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Biostatistics Framework | Mean, Median, Mode Explained + SD vs SEM · This Is Why with Dr. Busti

• 0:00
  SPEAKER_00: Well, welcome to this lecture where I'm going to be covering measures of central tenancy, variability, and data dispersion as the first topic in our series on summary statistics.
• 0:12
  SPEAKER_00: You can find a full playlist on YouTube or at the website thisiswhy.
• 0:19
  SPEAKER_00: These concepts are critical for both the researcher doing the study, right?
• 0:24
  SPEAKER_00: Typically at the time of the analysis, right?
• 0:27
  SPEAKER_00: Also for the clinician reading and understanding clinical literature.
• 0:32
  SPEAKER_00: With that, I'm Dr.
• 0:33
  SPEAKER_00: Bustae, your faculty and host on This Is Why, a show that helps healthcare professionals transform their medical knowledge from what to why, because when we know why we do what we do in the proper context of the evidence, it changes the how, and that changes everything about patient-oriented decisions that we make every day.
• 0:53
  SPEAKER_00: So going into our series, okay, so if you're trying to stay oriented and you want to follow that playlist and the collection, part one was really that statistical analysis plan, which is done before you start the study.
• 1:07
  SPEAKER_00: We are in part two, which is you've at the completion of the study, we're now doing our summary statistics specifically descriptive type, and then we'll eventually get to inferential.
• 1:18
  SPEAKER_00: And then there's a part three about diagnostic tests.
• 1:21
  SPEAKER_00: But part one was that establishing the you know the type of groups, the type of data, what is my endpoint, and then starting to think about what parametric or non-parametric statistical analysis do I need to do.
• 1:35
  SPEAKER_00: If I'm doing a study that requires inferential statistics, what is my alpha?
• 1:40
  SPEAKER_00: What is my power analysis?
• 1:42
  SPEAKER_00: But here's where we're at here today, okay?
• 1:45
  SPEAKER_00: We are at the at the completion of the study where you're going to be doing summary statistics, where you have descriptive and inferential statistical analysis.
• 1:55
  SPEAKER_00: Okay, and so we're on this first particular one right here about measures of central tenancy, variability, and dispersion of the data that we have collected.
• 2:08
  SPEAKER_00: Okay, so what are those components?
• 2:11
  SPEAKER_00: The measures of central tenancy are summarized in this table.
• 2:15
  SPEAKER_00: And those of you joining us on our podcast channels, okay, I'm sorry that you can't see it, but these are all available over at YouTube or at thisiswhy.health.
• 2:25
  SPEAKER_00: But I'll walk you through and keep people somewhat oriented.
• 2:28
  SPEAKER_00: There's three main rows mode, median, and the mean.
• 2:34
  SPEAKER_00: Okay, those are the main measures of central tendency.
• 2:39
  SPEAKER_00: Okay, what is going on with the data?
• 2:41
  SPEAKER_00: And then we're going to walk through with each one of those, what are the common descriptors?
• 2:48
  SPEAKER_00: What does that mean?
• 2:50
  SPEAKER_00: What is the data variability that we typically are going to use?
• 2:55
  SPEAKER_00: Okay, how do we assess dispersion if we can?
• 2:59
  SPEAKER_00: And then what type of data is that typically applied to?
• 3:02
  SPEAKER_00: So remember in part one, you're trying to understand what type of data that you're dealing with.
• 3:08
  SPEAKER_00: Okay, and if you don't know that, there's a whole lecture about that.
• 3:11
  SPEAKER_00: That's oriented back to your hypothesis and the question being answered.
• 3:18
  SPEAKER_00: Okay?
• 3:19
  SPEAKER_00: So let's start out first with mode.
• 3:22
  SPEAKER_00: Okay, that's our first and most the simplest form of central tendency that's out there.
• 3:28
  SPEAKER_00: Okay, the descriptor is the most frequently occurring.
• 3:33
  SPEAKER_00: So how many yeses?
• 3:35
  SPEAKER_00: How many no's?
• 3:37
  SPEAKER_00: Okay, so that gives us a data variability or dispersion of ability to describe it in frequency, how many of those things?
