Variables and Hypotheses

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1 Variables and Hypotheses When asked what part of marketing research presents them with the most difficulty, marketing students often reply that the statistics do. Ask this same question of professional marketing researchers, and they ll be more likely to reply that figuring out how to address a project s research questions is far more difficult than statistical analysis; after all, computers handle most of that task. Hopefully, as you ve studied the material on decision problems and research questions, you ve developed some appreciation for the difficulty of this part of the research process. The fact is that the early stages of the marketing research process require much in the way of creative thinking and application of marketing problems to a research context. Done well, this kind of creativity poses a far more difficult task than statistical analyses. Indeed, successful researchers are not those who can competently crunch the numbers; the best researchers are those who can most effectively decide what numbers to crunch, and for what purpose. These Web Notes cover the part of the research process that transitions from the highly creative and somewhat unstructured steps into more structured and analytical steps. We begin this transition with what we ll refer to here as conceptual hypotheses. They will serve as the foundation for answering the research questions that flowed from the decision problem. Importantly, conceptual hypotheses also add depth and insight to answering the research questions. In addition to conceptual hypotheses, these Web Notes cover two other related topics: variables and statistical hypotheses. Together, variables, conceptual hypotheses, and statistical hypotheses help researchers and decision makers determine which research questions merit answering with data and then suggest the most appropriate means of doing so. Many marketing research texts overlook the fundamental contributions to sound research made by conceptual hypotheses. Simply put, conceptual hypotheses are educated guesses about the relationships between two or more variables. In other words, hypotheses reflect our best guesses about the how the world operates. Note that this definition characterizes conceptual hypotheses in terms of variables. Therefore, before we can learn how conceptual hypotheses enrich marketing research, we must examine variables what they are and their role in addressing decision problems and research questions. Variables in Marketing Research The Nature of Variables For some students, the word variable conjures up memories of the letter x from calculus or algebra classes. In those classes you learned that a variable is simply any concept that can take on different values. For example, height is a variable. Every object in the physical world has a height, which ranges from microscopic to enormous. Likewise, every object in the

2 Hypotheses and Variables page 2 physical world has an age, which, depending on the object, holds values ranging from billionths of a second to billions of years. Marketing researchers think of variables as any measurable characteristic or attribute of a person, place, or thing. For our purposes, the term measurable means that values can be assigned to the variable and that those values can be meaningfully recorded. For example, suppose a marketing researcher wishes to know the likelihood that members of a certain target market will purchase a new car in the next 12 months. To obtain the information, the researcher may include the following item on a questionnaire: How likely do you believe it is that you will purchase a new car in the coming twelve months? Very Very Unlikely Likely Exhibit 1. Perceptual Measure of Car Purchase Likelihood The variable measured by the item in Exhibit 1, which we ll call car purchase likelihood, can be assigned a value by research participants and that value can be meaningfully recorded on the scale by circling a number. In this way, nearly any product or customer characteristic or attribute would qualify as a variable and could be easily and reliably measured. To some, however, defining variables is not so simple because in their view variables must be observable in order to be measurable. Proponents of this view argue that one cannot truly measure what cannot be seen. Therefore, they say that a consumer s own perceptions of their likelihood of buying a new car should not be used in research because these perceptions cannot be seen, precisely estimated, and are not capable of independent verification. In short, perceptions are too fuzzy for good measurement and so do not qualify as variables. They would argue that a more scientifically acceptable measure of car purchase likelihood might look like the questionnaire items in Exhibit 2, where greater frequency of these behaviors could represent greater car buying likelihood. About how many times per month do you look at new cars on the lots of local dealerships (even after dealer hours)? none one or two three or four five or more About how many times per week do you look closely at auto dealership advertisements in your local newspaper? none one or three or five or two four more Exhibit 2. Behavioral Measure of Car Purchase Likelihood According to advocates of limiting variables to observable phenomena, the behaviors measured in Exhibit 2 can be observed, they can be accurately estimated, and they are capable of being independently verified. Thus, they should make good reliable variables. On the other hand, it could be the case that many people with little or no likelihood of actually buying a new car may still enjoy the process of looking. Thus, visiting dealerships or reading newspaper ads may not always reflect true car buying likelihood. So, who s right? Should variables be limited to observable concepts? There are no easy answers. Indeed, the issue of whether science can truly understand what cannot be seen cuts to the core of one of the longest running debates in the philosophy of science: How do we know we know? My view is that variables need not be observable to be measured. Indeed,

