Students who are not proficient in the use of statistics while collecting Market Data, will find it helpful to use the following simple four step general procedure when applying tests of statistical significance. That procedure is discussed here in general terms, and later will be applied to each of the three methods of significance testing in more specific detail.
Use a Simple Four steps Procedure:
1. Observe an important difference
2. State a null hypothesis to be tested
3. Calculate the appropriate statistic
4. Compare the calculated statistic with an appropriate “critical value” of that statistic.
Observe a difference that can have important implications for the marketing manager: in any set of findings researchers can observe many differences, but only a few of those differences might have important implications for the marketing manager. Those are the differences that should be tested for significance.
State a Null Hypothesis that can be tested using one of the three methods discussed: When applying significance tests researchers often hypothesize that the observed differences is not statistically significant one that is they hypothesize that the observed difference could easily have occurred by chance because of sampling variation. Such a hypothesis is usually called a ‘null hypothesis’. If it is possible for researchers to obtain evidence that will lead them to reject the null hypothesis, they will be able to concluded that the observed difference is too large to have occurred by chance due to sampling variation. This also leads them to conclude that the observed difference must reflect a real difference that exists in the population being studied. When researchers obtain such evidence, they conclude that the observed difference is statistically significant.
Of course, if the researchers are unable to obtain such evidence; they will not be able to reject their null hypothesis nor will they be able to conclude that the observed difference is statistically significant.
In this step of the procedure, students who are not proficient in the use of statistics should specify the confidence level they would like to have when they decide whether or not to reject the null hypothesis. That is, they should specify that they want a 95 percent level of confidence, or a 99 percent level of confidence part of the null hypothesis.
In order to obtain the evidence they need to reject their null hypothesis, researchers must complete steps 3 and 4 of these general procedures.
Calculate the appropriate “Statistic” which quantifies the observed Difference relative to the sample used to gather the data: In all significance tests it is necessary to use one or more formulas to calculate the number (called a statistic) that qualifies and summarizes the observed difference, while also taking into consideration the size of the sample used to collect the data.
Example: If 30 percent of the women are aware of a certain television commercial and 25 percent of the men are aware of the same television commercial, the 5 percent differences is not likely to be considered large (i.e. significant) difference if the sample consisted of 20 women and 20 men. On the other hand, if 1,000 women and 1,000 men are interviewed, the 5 percent difference would very probably be considered significant.
Check to see if the calculated value of the Statistics is large enough to allow researchers to conclude that the observed difference is statistically significant: If the calculated value of the statistic is lager than a certain “critical value”, researchers will have the evidence they need to reject the null hypothesis. Therefore, to complete this step, researchers must have available a table of the critical values of the appropriate statistic.
To illustrate assume that the researchers wish to be 95 percent confident of the conclusion they reach regarding the statistical significance of an observed difference. Assume also that they have a table of the critical values of the appropriate statistics for a 95 percent level of confidence. In this step of the procedure, researchers compare the calculated value of the statistic (available from step 3) with the critical value of the statistics available from the able. If the calculated value is bigger than the critical value, researchers will have evidence indicating that the observed differences is too big to be attributable to sampling variation. Therefore, the researchers will reject their null hypothesis and conclude with a 95 percent level of confidence that the observed difference reflects a real differences existing in the population studied.