• 3:47
  SPEAKER_00: Right?
• 3:47
  SPEAKER_00: And what kind of data is being applied to that?
• 3:50
  SPEAKER_00: Nominal.
• 3:51
  SPEAKER_00: So it's typically a yes or no.
• 3:55
  SPEAKER_00: So how many yeses, how many no?
• 3:57
  SPEAKER_00: The frequency, okay?
• 3:59
  SPEAKER_00: And this is usually manifested in a in a bimodal distribution, right?
• 4:06
  SPEAKER_00: Because most of the time in studies that we are going to typically read, something like a mortality study, or do they achieve their goal, blood pressure, or lipid goal?
• 4:18
  SPEAKER_00: So at the end of the study, it was do they survive?
• 4:20
  SPEAKER_00: Yes or no.
• 4:22
  SPEAKER_00: Did they achieve their goal?
• 4:23
  SPEAKER_00: Yes or no.
• 4:24
  SPEAKER_00: Okay?
• 4:25
  SPEAKER_00: And so you are just how many yeses and how many no.
• 4:29
  SPEAKER_00: You can't be in between, so there's no mean.
• 4:32
  SPEAKER_00: Right?
• 4:33
  SPEAKER_00: There's no real middle most, kind of the middle number, which is the median.
• 4:38
  SPEAKER_00: So I I that hopefully makes sense visually.
• 4:41
  SPEAKER_00: Okay.
• 4:42
  SPEAKER_00: Moving on to the median, we start thinking about the data in the middle.
• 4:48
  SPEAKER_00: That middle number or the middle most, the what represents the 50th percentile.
• 4:54
  SPEAKER_00: So that means the extremes, the 25% on one end and the 25% on the other end, are excluded, and we're only looking at that middle portion of numbers or values.
• 5:06
  SPEAKER_00: Okay?
• 5:07
  SPEAKER_00: And so that gives us what is called the interquartile range.
• 5:11
  SPEAKER_00: So that gives us the 50th percentile, the 50% of the data.
• 5:17
  SPEAKER_00: We don't care about those extremes.
• 5:19
  SPEAKER_00: So we have the interquartile range of the 25th percentile and the 75th percentile, giving us the 50% in the middle.
• 5:28
  SPEAKER_00: Okay, and we typically apply median value in understanding to data that is ordinal or that follows a continuous set of rules.
• 5:43
  SPEAKER_00: However, there are outliers typically resulting in the data being skewed with the continuous.
• 5:50
  SPEAKER_00: Okay, because normally we think of continuous data being uh parametric, normal distributed, where we would actually get an average.
• 5:59
  SPEAKER_00: Okay.
• 6:01
  SPEAKER_00: So let's look at what that looks like.
• 6:03
  SPEAKER_00: So when you have median, that you're trying to figure out that 50th, that middle most, the middle number.
• 6:10
  SPEAKER_00: Okay, and so data many times is not following a normal or bell curve kind of distribution here, right?
• 6:18
  SPEAKER_00: The gray line that you see here.
• 6:20
  SPEAKER_00: So there's now either it's skewed one way or the other.
• 6:25
  SPEAKER_00: Okay, and again, with continuous data that has outliers, something is pulling it.
• 6:30
  SPEAKER_00: So on this example, where you see the tail over here, that is to the right.
• 6:37
  SPEAKER_00: It is positively skewed because on the x-axis it's the numbers are getting larger as you go over, right?
• 6:45
  SPEAKER_00: It's skewed to the right because that's the direction the tail is going.
• 6:49
  SPEAKER_00: Something is pulling it to the right, the tail is to the right, it's skewed to the right, it's larger.
• 6:56
  SPEAKER_00: So what ends up happening then is the average, which is why we don't use it to describe this type of data, is now greater than the median.
• 7:06
  SPEAKER_00: Okay, so the mean is greater than the median, and the median is now greater than the mode.
• 7:12
  SPEAKER_00: Which we just talked about, mode, which is that frequency, the how many yeses, how many no's are there, typically bimodal.