3 Hypotheses and Variables page 3 marketing researchers routinely measure unobservable variables. And not only do researchers measure unobservable variables, they do so accurately enough to predict observable marketplace behaviors reasonably well. So while the issue of observability is far from settled among philosophers of science, for our pragmatic purposes, we ll assume that unobservable variables can be reliably measured. Hypotheses in Marketing Research The preceding discussion of variables adds to our understanding of hypotheses because hypotheses predict relationships among or between variables. In the realm of marketing research, hypotheses serve two purposes. They permit researchers and decision makers to fully express their ideas about the world in which their products and brands are marketed, and they offer a framework for statistically testing those ideas. Given these two purposes, it s useful for us to distinguish between two types of hypotheses: conceptual hypotheses and statistical hypotheses. Conceptual Hypotheses Conceptual hypotheses predict theoretical relationships or differences between two or more variables. They are the educated guesses people make about relationships between and among variables. Conceptual hypotheses link together the research questions being posed by decision makers and marketing researchers with the data collection efforts that hopefully will answer the research questions. And, if done well, conceptual hypotheses provide an outline for the data analyses that follows data collection. How conceptual hypotheses relate to research questions. Recall from earlier Web Notes that research questions should be developed hierarchically. That is, general research questions can be broken apart into more specific or what we refer to as implied research questions, which can frequently be even further divided. This approach allows a more complete articulation of research questions that may be of interest to decision makers. Of course, just because a research question is asked does not automatically mean it s worth asking. Research questions framed to address a particular decision problem are not of equal value. Some research questions may seem to cut to the core of the decision problem while others may seem more tangential. In fact, if researchers and decision makers work well together, and the research team does an adequate job brainstorming, they should produce far more research questions than can be answered by a reasonably sized marketing research study. Therefore, researchers ordinarily discard many research questions, deeming them too unimportant for collecting the data needed to answer them. The problem facing researchers and decision makers at this juncture is deciding which research questions should be answered and which should be set aside. Conceptual hypotheses help enormously in this process by forcing the researcher to look at each question and figure out exactly why the question is being asked in the first place. Conceptual hypotheses provide a way for researchers to screen research questions and determine which are most important. Extended example. To illustrate how conceptual hypotheses assist in this process, let s work through an example. Suppose that a small chain of men s casual wear stores, which has been suffering from a steady decline in sales and in-store traffic, contacts a marketing research firm to investigate the situation. Their decision problem is straightforward; management needs to know how to change or reposition

