Welcome to the video on descriptive analysis. As the name would suggest descriptive analysis helps you describe the key trends in your data. Unlike in inferential analysis, you are not trying to infer anything about the broader population based on the data you collect. You're merely trying to describe data that you have. People oftentimes skip over descriptive analysis when they're reviewing studies, because they're more interested in the predictions that are being tested. However, I think this is a mistake because descriptive analysis can tell you really important information about the sample that you're studying. Remember the concept of external validity that we talked about in prior weeks. External validity is the extent to which you can generalize to a broader population from the data you've collected on your sample. Descriptive analysis is helpful when considering external validity because it tells you about the characteristics of the sample you're studying. So what are descriptive statistics? Well there are two key types of data that are reported in descriptive analysis that you'll see in tables in positive psychology articles. Let's talk first about measures of central tendency. There are three types of measures of central tendency. The mean or the average is the value after adding up all of the numbers in a distribution and dividing that value by the total. The mean is what's most typically used to report the center of the data. So this is what you'll see most often represented in a positive psychology article. The median or the middle, is the number that cuts the distribution in half. To find the median, you order the numbers from lowest to highest, and take the number in the middle. Or if there are two numbers in the middle, you take the average of those two values. You use the median when there are extreme numbers on either side of the distribution. For example, you would use the median when looking at income. Because there are some very wealthy people in our country who would skew the data if you just looked at the mean. And finally, you have the mode. The mode is the most common number that is repeated the most number of times in the data. You would use the mode if you're interested in the most typical response in your data. Let's take an example. So let's say that these 10 scores on this slide are individual scores, on a grit scale of 0 to 5. To get the mean, I'm going to add them all up and then divide by 10, and that is going to give me a mean of 3.4. To get the median am going to order the numbers from lowest to highest and take the number at the middle. In this case, 2 numbers are in the middle 3 and 4 so, i take the average of those two and get 3.5. To get the mode I'm going to take the most common response which is 5. You can see here that the mean and the median can get pretty similar responses. But if there was a scale with more of a range, there may have been an opportunity for more outliers, which could of influenced the mean. However, the mode tells you something different, because the most common response in this case, is different from the mean and the median. If you have categorical data where data are in categories rather than captured on a scale, descriptive data are reported as percentages or frequencies. So for example, gender would be reported as the percentage of males and the percentage of females. Next, you have measures of spread or variation. Measures of spread or variation tell you how the data is distributed around that middle of the data. So if all the data points are clustered around the average, we'd say that the average is a good representation of the data. However, if the data are very spread out then that average wouldn't be as good a representation. There are number of different types of spread or variation that you may see represented in positive psychology articles. The range will tell you the highest score minus the lowest score. And this is often displayed in articles to show you the scale for certain variables. The interquartile range captures the range of the middle 50% of the data. A percentile refers to a what percentage of scores fall below a given number. So for example, 10th percentile has 10% of the scores below it or the 90th percentile has 90% of the scores below it. You may see interquartile range and percentile represented in positive psychology articles. But the most common type of variation or spread to be reported is the standard deviation. Now I'm not going to go into the calculation for a standard deviation, but I just want to give you an idea of what the concept is capturing. The standard deviation tells you how much deviance or variation there is around the average. The closer all the data points are to the average the smaller the standard deviation. The more spread out they are the greater the standard deviation. So why does this matter? Well let's say that you're reporting the average grit of a sample of students and there's a large standard deviation. This would tell you that even if you know the mean, it might not be the case that this mean represents the sample of students all that well since there's a lot of variation around the mean. You can compare standard deviations at different variables to see where there is more or less variation. Finally, let's say that you have qualitative data. For example, notes from interview or focus groups or data that you've collected from observations. To analyze qualitative data researchers will develop a coding scheme where they have certain codes or themes that they are looking for in the data. If they're earlier in the process and trying to develop a construct or theory, the coding process may be more inductive where they are drawing codes from their observations. So for example, in the early stages of developing a positive psychology construct like grit. Angela Duckworth might interview individuals presumed to be high in grit to better understand their behavior. Once a construct has been developed then qualitative analysis is more deductive. Where researchers might be looking to see how well the data they have collected from whatever interviews, observations or focus groups they conducted maps on to the existing construct. In the case of grit there are two components, passion and perseverance. So qualitative analysis could see the extent to which individuals displayed these two dimensions of grit. So let's actually apply these concepts to positive psychology by looking at a table from the article we've been examining, True Grit. Table 2 on page 13, also here on this slide, displays all the variables in our analysis. Now we haven't yet talked about how to interpret correlations. But if you'll look down to the bottom of the table, you'll see the mean and standard deviation for each variable. So for variable 1 which is grit, the range of our resume coding scale is 0 to 6. The mean tells us the average score of all the teachers in our sample. And the standard deviation tells us how spread out the data is around that average. Now you can compare that to variable two, the leadership rating. The range for leadership was captured on a scale of 1 to 5, and has a slightly lower mean. The standard deviation for leadership is also lower at 0.97, which means there's less variation in leadership when compared to grit. The next two variables 3 and 4, college GPA and SAT scores also tell us something interesting about our sample. Namely that it doesn't appear to be your typical sample of teachers. The mean college GPA is 3.56, with very little variation given a standard deviation of 0.26. And an average SAT score, now this is on the old SAT score range with the range of up to 1,600 of 1,344. So this sample of teachers has higher academic achievement than the typical college graduate or the typical teacher. As this example makes clear, you should always look for the descriptive table in a study because it can help you understand the sample. So you can think about how generalizable the results actually are. In this true grit example, the descriptive analysis can show us that the external validity of the study is limited. Because this sample is not representative of the broader teacher core. Once descriptive analysis is complete, researchers turn to inferential analysis which is typically the meat of the paper. In the next video, we'll talk about how to interpret inferential analysis. But hopefully this video has made clear that descriptive analysis is just as important.