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Correlation vs R Squared Explained This Is Why It Matters · This Is Why with Dr. Busti

• 0:00
  SPEAKER_00: Alright guys, well, welcome to this lecture where I'm going to be covering the focused topic on correlation coefficients and coefficients of determination.
• 0:11
  SPEAKER_00: Okay, this is the second part of the series in our summary statistics.
• 0:16
  SPEAKER_00: I don't want you to get confused.
• 0:18
  SPEAKER_00: This is not about coefficient of variation or CV.
• 0:21
  SPEAKER_00: That was discussing the measures of central tenancy, which really is geared about one column or one sample of data.
• 0:30
  SPEAKER_00: What this topic is about is looking at when you have two variables or samples of data and you're trying to look at their relationship in association with each other.
• 0:41
  SPEAKER_00: Now you can find the full playlist on our channel at YouTube, or you can go to the website at thisiswhy.health.
• 0:49
  SPEAKER_00: And these concepts are critical for both the researcher who is doing the study, especially at that point of analysis, and the clinician reading and understanding the literature.
• 1:01
  SPEAKER_00: Alright, guys, I'm Dr.
• 1:02
  SPEAKER_00: Bustae, your faculty and host on This Is Why, a show that helps healthcare professionals transform medical knowledge from what to why, because when you know why you do what you do in the proper context of the evidence, it changes how.
• 1:17
  SPEAKER_00: And that changes everything about the patient-oriented decisions that we make every day, doesn't it?
• 1:22
  SPEAKER_00: Okay.
• 1:23
  SPEAKER_00: Now remember, we are part two.
• 1:25
  SPEAKER_00: So just to keep us oriented, if you need that orientation, part one was really about the development of the statistical analysis plan.
• 1:35
  SPEAKER_00: What you do before or what the researcher does before starting their study, right?
• 1:41
  SPEAKER_00: Determining the types of groups, the type of data, is it nominal, ordinal, continuous, and then deciding based on what our outcomes are and that type of data, what are we going to be, what kind of statistical analysis?
• 1:54
  SPEAKER_00: So we're going to be using parametric, non-parametric analysis.
• 1:57
  SPEAKER_00: If we're going to do inferential statistics, right, then we need to establish an alpha and then obviously do power analysis.
• 2:06
  SPEAKER_00: But we're in part two on the summary statistics within the descriptive statistics section.
• 2:12
  SPEAKER_00: Okay, so if you need a little bit of foundation or background on measures of central tendency, variability, and data distribution or dispersion, then you go to that lecture.
• 2:22
  SPEAKER_00: I'm on the measure of correlation and coefficient of determination.
• 2:29
  SPEAKER_00: Okay.
• 2:30
  SPEAKER_00: And then the next section will be on inferential statistics.
• 2:34
  SPEAKER_00: What is the p-value?
• 2:35
  SPEAKER_00: What does it mean?
• 2:36
  SPEAKER_00: 95% confidence intervals and more depth, you know, ratios and those kind of things.
• 2:41
  SPEAKER_00: Okay?
• 2:41
  SPEAKER_00: And then part three is more geared about diagnostic tests in specific.
• 2:46
  SPEAKER_00: Okay?
• 2:47
  SPEAKER_00: Now, correlation coefficient.
• 2:50
  SPEAKER_00: I want you to pay attention to the uh identifier.
• 2:56
  SPEAKER_00: It's the lower, typically the lower case r.
• 3:00
  SPEAKER_00: Okay?
• 3:01
  SPEAKER_00: And it can be either as far as negative one or all the way up to positive one.
• 3:07
  SPEAKER_00: And the strength, what this is looking at is that strength of a relationship between two variables.
• 3:15
  SPEAKER_00: Okay.
• 3:16
  SPEAKER_00: Whereas, you know, things like regression analysis provides the predictability of one variable on another.
• 3:22
  SPEAKER_00: So correlation does not imply causation.
• 3:26
  SPEAKER_00: That's really important.
• 3:28
  SPEAKER_00: Okay, and correlation does not imply causation.
• 3:34
  SPEAKER_00: But the closer the absolute value is to positive one, the stronger the positive correlation or relationship between those variables.
• 3:46
  SPEAKER_00: Okay.
• 3:48
  SPEAKER_00: So that's what that's the range what you're trying to look for.
• 3:51
  SPEAKER_00: That becomes very important.
• 3:52
  SPEAKER_00: Where do we see this fall in our statistical analysis?
• 3:57
  SPEAKER_00: And you may remember this when I went over non-parametric versus parametric statistical analysis in part one.
• 4:04
  SPEAKER_00: Okay, and this table on standardized statistical test is available at thisiswhy.health for you to download.
• 4:12
  SPEAKER_00: It's for free.
• 4:12
  SPEAKER_00: You use it to study for, it's good for board exam stuff.