4 Hypotheses and Variables page 4 their stores in order to rebuild traffic and sales After some discussion, the decision makers and researchers agree on a set of general research questions. The research team them develops a hierarchy of general and implied questions, two of which are shown in Exhibit 3. Exhibit 3. Hypothetical Research Questions General Question 1: What are the current shopping patterns among men who buy casual wear? Implied Questions: Do they ordinarily shop for men s casual wear at specialty stores or department stores? When and how frequently? How many times per year do they shop for clothes? What days of the week do they shop most frequently? How many items do they typically buy? How much do they usually spend on each shopping trip? General Question 2: What do men consider important when they select a men s casual wear store? Implied Questions: product lines? brand familiarity? brand prestige? number of product lines? price? How aware of prices are they? Do they wait for products to go on sale? service level? sales personnel? alterations? location? size of location distance of location from home or work? number of locations? Note that this hypothetical example contains only two general questions and a few implied questions for each. In reality, these numbers should be much higher. Assuming that a satisfactory amount of thought and brainstorming took place, each general question could conceivably produce one to two dozen implied questions. And if each of those questions were important enough to warrant answering with data, then at least one questionnaire item would be needed for every implied question, which could result in a questionnaire that contains hundreds of items. A questionnaire that long would likely produce poor response. Therefore, as they re developed, each implied question must be evaluated to see whether it actually is important enough to collect data. Each time an implied question is proposed, researchers must ask, Why is this important to know? Conceptual hypotheses provide possible answers to this question of why. Here s how they work. Look at Exhibit 3 and the first implied question under the first general question, Do they ordinarily shop for men s wear at specialty stores or department stores? The researchers must ask why this is important for the decision maker to know. One possible reason might be that on average, men who shop at specialty stores spend more money than those who ordinarily shop at department stores. Most decision makers for men s casual wear specialty stores would probably like to know whether the average purchase at their stores was larger than at department stores. That seems like a good reason for asking where men usually shop. By this reasoning, there appears to be justification for collecting data about where men shop for casual wear and how much money they typically spend per trip. The preceding discussion raises the important point that conceptual hypotheses provide the justification for keeping research questions and then developing questionnaire

5 Variables and Hypotheses page 5 Exhibit 4. Research Questions and Conceptual Hypotheses Research Questions General Question 1: What are the current shopping patterns among men who buy casual wear? Implied Questions: Do they ordinarily shop for men s casual wear at specialty stores or department stores? When and how frequently? How many times per year do they shop for clothes? What days of the week do they shop most frequently? How many items do they typically buy? How much do they usually spend on each shopping trip? General Question 2: What do men consider important when they select a men s casual wear store? Implied Questions: product lines? brand familiarity? brand prestige? number of product lines? price? How aware of prices are they? Do they wait for products to go on sale? service level? sales personnel? alterations? location? size of location distance of location from home or work? number of locations? Conceptual Hypotheses (Why ask the research question?) 1. Men who shop for casual wear at specialty stores spend more per trip than men shopping at department stores. 2. The fewer times per year men shop for casual wear, the more they spend per trip. 3. Men who shop for casual wear at specialty stores will desire more prestigious brands than men who shop at department 4. Men who buy casual wear only when it s on sale spend more per trip than men who do not wait for sales. 5. The more men desire prestigious casual wear brands, the more distance they will be willing to travel to get them.

6 Variables and Hypotheses page 6 items to collect the information that answers them. For example, in providing a reason for asking whether men typically shop for casual wear at specialty stores or department stores, we speculated that men who shop at specialty stores may spend more per trip. This speculation is actually an educated guess of sorts in other words, a conceptual hypothesis. That is, it predicts a relationship between two variables: the type of store men s casual wear shoppers purchase from and the amount they usually spend. The conceptual hypothesis predicts that average men s casual wear purchases from specialty stores will be larger than average men s casual wear purchases from department stores. To the extent that this hypothesis interests the decision maker, then the two relevant research questions should be developed into questionnaire items. Exhibit 4 on the preceding page shows how this and four other conceptual hypotheses relate to the research questions. To emphasize and better explain these relationships, the conceptual hypotheses have been color coded so you may clearly see how the hypotheses tie together research questions. Examine the coloring on the first conceptual hypothesis shown in Exhibit 4. The portions colored red relate to a variable that captures where men typically shop, specialty stores or department stores. We can call this variable, frequented store type. The portion of the conceptual hypothesis colored blue relate to a variable that captures about how much men spend each time they shop for casual wear. We can call this variable usual amount spent. The conceptual hypothesis predicts that the usual amount spent will be greater among men who select specialty stores as their frequented store type. You can follow similar reasoning for the remaining conceptual hypotheses. Note how each links information from a pair of implied research questions. Also note how each implied question is worded to gather information for one variable. Importantly, if a research question is not involved in any worthwhile conceptual hypotheses, that research question should be completely discarded. If researchers do a good job of brainstorming research questions, then they will likely produce many more questions than they could possibly use. Which to discard and which to keep depends on whether they contribute to the formulation of useful conceptual hypotheses. Returning to Exhibit 4, suppose the research team formulates no conceptual hypotheses pertaining to alteration services. That research question should then be dropped and no questionnaire items asking about alteration services should be developed. Phrasing of conceptual hypotheses. If you carefully examined the conceptual hypotheses in Exhibit 4, you may have noticed that each is phrased in one of two ways. The first, third, and fourth hypotheses use phrasing that predict differences between groups. The first conceptual hypothesis ostensibly divides men s casual wear shoppers into two groups: those who frequent specialty stores and those who frequent department stores. It then makes a comparative prediction about the amount spent per trip by each group. The third conceptual hypothesis divides shoppers into the same two groups as the first, then predicts differences in desire for prestigious brands. The fourth conceptual hypothesis divides men s casual wear shoppers into those who wait for sales and those who do not, then makes a comparative prediction about per trip spending. We ll refer to such conceptual hypotheses such as these as difference hypotheses. Difference hypotheses predict that variables of interest will differ when data is grouped according some other