• 7:20
  SPEAKER_00: Okay.
• 7:21
  SPEAKER_00: So when they're that way, what about if it's negatively skewed?
• 7:26
  SPEAKER_00: The data is being pulled to the left, and on that x-axis the number is smaller.
• 7:32
  SPEAKER_00: Okay?
• 7:33
  SPEAKER_00: So it's skewed to the left.
• 7:34
  SPEAKER_00: So that means the mean value is going to be smaller than the middle most.
• 7:41
  SPEAKER_00: It's gonna be less.
• 7:43
  SPEAKER_00: So the mean is less than the median, and the median is less than the mode, the most frequently occurring.
• 7:51
  SPEAKER_00: And you see that you can just look at the numbers, and as you're assessing your own data, or maybe they're presenting it to you, you can see that without even a graph.
• 8:03
  SPEAKER_00: Okay.
• 8:04
  SPEAKER_00: Now, as we step into data that we can describe as a mean, all right, we are thinking about the mathematical average.
• 8:14
  SPEAKER_00: Okay?
• 8:15
  SPEAKER_00: And that's where we can generate things like standard deviations.
• 8:19
  SPEAKER_00: And it's typically associated with continuous data that is meeting and following the various boundaries and rules, usually has a larger sample size, has no weird outliers.
• 8:30
  SPEAKER_00: And when you look at it, the data is following a normal distribution or bell curve.
• 8:38
  SPEAKER_00: Okay?
• 8:40
  SPEAKER_00: And so when you line up the mean and the median and the mode, they are roughly equal.
• 8:45
  SPEAKER_00: Now I know on this diagram that I'm showing you, it says mean equals median and equals the mode.
• 8:53
  SPEAKER_00: It doesn't have to be the exact number, but it's so relatively close that there's no skewing of the curve or the distribution or the histogram of the data that you are assessing.
• 9:07
  SPEAKER_00: Right?
• 9:08
  SPEAKER_00: So that data dispers uh dispersion is allowing us to see it.
• 9:12
  SPEAKER_00: So if we take this one step further and we start thinking about standard deviations, because this really gets down into those uh determination of the what going back to alpha, when is something statistically significant?
• 9:25
  SPEAKER_00: We got one-sided, two-sided, we start talking about p-values, okay, uh, and then you start thinking about standard deviations when you put it in the context of even 95% confidence intervals.
• 9:37
  SPEAKER_00: So, what does what are these standard deviations?
• 9:40
  SPEAKER_00: Are they telling us?
• 9:40
  SPEAKER_00: So if you have one standard deviation of the need, and the mean, and you're assuming a normal distribution, so this is continuous data.
• 9:48
  SPEAKER_00: We're not doing standard deviations on median data, uh mode, okay, doesn't work.
• 9:56
  SPEAKER_00: So that's about 68% of the observations of the as your data falls inside there.
• 10:03
  SPEAKER_00: Most people, books, if you read them reviews on this, will just round that up to 70% just because it's cleaner.
• 10:10
  SPEAKER_00: But it's roughly 68%, which is why you don't see the exact equal sign there.
• 10:17
  SPEAKER_00: When you go to two standard deviations out, now you're representing 95% of the observations that were collected.
• 10:28
  SPEAKER_00: Okay, a third level of standard deviation goes to 99.7% of the overall observations.
• 10:38
  SPEAKER_00: Okay, so where does your data fall and how many standard deviations are you willing to embrace, right?
• 10:45
  SPEAKER_00: Because what you at the end of the st at the end of the day, remember, our study is always trying to decide.
• 10:50
  SPEAKER_00: Do I have a difference when one actually exists and is it real?
• 10:55
  SPEAKER_00: And that's where your alpha value typically comes from.
• 10:58
  SPEAKER_00: And if you think about going back to the alpha values lecture, which if you're not sure what that is, remember that's your risk of making a type one error.
• 11:07
  SPEAKER_00: We typically assign that to be 0.05, which is a 5% chance of making a type 1 error.
• 11:13
  SPEAKER_00: Well, again, it's influenced by the direction and the distribution.