• 4:15
  SPEAKER_00: You memorize this and you're gonna be alright on an exam.
• 4:19
  SPEAKER_00: If you're preparing to do a study, you're gonna be in good shape using this based on the type of data, how many groups you have to get to that.
• 4:29
  SPEAKER_00: If you're reading the paper and trying to figure out that they do the right thing, this helps you.
• 4:33
  SPEAKER_00: So it's a tool that I've developed and used over time, taught from for many years, that will help you wrap your mind around the core content.
• 4:43
  SPEAKER_00: But where I want to point your attention to, is remember we have two main two main areas.
• 4:48
  SPEAKER_00: We have the non-parametric, which are ordinal and nominal data, okay, and then we have our parametric or continuous data, those are your rows.
• 4:59
  SPEAKER_00: When you go to the far end, there's our measures of correlation for each of those types.
• 5:05
  SPEAKER_00: And I pointed out those studies or the statistical analysis that you would do based on the type of data you're dealing with with these variables, okay?
• 5:16
  SPEAKER_00: So I wanted you to see that.
• 5:19
  SPEAKER_00: So how do we interpret this R value?
• 5:24
  SPEAKER_00: So through a uh though a strong association, which is obviously that positive one, may exist between variables, it does not imply that one event or variable member caused another.
• 5:37
  SPEAKER_00: The R value does not have the ability to determine which one came first.
• 5:43
  SPEAKER_00: So it doesn't form determine the causality, it also doesn't tell you which came first.
• 5:49
  SPEAKER_00: Okay.
• 5:49
  SPEAKER_00: Some other variable may also be influencing the relationship that's not being considered.
• 5:54
  SPEAKER_00: Okay.
• 5:55
  SPEAKER_00: Most complex relationships can rarely be explained by only two variables.
• 6:01
  SPEAKER_00: Okay.
• 6:02
  SPEAKER_00: But a general rule of thumb for the strength, anytime the r is greater than 0.5 in a positive direction, it's usually strong.
• 6:10
  SPEAKER_00: Okay.
• 6:11
  SPEAKER_00: Now, there's Spearman's, Spearman and Pearson's correlation.
• 6:17
  SPEAKER_00: That was from that table.
• 6:19
  SPEAKER_00: And this is predominantly in the context of obviously parametric analysis.
• 6:25
  SPEAKER_00: So continuous data.
• 6:29
  SPEAKER_00: So these are descriptors of strength and the direction of the relationship.
• 6:34
  SPEAKER_00: So Pearson assumes a linear relationship of normally distributed continuous data.
• 6:42
  SPEAKER_00: In Spearman's is for rank-based, non-parametric usually assessments.
• 6:50
  SPEAKER_00: Okay.
• 6:51
  SPEAKER_00: It's more robust for ordinal or skewed data and clinical variables that are common in medicine.
• 6:59
  SPEAKER_00: Now, what about the coefficient of determination?
• 7:03
  SPEAKER_00: Okay, this is also sometimes very confused by the coefficient of variation that I discussed in the measures of central tendency and variability and dispersion.
• 7:15
  SPEAKER_00: Why do I cover it in that lecture and not here?
• 7:18
  SPEAKER_00: Well, because remember, in that lecture, we're talking about the understanding the descriptors about that data in the sample that we studied.
• 7:28
  SPEAKER_00: And in most cases, it's one set of data.
• 7:32
  SPEAKER_00: This is looking at more than that.
• 7:35
  SPEAKER_00: Okay, what are two different variables and how do they how do they re interact with each other?
• 7:41
  SPEAKER_00: Okay?
• 7:45
  SPEAKER_00: So the coefficient of variation, right?
• 7:49
  SPEAKER_00: That C V, the thing that sometimes is confused as a reminder.
• 7:53
  SPEAKER_00: That's the measure of the spread of one set of numbers or how noisy it is around compared to the average.
• 8:00
  SPEAKER_00: It's univariate.
• 8:01
  SPEAKER_00: It looks at one column of data.
• 8:04
  SPEAKER_00: Okay?
• 8:04
  SPEAKER_00: Again, we talked about lab precision and results in that sample, in that discussion.
• 8:10
  SPEAKER_00: Coefficient of determination is r squared.
• 8:17
  SPEAKER_00: How much of the spread in one variable is explained by another variable.
• 8:23
  SPEAKER_00: So there's two.
• 8:25
  SPEAKER_00: And r squared can be from zero all the way up to 100%.
• 8:30
  SPEAKER_00: It's bivariate because it's looking at relationships between two columns or sets of data.
• 8:38
  SPEAKER_00: Okay?
• 8:39
  SPEAKER_00: And so I'm giving you an example here.
• 8:42
  SPEAKER_00: If we think about the number of calories that someone consumes and weight gain, those are two different variables.
• 8:50
  SPEAKER_00: Okay?
