Speaker 1: Now that we've identified our correct answer, let's move on to the next question. Now that we have identified our correct sampling procedure, and hopefully we have selected

Speaker 2: a probabilistic sampling method, it's now time to determine just how big our final sample

Speaker 1: size should be.

Speaker 2: So a common refrain in marketing research is, just how big should my sample size be? Well, one of the common approaches to answering this question is, pick a sample size that sounds large enough. A sample size of 100, or a sample size of 1000, or a sample size of 2000. Usually a nice, whole, round number that sounds impressive when described to other individuals about what the sample size was. Another very common approach is simply to collect as much data as budget and time allows. If a consulting firm was allocated $10,000 and two weeks to collect data for a consumer survey, spend every single last penny and see how much data you can collect in those two weeks. But even Drake knows that these are both inappropriate approaches to determining the optimal sample size. And again, Drake has our back. The approach that we should strive for when determining optimal sample size is to calculate a precise sample size that's required that accommodates the level of precision and uncertainty that we're willing to tolerate as part of our analysis. In other words, when we think about trying to calculate the optimal sample size in a marketing research study, we're trying to balance between two heavy burdens. On one hand, intuitively we recognize that any sample will inherently have some error or uncertainty when we try to generalize those results to the entire population. We didn't study every single person, so when we project the results of our sample onto a population, there's going to be some amount of error. On the other hand, it's also true that collecting more data generally means more time, money, and effort required. And these two weights pull us entirely different directions. On one hand, if samples inherently have more error, that's going to drive us to wanting to collect more data to get more accurate results. Marketing researchers definitely want accurate results. On the other hand, collecting more data means more time, money, and effort, which means marketing researchers like most marketers, we try not to expend unnecessary energy. So this motivates us to collect even less data. So on one hand, we want to collect a census. On the other hand, we want to collect no data at all. In truth, the job of a marketing researcher is to figure out how to balance these two heavy facts so that we are willing to live with the weights of both. Thus, with just a little thought and care, we can use statistics to determine the optimal sample size we're going to need. Notice here I use Microsoft WordArt for the word statistics to make it more enticing and

Speaker 1: exciting for you.

Speaker 2: In this class, we're going to keep it simple when it comes to determining the optimal sample size, and we're going to focus on just using the two most simple formulas. However, before we introduce those formulas, we need to lay out the prerequisites that we have to have in place to determine the optimal sample size. First, we need to have a well-defined population. That should hopefully already be done. If the whole point is that we want to generalize our sample to the population, we need to have a clear definition of that for our study. In addition, to determine the optimal sample size, we already have to have our finalized instruments or questionnaire items that we're going to be using to collect our data. In addition, our sampling method has to be a probabilistic method. Stratified sampling, simple random sampling, cluster sampling. Notably, in our Marketing 470 class, we ignore this detail. We do, in fact, collect a convenient sample, but still use statistical analysis. All sample size formulas are built on the underlying assumption that a probabilistic sampling method was used to generate the data. If we use a sample size calculation, but then go collect data using non-probabilistic method, the results really have no meaning. Finally, to determine the optimal sample size formula, the fourth prerequisite is we already have to have a clear idea of the statistical test, calculation, or comparison that we want to do it. If we're going to determine how much data we even need to collect in the first place. That brings us back to the two sample size formulas that we're going to be focusing on in this instructional tutorial. We're going to focus on just two types of very simple analysis we might want to do. In the first scenario, we simply want to estimate a single percentage value, such as what percent of people like Brussels sprouts. Or we want to determine the optimal sample size to calculate a single average, such as what is the average customer satisfaction score on a 7-point customer satisfaction scale. There are a lot more advanced type of statistical tests and analyses we might want to do, such as testing for correlation, testing for the difference of a percentage between two groups. And in these more advanced types of analyses, there's in turn more advanced type of sample size formulas that might need to be used. We won't worry about learning about those specific formulas in this class, but I do need to alert you that different types of analysis would call for different types of sample size formulas. Now let's circle back and see those four different prerequisites in action. Consider the following statement, I will be using simple random sampling of currently enrolled lower division SDSU students to see whether at least 60% either like or really like the new waitlist system on a 5-point liking scale. Let's see if all four prerequisites exist in this simple statement. Here we have our well-defined population. Here we have our finalized research instrument. Here we clarify that we are in fact doing simple random sampling, a form of probabilistic sampling. And finally, we've already articulated the type of analysis that we want to do. We want to calculate the percentage of individuals who select like or really like to the question. With all four criteria present, we can then proceed to determine what the optimal sample

Speaker 1: size should be for this particular study.

Speaker 2: There's only two sample size equations that we're going to focus on in this class, and they're very similar. The only difference depends on what type of variable we're dealing with. Whether we're calculating a percentage, which is usually called a dichotomous variable or a variable that's coded simply as a 0 or 1, or it's also called a nominal variable that has exactly two categories, or a continuous variable. Continuous variables are variables that are interval or ratio level data. You may recall, interval and ratio level data are the only types of measurement levels where we can calculate an average. These are the two different formulas that we're using for the sample size equations. Let's touch on each one of the elements of these equations briefly, and then we'll unpack them more in the later part of the video. First, if we glance at these, they look quite similar, just with one small distinction. In both cases, we're solving for n, little n, which is the optimal sample size we're trying to determine. And the first thing that goes into the equation is we set our confidence interval, represented as z squared. This corresponds to the percentage level of confidence that we want to specify for our study. The e squared represents the acceptable sample error, or the margin of error, that we're willing to tolerate in our estimates. And finally, the third component, which looks different between the two different equations, is the estimated variance in the population. One is represented as p times q, which is simply the percentage of yays and the percentage of nays, or yeses and nos, or whatever the two different groups are for the percentage variable. And s squared, represented in the continuous case, is simply the estimate of variance, a statistical term that you should be familiar with from previous statistics courses. Don't worry, we're going to unpack each one of these ideas and their role that they play in the sample size equation shortly. One thing we need to keep in mind is these first two pieces, the confidence interval and the acceptable sample error, is something we get to set. The marketing researcher actually specifies the level of confidence and allowable error that we're willing to tolerate. On the other hand, estimated variance is something that's calculated based on our best understanding of what's actually true in the real world.