• 11:16
  SPEAKER_00: Is it one-sided, one-tailed, two-tailed, or one or two-sided, right?
• 11:20
  SPEAKER_00: Because you have to split that 0.5, 0.05, or 5%, either in one direction or two, divide it out.
• 11:27
  SPEAKER_00: So go back to that lecture if you're not familiar with that topic, but it comes back to this.
• 11:33
  SPEAKER_00: Okay.
• 11:34
  SPEAKER_00: So this is the totality of when we think about measures of central tendency and that variability, it's important to recognize the descriptor and then how we describe and report the data variability and its dispersion.
• 11:50
  SPEAKER_00: Okay, now we're gonna we're gonna dive just a little bit deeper into that because I want to I want to bring to light some issues about standard error of the mean and standard deviation.
• 12:01
  SPEAKER_00: But really to kind of get there, we have to talk about variations in the sample.
• 12:04
  SPEAKER_00: Remember, you're not studying the entire world.
• 12:08
  SPEAKER_00: That'd be great, right?
• 12:10
  SPEAKER_00: Because then it would be the population mean and average and median, you'd know what those numbers are.
• 12:15
  SPEAKER_00: You're taking a sample of people from the larger population, you study them, and you were tempting to make judgment back or inference back onto the general population as a whole, right?
• 12:30
  SPEAKER_00: Because that's the reality, that's all we can do.
• 12:33
  SPEAKER_00: And as a result of chance alone, okay, when you just grab a sample of people out of the population and you generate their data, and you were to repeat the study again and grab a different set of patients and a sample from the population, those data points might look different.
• 12:56
  SPEAKER_00: Okay, and that's the concept that I want you to see.
• 13:00
  SPEAKER_00: And that's what really is helping us to understand the term standard deviation versus standard error of the mean.
• 13:07
  SPEAKER_00: And some people use the standard error of the mean because it looks tighter, right?
• 13:13
  SPEAKER_00: It somewhat can be uh deceiving if you don't know the difference, okay?
• 13:19
  SPEAKER_00: And if if a if an author is reporting data that way and they don't give you the standard deviation, it's a little bit of a red flag, okay, because it's kind of not being fully honest or transparent.
• 13:33
  SPEAKER_00: So, what I put up here for you on this particular uh slide is to show you this the formula for standard deviation so you know how to calculate it.
• 13:42
  SPEAKER_00: Okay, but remember it's an estimate of the degree of scatter in a sample of data points about that sample's mean.
• 13:52
  SPEAKER_00: Okay, I'm gonna show you a picture here in a second, so this is gonna help a lot.
• 13:57
  SPEAKER_00: But it's most commonly, obviously, with parametric data, so it's continuous.
• 14:02
  SPEAKER_00: It follows a normal distribution, it has a bell curve.
• 14:05
  SPEAKER_00: Look, so that's you can get that mean because you need it.
• 14:09
  SPEAKER_00: Okay.
• 14:10
  SPEAKER_00: Whereas the standard error of the mean, okay, the standard error of the mean here, this is the average variability within a sampling distribution.
• 14:22
  SPEAKER_00: So remember, if you take multiple samples and you now say, well, what are the what is the variability between the means of these samples and their standard deviations?
• 14:32
  SPEAKER_00: And that that visual is right here.
• 14:35
  SPEAKER_00: Okay, so when you talk about a standard deviation, you're talking about one characterizing the data around its mean in one sample, one group from the population.
• 14:50
  SPEAKER_00: But remember, if you so this is over here, let's say you do another study sample from the same population and a third one, they all have their own individual sample means, and inside of each of those study samples they have their own standard deviations.
• 15:09
  SPEAKER_00: But now how do those compare?
• 15:12
  SPEAKER_00: What's the variability?
• 15:14
  SPEAKER_00: Because theoretically, right, if you've appropriately acquired your sample, they should look similar.
• 15:22
  SPEAKER_00: You want them to be close.
• 15:24
  SPEAKER_00: We want small standard deviations and we want smaller standard errors of the mean, because then that means our sample is more likely looking like the general population that we need to apply it to.