7 Hypotheses and Variables page 7 variable of interest. Given this purpose, difference hypotheses should utilize what we refer to as more than phrasing or less than phrasing. That is, these conceptual hypotheses should predict that one group will have levels of some variable that are more than or less than another group. Look again at the first, third, and fourth conceptual hypotheses in Exhibit 4. Notice the more than phrasing in each, what variables are used to create the groups, and what variables are being compared across the groups. The second and fifth conceptual hypotheses in Exhibit 4 make a different type of prediction, which we ll refer to as correlative hypotheses. Notice that these conceptual hypotheses do not predict differences but predict relationships between variables. The second conceptual hypothesis predicts that as the number of casual wear shopping trips per year decreases, the amount men purchase per trip increases. In other words, the conceptual hypothesis predicts a negative relationship between trips per year and usual amount spent. The fifth conceptual hypothesis predicts that as men s desire for prestigious brands increases, the distance they re willing to travel to buy casual wear will also increase. This conceptual hypothesis predicts a positive relationship between prestige brand desire and travel willingness. Correlative hypotheses utilize what we ll refer to as more-more phrasing or more-less phrasing. When two variables are expected to positively relate to one another (i.e., as one goes up, the other should go up too), the conceptual hypothesis should use more-more phrasing. That is, more of one variable will occur with more of another variable. Conversely, when a negative relationship is expected between two variables (i.e., as one variable goes up, the other should go down), the conceptual hypothesis should use more-less phrasing. That is, more of one variable should occur with less of another variable (or the reverse: less of one variable will occur with more of the other). Statistical Hypotheses Statistical hypotheses do nothing more than provide a framework for empirically testing conceptual hypotheses. In other words, once data are collected, statistical hypotheses are necessary to determine whether or not the data support the predictions expressed in the conceptual hypotheses. In class we will discuss at length the details of how statistical and conceptual hypotheses work together as you learn how to interpret computer output from the data analysis software, SPSS. In this section, you ll learn a few of the basics of statistical hypotheses. Structure of statistical hypotheses. By way of review, statistical hypotheses always come in pairs: one called a null hypothesis, the other called an alternative hypothesis. For our purposes, null and alternative hypotheses will always be logical opposites of one another. That is, if data suggest that one is true, the other must be false and no other possibilities can exist. No matter what s being tested and the procedure being used, the null hypothesis always predicts null results. In the case of difference conceptual hypotheses, this means that the null hypothesis will always predict that no statistically significant difference between the groups being compared. In the case of correlative conceptual hypotheses, the null hypothesis always predicts that no relationship exists between the variables being tested. Because null hypotheses always predict no difference or no relationship, they are abbreviated as H 0. People frequently

