of this study’s , because the two percentages rep-resented in the null hypothesis refer to the population of people in T work groups and the population of people in WT work groups. Without exception, null hy-potheses always are focused on populations (and this is true for studies that focus on means, correlations, percentages, or anything else).
Excerpt 7.4 shows a null hypothesis that involves four population means. The s in this null hypothesis correspond to the means of the four populations repre-sented by the different kinds of families involved in this study. In the stated , is connected to families with a laissez-faire style of communication, is connected to families having a protective style of communication, and so on. The data of the study came from the parents in each of the four samples who were asked to indicate how much influence their adolescent children had on their (the parents’) decisions to purchase various items (e.g., cell phones, fast food, clothing).
Before we leave our discussion of the null hypothesis, it should be noted that does not always represent the researcher’s personal belief, or hunch, as to the true state of affairs in the population(s) of interest. In fact, the vast majority of null hypotheses are set up by researchers in such a way as to disagree with what they actually believe to be the case. We return to this point later in the chapter; for now, however, I want to alert you to the fact that the associated with any given study probably is not an ar-ticulation of the researcher’s personal belief concerning the involved population(s).