• 8:51
  SPEAKER_00: If the R was 0.84, then the R squared is about 0.71.
• 8:59
  SPEAKER_00: That means that 71%, remember it's a percent.
• 9:03
  SPEAKER_00: Coefficient of determination is a percent.
• 9:06
  SPEAKER_00: 71% of the variation of y is accounted for by x.
• 9:13
  SPEAKER_00: So let's make it real as it relates to calories and weight.
• 9:17
  SPEAKER_00: This implies that about 70 to 71% of the variability in weight gain can be attributed to the variability in the amount of calories that we consume.
• 9:28
  SPEAKER_00: Well, we know that's true.
• 9:30
  SPEAKER_00: That makes sense.
• 9:32
  SPEAKER_00: But it's not 100%, is it?
• 9:34
  SPEAKER_00: 70 to 71 percent, okay, depending on how you manipulate the numbers and your math.
• 9:40
  SPEAKER_00: I'm not trying to be nitpicky here, but but there's 30% of something else factoring in, isn't it?
• 9:50
  SPEAKER_00: Some third, fourth, fifth variable, but we don't know what those are.
• 9:54
  SPEAKER_00: So if you just talk about these two variables, how are they influencing each other?
• 10:01
  SPEAKER_00: Okay?
• 10:01
  SPEAKER_00: So when we talk about coefficients, and to keep us all on the same page, because I know this is a little bit kind of wonky, confusing, there's correlation coefficient r, lowercase.
• 10:14
  SPEAKER_00: Remember that's how strong a relationship there are.
• 10:17
  SPEAKER_00: It's not determining causality.
• 10:20
  SPEAKER_00: Then we have coefficient of determination, when it takes that co-correlation coefficient, the r, and square it.
• 10:27
  SPEAKER_00: And that's how much difference that you actually see being explained from one variable over another.
• 10:34
  SPEAKER_00: Okay?
• 10:35
  SPEAKER_00: And then remember that coefficient of variation, Cv, that is how consistent and reliable are these measurements within one sample or group of data.
• 10:48
  SPEAKER_00: Okay?
• 10:49
  SPEAKER_00: I I know.
• 10:50
  SPEAKER_00: You almost have to listen to that twice or three times, and you have to study that terminology.
• 10:56
  SPEAKER_00: But it's important to differentiate the terms, the abbreviations, and what they mean and what you when do you use them.
• 11:04
  SPEAKER_00: Okay, and that's why I orient you back to that table on statistical tests that are the most common.
• 11:10
  SPEAKER_00: It's not exhaustive of everything, right?
• 11:13
  SPEAKER_00: But I can tell you, having done clinical research and then even my own training at Oxford, where in my in my master's in evidence-based healthcare, we used that approach to wrap our minds as we interpret papers.
• 11:29
  SPEAKER_00: So, from a clinical perspective, you need to know how to read a paper and interpret it so you can apply it appropriately.
• 11:34
  SPEAKER_00: That's the one of the steps in evidence-based medicine, right?
• 11:37
  SPEAKER_00: There's five A's.
• 11:39
  SPEAKER_00: And number number four is the apply, and then number five, which everybody ignores, seems to forget, is actually you assessing your own practice of application of evidence to your patients.
• 11:51
  SPEAKER_00: All right, guys, I uh I wanted to make sure I give you some orientation.
• 11:55
  SPEAKER_00: I want to encourage you to continue learning with us as we cover the building blocks needed to confidently and appropriately interpret and understand papers that you read.
• 12:06
  SPEAKER_00: Okay, so I check out the full summary statistics playlist as well as our other EBM and biostatistics playlist at thisiswhy.
• 12:14
  SPEAKER_00: Okay, I'm Dr.
• 12:15
  SPEAKER_00: Busai, and thanks so much for joining us.
• 12:18
  SPEAKER_00: If you're enjoying this content, please leave us a comment, give us a like, subscribe, all that stuff really is appreciated and help.
• 12:26
  SPEAKER_00: But if you need, or you're a program director, faculty, or preceptor, and you want, or you're even a resident, you want to take this to your program, we do offer structured curriculums, even with reports that you can apply to your program.
• 12:38
  SPEAKER_00: We have residency training programs around the country that use this.
• 12:42
  SPEAKER_00: Okay, it's helpful to codify that you've accomplished some knowledge and awareness, especially if you're doing research.
• 12:49
  SPEAKER_00: Okay.
• 12:50
  SPEAKER_00: You can find links to how to get access to that information at High Yield Meta Reviews in the descriptions below in the channel or on our podcast channel.
• 12:59
  SPEAKER_00: So thank you so much for joining.
• 13:01
  SPEAKER_00: I hope you found it helpful.
• 13:03
  SPEAKER_00: We'll see you next time on the next episode.
• 13:05
  SPEAKER_00: Take care, everybody.