8 Hypotheses and Variables page 8 make the mistake of referring to the null hypothesis as H Oh, as in the letter O. In reality, it s actually H zero. The zero subscript in H 0 reminds us that the null hypothesis predicts zero difference or zero relationship. The alternative hypothesis, or H A, will always predict either that a relationship does exist between variables or that variables do in fact differ between groups. In our class, alternative hypotheses will only predict the existence of relationships or differences; they will not specify the nature of those relationships or differences. This is an important point, which will be emphasized several times both in these Web Notes and in class discussions. What it means exactly will also become more apparent as we go through examples using SPSS software. Testing conceptual hypotheses with statistical hypotheses. Together, null and alternative hypotheses provide a structure for testing whether data provide support for conceptual hypotheses. Let s consider an example with the fifth conceptual hypothesis in Exhibit 4, which predicts that the more desire men have for prestigious brands, the farther men will be willing to drive to shop for casual wear. Notice that the conceptual hypothesis contains two variables. One is the degree to which men desire prestigious casual wear brands; the other is the distance they re willing to drive to get the desired casual wear brands. The conceptual hypothesis in this example is a correlative hypothesis and uses more-more phrasing. That is, it predicts that when more of one variable is observed, more of the other variable will also be observed. Now suppose that the researcher collected the data needed to test the conceptual hypothesis. Doing so would require that the questionnaire sent to sample members contained one question that assesses the importance of prestigious brands, the other asking how many miles men would be willing to travel to get the casual wear brands they wanted. Testing this conceptual hypothesis would require structuring statistical hypotheses as shown in Exhibit 5 below. Exhibit 5. Conceptual and Statistical Hypotheses Conceptual Hypothesis: The more men desire prestigious casual wear brands, the more distance they will be willing to travel to get them. H 0: There will be no relationship between desire for prestigious brands and distance willing to travel for men s casual wear. H A: There will be a relationship between desire for prestigious brands and distance willing to travel for men s casual wear. As noted earlier, in all statistical hypothesis tests, the null hypothesis predicts no difference or no relationship between variables. Therefore, the null hypothesis shown in Exhibit 5 states that no relationship will exist between desire for prestigious brands and the distance a shopper is willing to drive for casual wear. The alternative hypothesis shown in Exhibit 5 states the logical converse of the null hypothesis. That is, it predicts that a relationship does exist between the variables desire for prestigious brands and the distance willing to travel. So how do the null and alternative hypotheses pertain to conceptual hypotheses? Recall that statistical hypotheses only provide a structure to test the educated guesses made in conceptual hypotheses. Researchers wish to know if the data they collect will support their guesses, and statistical hypotheses provide the mechanism for finding out. Exhibit 6

