One-Way ANOVA in R Studio

Jessie Morrill Author

11/07/2024 Added

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Dr. Jessie Morrill shares how to perform a One-Way ANOVA with Pairwise Comparisons in R Studio.

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[00:00:00.000]All right, so welcome to this video. I am going to be showing you how to run a one-way ANOVA in our studio.
[00:00:15.080]So to do this, you need to have a couple of packages installed onto your computer, and to get started, you need to call those packages to the library.
[00:00:27.060]So the two packages that you need for this example are going to be ggpubr as well as dplyr.
[00:00:35.040]So to call those to the working environment, I'm going to select those two lines of code and click run.
[00:00:41.520]So you can see in the bottom left-hand screen, you can see that those show up in the console indicating that it's been run.
[00:00:49.840]So if you are doing a one-way ANOVA on your own data set,
[00:00:56.460]you would first need to make sure that you set your working directory
[00:01:00.220]and then read in your data file that you have all of your data stored in.
[00:01:06.320]For today's example, I'm not showing you that because I'm going to be using a preloaded R data set.
[00:01:12.840]So you're able to actually follow along with this on your own individual computers without me having to share a data set with you.
[00:01:21.140]So to load this preloaded R data set, you can use...
[00:01:25.860]use the line of code "data" then in parentheses and quotes put in the phrase "plant growth".
[00:01:34.180]It's really important that you have a capital P and a capital G when you type that in and run it.
[00:01:41.740]So you can see in the upper right hand corner now plant growth is a part of our environment.
[00:01:48.060]So to preview that data, you can use the function "head" to give you a preview
[00:01:55.260]of the column headings, and then put in your parentheses "plant growth," select
[00:02:01.500]that line of code, run it. What you can see down in the console is this data
[00:02:07.140]frame has two columns in it. The first column is going to have a value for
[00:02:12.260]weight. That's going to be the response variable that we are looking at. It also
[00:02:16.860]has a column called "group." The group column has the names of all of the
[00:02:22.200]different treatment groups in the particular
[00:02:24.660]data set that we are looking at. To get a better preview of this data, I've
[00:02:30.420]added some code in here to be able to create a ggbarplot. The ggbarplot
[00:02:36.720]function is a part of the GGR package. To be able to take a look at this data,
[00:02:43.920]what we have on the x-axis is each of the treatment groups. On the y-axis, we
[00:02:49.920]have the plant weight again, which is the response variable.
[00:02:54.060]You can see the black dots in each of these bars is going to be
[00:02:59.960]representative of the experimental units that are associated with each of
[00:03:05.880]those treatment groups. Next, what we want to be able to do is calculate some
[00:03:11.860]summary statistics. What I mean by that is we want to be able to know what
[00:03:16.880]is the mean of the control group and the mean of the treatment one group and the
[00:03:23.960]mean of the treatment two group. We also want to know what the standard error of
[00:03:28.560]the mean is. By standard error of the mean, what I'm referring to is the
[00:03:32.900]standard deviation of the response variable, which is weight. To
[00:03:38.460]calculate the standard error of the mean, we also need to take the square root of
[00:03:41.720]n. In this case, that's going to be the square root of the number of
[00:03:46.020]experimental units per treatment group. If you were to count those
[00:03:49.940]dots, we'd be dividing by the square root of the number of those
[00:03:53.860]dots on that bar graph. To be able to calculate those summary
[00:03:58.260]statistics, I've got a couple lines of code here
[00:04:00.920]that I've set equal to plant growth summary. I'm using the function
[00:04:06.560]summarize, and then I'm grouping the data in the original data frame
[00:04:12.040]called plant growth by group. I'm grouping the data by group.
[00:04:18.540]The next thing I'm doing is I'm calculating the mean
[00:04:21.880]weight of
[00:04:23.760]the weight column for each of those treatment groups, and then I'm
[00:04:28.500]calculating the SEM, or standard error of the mean, and the equation that I'm
[00:04:33.060]using to do that is the standard deviation of weight divided by the
[00:04:37.440]square root of n. So if I run this line of code, these few lines of code, what
[00:04:42.660]ends up happening? You can see now in the environment that we have an object
[00:04:48.420]called plant growth summary. It has three observations of three variables.
[00:04:53.660]So now if I come down and I want to display those summary statistics, I'm
[00:04:59.120]going to select plant growth summary, run that, and it'll show up in my console
[00:05:06.160]down in the bottom left of my screen. And so you can see in the first column we
[00:05:11.960]have the groups, which is control treatment 1 and treatment 2. We also have
[00:05:16.780]the mean weight that we calculated, which is going to be 5.03, 4.66, and