• 15:38
  SPEAKER_00: And that's why it matters.
• 15:40
  SPEAKER_00: But it's very important that you understand the difference of what those numbers or those values are telling you.
• 15:48
  SPEAKER_00: And sometimes, if you when you look at it, the standard error of the mean is going to be smaller than standard deviation.
• 15:53
  SPEAKER_00: And I'm going to show you another sort of picture here in a minute because we start thinking about also coefficients of variation.
• 16:02
  SPEAKER_00: Okay.
• 16:02
  SPEAKER_00: Now, this is that sometimes referred to coefficient of variability.
• 16:07
  SPEAKER_00: This is not the same as coefficient of determination, which I don't want to confuse you, right?
• 16:15
  SPEAKER_00: But we're talking about one sample, it's univariate, it's one group of data.
• 16:21
  SPEAKER_00: Coefficients of determination are squared.
• 16:26
  SPEAKER_00: That is about bivariate data, two different things and how they relate and interact with each other.
• 16:35
  SPEAKER_00: Okay?
• 16:36
  SPEAKER_00: So an expression of standard deviation is really a percentage of the sample mean.
• 16:42
  SPEAKER_00: It's univariate, it's around the one sample.
• 16:46
  SPEAKER_00: Okay?
• 16:47
  SPEAKER_00: And the coefficient of variation or C V can be calculated with this formula.
• 16:54
  SPEAKER_00: Okay?
• 16:55
  SPEAKER_00: It's unitless.
• 16:57
  SPEAKER_00: Okay.
• 16:58
  SPEAKER_00: But it helps to normalize the standard deviation by the mean.
• 17:05
  SPEAKER_00: Now, coefficient of variation is also helpful when there's an interest in the size of variance as it relates to the magnitude of observation or the average value.
• 17:16
  SPEAKER_00: Okay, let's think about this in a clinical application because you're like, dear God, what is he talking about?
• 17:22
  SPEAKER_00: Lab tests.
• 17:24
  SPEAKER_00: We order them.
• 17:25
  SPEAKER_00: Sometimes we order them again.
• 17:28
  SPEAKER_00: And we look at the I'll see variability between one sample of one hour and over another.
• 17:34
  SPEAKER_00: Well, is that normal or does that mean something's changed?
• 17:37
  SPEAKER_00: So when we talk about lab test reliability or precision, that is where this coefficient of variation comes in.
• 17:46
  SPEAKER_00: We want a test that has a low coefficient of variation.
• 17:53
  SPEAKER_00: Usually, most lab tests accept something less than 5%.
• 17:58
  SPEAKER_00: Because that means the test is consistent and it's reproducible when the sample is being retested and retested repeatedly.
• 18:08
  SPEAKER_00: That means that the lab is something you can trust.
• 18:13
  SPEAKER_00: Okay, so we want low coefficients of variation and variability inside a lab test so that if we repeat it, that variability that we see sometimes is hopefully so small that it doesn't mean anything.
• 18:28
  SPEAKER_00: It's just the normal lab variance.
• 18:32
  SPEAKER_00: Okay.
• 18:33
  SPEAKER_00: So again, you might get that variable, that percent, depending on the study that you're you're reading about.
• 18:41
  SPEAKER_00: So coefficient of variation, okay?
• 18:44
  SPEAKER_00: When you see a mean plus or minus standard deviation in a table or paper, you need to quickly ask yourself what is the coefficient of variation or the CV?
• 18:56
  SPEAKER_00: Okay.
• 18:57
  SPEAKER_00: A slow CV of less than 5%, typically for labs, that's tight.
• 19:02
  SPEAKER_00: It's a reliable test and data.
• 19:05
  SPEAKER_00: High?
• 19:05
  SPEAKER_00: Again, some people will say 20 to 30 percent, depending on the test.
• 19:11
  SPEAKER_00: Okay, that means there's a lot of scattering going on.
• 19:14
  SPEAKER_00: You need to reinterpret those results a little bit more cautiously.
• 19:18
  SPEAKER_00: Think about why those measurements are varying so much.
• 19:22
  SPEAKER_00: Okay?