9 Hypotheses and Variables page 9 provides some insights into how this mechanism works. Exhibit 6. How Statistical Hypothesis Pertain to Conceptual Hypotheses Conceptual Hypothesis: The more men desire prestigious casual wear brands, the more distance they will be willing to travel to get them. H 0: There will be no relationship between desire for prestigious brands and distance willing to travel for men s casual wear. H A: There will be a relationship between desire for prestigious brands and distance willing to travel for men s casual wear. Predicts no support for the conceptual hypothesis. (The conceptual hypothesis will not be true.) Predicts possible support for the conceptual hypothesis. (The conceptual hypothesis might be true.) As the example in Exhibit 6 shows, the null hypothesis essentially predicts that the conceptual hypothesis will be false. This will be the case for all statistical tests conducted in this class, and the vast majority of the tests you might conduct as a marketing professional. There are a few instances when this basic format would not hold, but those instances are very few in number. Therefore, for all our purposes, the null hypothesis will always predict that the data will not support the prediction made by the conceptual hypothesis. Interpreting the alternative hypothesis is a little more complicated than interpreting the null. As Exhibit 6 shows, the alternative hypothesis predicts that the data might support the conceptual hypothesis, but leaves open the possibility that the data still won t support the conceptual hypothesis. This somewhat equivocal prediction can be explained by differences in how the alternative hypothesis and the conceptual hypothesis are worded. Look first at the conceptual hypothesis in Exhibit 6. It not only predicts that a relationship will exist between desire for prestigious brands and distance willing to travel, but it also specifies that the relationship will be positive in direction. As shown by its more-more phrasing, the conceptual hypothesis predicts that more desire for prestigious brands will occur with willingness to drive more distance to get those brands. Now look at the alternative hypothesis in Exhibit 6. It simply predicts that a relationship will exist between desire for prestigious brands and distance willing to travel. However, it makes no prediction about the direction of the relationship. Once the data are collected and tested, the data could possibly show that a relationship between the variables exists, but instead of being positive, the relationship might actually turn out to be negative. In other words, the data could possibly show that greater desire for prestigious brands occurs with a lower willingness to travel. This may create some confusion about how to handle this situation. We will clear up that confusion in the following section. Importantly, statistical hypotheses tests are structured analogously for difference hypotheses as well. The example from Exhibits 5 and 6 pertain to a correlative conceptual hypothesis. Difference conceptual hypotheses predict that one group will possess more of some attribute than another group. The related statistical hypotheses will make predictions about differences as well. The null hypothesis will predict no difference between groups, the alternative will predict a difference between the groups, but will not specify which group is greater on that attribute. Testing statistical hypotheses. The obvious question at this point is how we decide if data support null hypotheses or if they support alternative hypotheses. And if

10 Hypotheses and Variables page 10 the data support the alternative hypotheses, how do we determine if that lends support to the conceptual hypotheses? Making these determinations requires analyzing data using a statistical program such as SPSS. In class, we will discuss at length how to use and interpret computer output from SPSS. This section outlines briefly the basic process for testing statistical hypotheses. Let s continue with our example. Exhibit 7 contains a simple flowchart that shows basically how statistical hypothesis testing works in our class. Testing the conceptual hypothesis requires structuring a statistical hypothesis test, which must have null and alternative hypotheses. As noted earlier, the null predicts no significant relationship between variables, while the alternative hypothesis predicts that a relationship does exist. The exhibit them points to the statistical procedure needed to conduct the test. In this case, it would be to calculate the correlation between the two variables and the p-value for that correlation. (We will go into detail in class about how to select the appropriate statistical procedure and how to interpret p-values.) The decision rule in all statistical hypothesis testing done for this class is simple: If the p-value is smaller than.05, reject the null hypothesis. Exhibit 7 shows the process reaching that decision rule by asking Is the p-value smaller than.05? If the answer is no (i.e., the p-value is greater than.05), then we accept the null hypothesis as correct, conclude that no relationship exists between desire for prestigious brands and distance willing to travel, and find no support for the conceptual hypothesis. If the answer to the question is yes (i.e., the p-value is smaller than.05), then we reject the null hypothesis, accept the alternative hypothesis as correct, and conclude that a relationship does exist between desire for prestigious brands and distance willing to travel. But, we can t yet say that the data support the conceptual hypothesis because we don t know if the correlation between these variables is positive, as the conceptual hypothesis predicted. Thus, we must take one simple additional step and look at the correlation coefficient calculated by SPSS. If that coefficient turns out to be negative, this means that more desire for prestigious brands occurs with less willingness to travel to obtain those brands, which is the opposite of what the conceptual hypothesis predicted. Therefore, despite the statistical significance of the relationship between the variables, the data would still not support the conceptual hypothesis. However, if the correlation coefficient was positive, this would mean that the relationship was as the conceptual hypothesis predicted, lending support to the conceptual hypothesis. Exhibit 8 contains a flowchart similar to that in Exhibit 7, except that Exhibit 8 shows the process for testing a difference conceptual hypothesis. The processes are nearly identical but differ in three important ways. First, note that none of the hypotheses give predictions about relationships between variables. Instead, all make predictions about how a variable differs between groups. Second, the statistical procedure used to test the hypotheses is not a correlation but a t-test. Again, we will cover in class how to make those distinctions. Importantly, the t-test also produces a p-value and we apply the same decision rule: Is the p-value smaller than.05? Third, notice that if the p-value is smaller than.05, we must look to see whether the mean amount spent per trip is larger for specialty stores than for department stores. If it s not, then we have no support for the conceptual hypothesis. If it is, then the conceptual hypothesis is supported.