[00:05:23.560]5.53. So if you come over to your bar graph, you can see
[00:05:28.420]see that the control group is approximately five. You can see that treatment one is slightly lower
[00:05:35.630]than that, around 4.66, and then you can see that the treatment two group is higher than the rest of
[00:05:43.630]those in the value for the mean here. The top of the bar is 5.53. You can also see the standard
[00:05:51.310]error of the mean, and so for the control group, that's going to be 0.18, and so you can also
[00:06:00.350]appreciate that in this data set, the largest standard error of the mean is 0.25, and if you
[00:06:09.590]look here on the error bars of each of these three treatment groups, the one with the largest error
[00:06:18.270]bars is going to be this treatment one group.
[00:06:21.010]And you can see the length of these error bars around the mean, and that happens to be the
[00:06:27.850]largest one. So being able to plot the data always helps me to be able to make sense of the numbers
[00:06:34.870]that I see in my summary statistics, and so it's a good habit to always do, and it also just gives
[00:06:41.610]you more confidence in understanding what's happening with your data set when you're working
[00:06:46.650]to interpret the results.
[00:06:48.870]So now the next thing we want to do...
[00:06:50.970]...is actually run the ANOVA.
[00:06:53.310]So the function to be able to run an analysis of variance is abbreviated AOV, analysis of variance.
[00:07:01.850]And then in parentheses, what we have first is we have the...
[00:07:06.210]oops, excuse me.
[00:07:07.230]We have the response variable, which happens to be weight.
[00:07:13.350]And then we have, in this case, the identifier for the treatment groups.
[00:07:19.690]And so this is referring to...
[00:07:20.970]to the column where all the treatment groups are indicated in the data frame.
[00:07:25.970]And that happened to be called group.
[00:07:27.990]So next, in this particular function, we need to tell R what data set to look at.
[00:07:35.430]So in this case, the data that we are looking at is called plant growth.
[00:07:39.350]So we're going to go ahead and run this line of code.
[00:07:43.030]And we're setting it equal to plant growth AOV.
[00:07:47.170]So when we run that, now you can see...
[00:07:50.850]Plant growth AOV shows up as a list of 13 items in the working environment.
[00:07:59.070]So now if we come down and want to display the results of that ANOVA in table format,
[00:08:07.030]we're going to use the word summary and then in parentheses put plant growth AOV.
[00:08:12.310]Now if we run that, the ANOVA table shows up in our console.
[00:08:19.190]And you can see...
[00:08:20.730]The sums of squares, you can see the degrees of freedom for the group as well as the residuals.
[00:08:26.310]You can see the mean square error.
[00:08:28.370]You can also see the F value as well as the P value.
[00:08:32.590]So in this case, the P value ends up being 0.0159.
[00:08:38.290]Now with ANOVA, any time that you have a P value that is considered significant for this effect that we are looking at,
[00:08:50.610]we are able to do something called pairwise comparisons.
[00:08:53.610]What pairwise comparisons essentially is, is it's a t-test that allows us to compare each of the treatment groups that we have to each other.
[00:09:03.610]So it allows us to compare the control group only to treatment 1 and the control group only to treatment 2,
[00:09:11.610]and then treatment 1 compared to treatment 2.
[00:09:15.610]And so to be able to do those pairwise comparisons, to be able to determine
[00:09:20.490]if our treatment groups are different from each other, we can use the function "tukiHSD".
[00:09:28.370]And then in parentheses, what we put is the plant growth AOV results that we have.
[00:09:34.370]And if we run that, what you end up getting is now the pairwise comparisons for each of the treatments.
[00:09:42.370]So we have treatment 1 versus the control.
[00:09:45.370]You can see that the p-value comes out to be 0.39.
[00:09:50.370]So that's not considered to be significantly different.
[00:09:53.250]Next, we can look at treatment 2 versus the control.
[00:09:57.250]And you can see that treatment 2 versus the control has a p-value of 0.19,
[00:10:02.250]which in our case we're going to say is not considered significantly different.
[00:10:06.250]Next, you can see treatment 2 versus treatment 1.
[00:10:10.250]The p-value comes out to be 0.01.
[00:10:14.250]And so in our case, that is going to be considered statistically significant.
[00:10:20.250]So you can appreciate that the control is intermediate between treatment 1 and treatment 2.
[00:10:27.130]And the control is not statistically different from treatment 1 or treatment 2.
[00:10:36.130]But you can appreciate that treatment 1 has the lowest mean value
[00:10:41.130]and is statistically different from treatment 2, which does happen to have the highest mean value.
[00:10:50.130]Thank you for watching this video, and I encourage you to try this out using both the plant growth data as well as the data set that you have.

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One-Way ANOVA in R Studio

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