• 19:23
  SPEAKER_00: Now recommend, now note that there are the exact accessible that we are okay with coefficients of variation by as differs by the analytic itself and the intra and uh inter assays that are that are done.
• 19:42
  SPEAKER_00: Okay, now visually, we go back to our normal distribution and bell curve where we calculate means, we're able to generate a standard deviation, which then allows us to generate a standard error of the mean, which then also allows us to assess our confidence intervals.
• 20:02
  SPEAKER_00: When you just look at the width of those lines, you see that the standard deviation is always larger than the standard error of the mean.
• 20:12
  SPEAKER_00: And when we teach about this and people look at papers and they read these numbers, what they want to see is tight intervals.
• 20:20
  SPEAKER_00: We don't want those lines to be wide, we want them to be really tight.
• 20:26
  SPEAKER_00: And the way you get them tighter typically is you increase the sample size.
• 20:31
  SPEAKER_00: Because the more you people you include, guess what you start looking more and more alike?
• 20:36
  SPEAKER_00: The populations mean.
• 20:39
  SPEAKER_00: You're regressing towards it.
• 20:42
  SPEAKER_00: Right?
• 20:42
  SPEAKER_00: And that's helpful.
• 20:44
  SPEAKER_00: So this visual should be in your mind about those intervals and what they kind of generically look like and when they're applied, but we're not applying standard deviation to median data.
• 20:56
  SPEAKER_00: You should never see that.
• 20:59
  SPEAKER_00: Mode.
• 21:01
  SPEAKER_00: Okay?
• 21:01
  SPEAKER_00: This is continuous parametric data where your data is meeting certain rules.
• 21:08
  SPEAKER_00: Okay, so the core concepts here are that you use a median, usually implies that if someone did that, they're implying to you there's some outliers.
• 21:18
  SPEAKER_00: Something skewing the data that could affect the mean in one way or the other.
• 21:24
  SPEAKER_00: Okay.
• 21:26
  SPEAKER_00: The standard error of the mean is remember, looking at that variability between samples, and we want it to be small.
• 21:32
  SPEAKER_00: It is smaller than a standard deviation.
• 21:35
  SPEAKER_00: Okay.
• 21:37
  SPEAKER_00: And then 95% confidence interval ranges would include the population result.
• 21:42
  SPEAKER_00: So that's why we want these really tight, narrow confidence intervals because we want to feel confident that the results that we're reading about in this paper are what the population is likely to experience if we apply this information to it.
• 22:00
  SPEAKER_00: Alright, guys.
• 22:01
  SPEAKER_00: So our mission is to impact healthcare for good as we strive together to understand why we do what we do.
• 22:07
  SPEAKER_00: And if you need practice questions structured around this kind of topic area, or you need a structured curriculum if you're a program director or resident, or maybe you want to take it to your program, you know, I've developed some of these tools at high yield med reviews to meet those needs for you.
• 22:23
  SPEAKER_00: Because most of every one of us, I've taken board exams in nursing, pharmacy, and medicine, and every one of them required me to understand biostatistical interpretation.
• 22:31
  SPEAKER_00: Okay, and you can find links to that in our show notes, whether you're at YouTube or on our podcast channels.
• 22:36
  SPEAKER_00: And I hope you that enjoyed this episode.
• 22:38
  SPEAKER_00: Make sure you check out the full analysis of the study data playlist so that you can see the rest of our EBM and biostatistics content, not only at YouTube, but thisiswhy.
• 22:50
  SPEAKER_00: Okay?
• 22:51
  SPEAKER_00: I'm Dr.
• 22:52
  SPEAKER_00: Busai and thank you so much for joining us.
• 22:54
  SPEAKER_00: And if you're enjoying this, please give us a like, subscribe, and leave a comment.
• 22:59
  SPEAKER_00: Uh, maybe contribute to something that you thought also was helpful or that you've learned, because that's how we all learn together.
• 23:05
  SPEAKER_00: And we'll see you on the next lecture.
• 23:07
  SPEAKER_00: Take care.
• 23:08
  SPEAKER_00: Bye.