11 Hypotheses and Variables page 11 Exhibit 7. Flowchart for Statistical Hypothesis Testing: Correlational Conceptual Hypothesis Conceptual Hypothesis: The more men desire prestigious casual wear brands, the more distance they will be willing to travel to get them. Statistical Hypotheses: H 0: There will be no relationship between desire for prestigious brands and distance willing to travel for men s casual wear. H A: There will be a relationship between desire for prestigious brands and distance willing to travel for men s casual wear. Data Analysis Procedure: Calculate correlation and p-value between desire for prestigious brands and distance willing to travel. No Is p-value smaller than.05? Yes Accept the null hypothesis, H 0. Data suggests no relationship exists. Reject the null hypothesis, H 0 and accept the alternative hypothesis, H A. Data suggest relationship does exist. Conclude that the data do not support the conceptual hypothesis. No Is the correlation coefficient as predicted (positive in this case)? Yes Conclude that the data do support the conceptual hypothesis.

12 Hypotheses and Variables page 12 Exhibit 8. Flowchart for Statistical Hypothesis Testing: Difference Conceptual Hypothesis Conceptual Hypothesis: Men who shop for casual wear at specialty stores spend more per trip than men shopping at department stores. Statistical Hypotheses: H 0: There will be no difference in amount spent per trip between men who shop specialty stores and men who shop department stores. H A: There will be a difference in amount spent per trip between men who shop specialty stores and men who shop department stores Data Analysis Procedure: Conduct t-test of difference in amount spent per trip for men who shop specialty stores and men who shop department stores. Calculate p-value. No Is p-value smaller than.05? Yes Accept the null hypothesis, H 0. Data suggests no difference exists. Reject the null hypothesis, H 0 and accept the alternative hypothesis, H A. Data suggest difference does exist. Conclude that the data do not support the conceptual hypothesis. No Are means as predicted (specialty store amount larger)? Yes Conclude that the data do support the conceptual hypothesis.

13 Exhibits 7 and 8 attempt to graphically simplify the basic process of conducting statistical hypothesis tests. These diagrams are important to understanding this material and you should study them carefully. In addition, you should follow along with this process when you complete the SPSS homework assignments, which will require that you structure and complete statistical hypothesis tests. Concluding comments. At several points in these Web Notes, I use phrases such as in our class or in this class. This is intended to emphasize that the approach we take to statistical hypothesis testing can be modified in some ways and that our approach is not the only approach. My hope is that the approach we ve adopted is the easiest to understand. The approach taken in our class is based on two-tailed tests of statistical significance. With two-tailed tests, we must use alternative hypotheses that only predict that relationships (in the case of correlative tests) or differences (in the case of difference tests) exist between variables but do not specify anything beyond that. That s why, as illustrated in Exhibits 7 and 8, if the null hypothesis is rejected and the alternative accepted, we must take the additional but simple step of checking the correlation coefficients (Exhibit 7) or the group means (Exhibit 8) to see whether the data support the conceptual hypotheses. Hypotheses and Variables page 13

Homework #3 is due Friday by 5pm. Homework #4 will be posted to the class website later this week. It will be due Friday, March 7 th, at 5pm.

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