WK 3 DIS, Data

BARBARA NIEDZ: Hi, all. Dr. Niedz here again and moving on to a brief discussion about descriptive statistics. So we'll talk a bit about measures of central tendency and measures of dispersion, and you'll see how they work for continuous variables. We'll also talk about frequencies and percentages and how they fit for categorical data. We'll use, revisit a little research lingo, and talk about null directional and non-directional hypotheses. We'll also visit the standardized infection rate, the standardized infection ratio measure, and how that's used in research, quality improvement, and DNP. And we're also going to spend a little time talking about the differences between type one and type two measurement errors and how they figure into research projects. Four levels of measurement, two categorical and two continuous-- very important concepts and very important aspects of measurement. Categorical data is usually displayed by counts and percentages. So for example, nominal level data might be gender. Male, female, and transgender people might fall into those three buckets. And there's no value placed. Men are not better than women. Women are not better than men. Transgender are not better than men or women, and the data is equal in terms of the value of those contributions to the data set. Whereas ordinal data is ranked. So, for example, if you collected a demographic data on educational level for some reason, whether you were talking about health literacy or staff educational backgrounds, those data are ranked. People who only completed fifth grade and never completed grade school have less education than those people who completed high school who have less education than those people who have some college as opposed to those people who have advanced degrees. So categorical data come in two forms-- nominal and ordinal. Ordinal is ranked, nominal is not. Continuous data is actually from the type of data that you can do an average with that makes sense. So for example, interval level data, where you have some scale that measures something-- let's say perceived stress-- from a number that is as low as zero with no perceived stress to as high as 21, where this is the most stress you can possibly imagine. The differences between the divisions, even though there might be zero, is very soft because a lot of stress compared to some stress is not exactly something that you can multiply or divide by, whereas ratio level data is. So suppose ratio level data-- for example, income, annual income, zero-- is very different from annual income of $50,000 a year, which is half the amount of $100,000 a year. So ratio data has equal divisions, has an absolute zero. But they're all useful and you're going to see some examples of that. Measures of central tendency-- the mean, as I mentioned, is the arithmetic average. The mode is the most frequently occurring value in a data set. And the median is that point at which you have an equal number of observations above and below that point. You see them represented in, in published work and in projects. They're all very useful. The mean is subject to extremes, and if there are outliers present in the data, the median is a much more useful tool. Standard deviation tells you about that variation away from the mean. The variance is simply the standard deviation squared. And the range is the lowest point to the highest point in the data set. So measures of central tendency and measures of dispersion are very useful tools. The chapters that I've selected out for every week in Salkind and Frey are really useful tools, and understanding these concepts takes more than a 15 minute video, and I hope you'll consult with Salkind and Frey in order to be able to complete assignments, in order to be able to address the discussion questions in the classroom, and certainly the ability to answer the knowledge check questions. So, means and standard deviations, very, very useful for continuous data. Counts and percentages, also important. Percentile rankings allow you to do some comparisons. And confidence intervals are not exactly prediction, but it tells you something about that spread of data and what you might expect in terms of the relationship between the sample and the population. So, just a little bit of information on those four types of concepts can be very helpful. So a picture is worth a thousand words, and you can see the differences between categorical data on the left with a bar graph and continuous data on the right with a histogram. And in the histogram, you can see that that is essentially continuous data-- no spaces, no gaps between the bars-- whereas the categorical data on the left is summarized in a bar chart. And you can see that there are no gaps between the bars, and they are, in fact, separate and apart. Now, this is only a portion of the table in Sood et al that is presented on page 144 and is actually a way to present demographic variables and other important variables, independent and dependent variables, in a study all efficiently in one small table. And you can see that there are both categorical variables-- for example, ethnicity, with 1,086 participants, broken down into the counts by different groupings-- Asians, Hispanic, Black, Hispanic, white, and others-- and also the percentages of the sample. You could easily do this manually to just figure out those percentages, but it's awfully nice when they're presented like this in a published piece. You can also see that the age and gestational age in this study are presented as the mean and the standard deviation plus or minus 1 standard deviation. So you get an idea of what the spread of data might look like. Median BMI and the range-- again, it's an ordinal level of measurement. And so the mean might make good sense for the way that is presented and time in minutes also presented in the average with the standard deviation. So, can be a very efficient and useful way of summarizing data. There are three types of hypotheses that are actually usually implicit and not stated unless you were reading a PhD dissertation from Proquest. The null hypothesis states that there is no relationship, no association, between the variables, between the dependent and the independent variables. The alternate hypothesis states that there is a relationship or association between those independent and dependent variables, and hypothesis can go in one direction or not, depending on the nature of that comparison. And that can also be an important concept. So here's an example. Take a look at the study that's in the resources for this week by Bedouin and others from 2022. It's a study about perioperative prophylaxis practices and surgical site infections. And the null hypothesis would essentially say there is no association. There is no relationship, and there's no differences in perioperative prophylaxis practices and the SSI rate. However, an alternate hypothesis would posit a relationship between those two types of variables in a specific type of surgical procedure and would perhaps even be more specific in electing a certain type of prophylaxis over another. So, null, alternative, directional, or non-directional hypotheses. So the standardized infection rate or the standardized infection ratio, the SIR, is a very useful tool that's been developed by the NHSN that allows us to take a look at infections and make some comparisons on the basis of risk adjustment. So how sick are the patients, and what is the predicted rate of infection for a particular type of surgical procedure? It compares the actual rate to the prediction. So a SIR of greater than 1 indicates more hospital acquired infections than predicted, and an SIR error rate of less than 1 indicates fewer hospital acquired infections than predicted. So I played around with the literature and the SIR rate as I was preparing these slides and videos, and I live in New Jersey. And so I just said, well, let me see what I can find about this that's publicly available. And there is, in New Jersey, the State Department of Health publishes by hospital comparisons for different types of surgeries across the state and provides hospital-specific SIR rates for these different surgical procedures. So I challenge you to look in your own state and see what you can find out in terms of published SIR rates. And if you can't find anything, look up New Jersey Department of Health, and you'll be able to see a variety of hospitals in New Jersey. So we typically use probability theory and the normal curve in order to be able to understand prediction, and our statistics, our statistical analysis that we'll move into starting next week, will allow us to define a critical value, the point at which we can make a decision about rejecting the null hypothesis, that there is no difference or no association, in favor of the alternate hypothesis that says essentially, if you were to repeat the test with a different sample, you'd likely get a similar result 95% of the time or 99% of the time, depending on what that p value is, or whether it is in this part of the curve, where 95% of the values are, that allows you to see that difference between rejecting and not rejecting the hypothesis, the null hypothesis. There is actually excellent information in Salkind and Frey on pages 215 to 217 on this concept. Now, one characteristic that you can see in the SOOD et al article is about whether or not there's a P value. If there's a P value, you can infer from that there is an inferential test of significance that is being used. And you can see this in table two in Sood et al. The last key point I want to make in this video is about measurement error. A type one error is the type of error that is made when statistical significance is found, but it's not really there. And your protection against this is the all important p value. Type two error is the type of error that you make when you don't find significance, but it's really there. And sample size is the biggest protection that we have. Key points in this video on this slide. Don't forget the value of the reading.