BIO2POS: DA Computer Lab 3

Topic 3: ANOVAs in jamovi

Welcome to Computer Lab 3 for the Data Analysis (DA) component of BIO2POS!

In DA Topic 3, we introduced one-way ANOVA (analysis/analyses of variance) and repeated measures ANOVA, which can be viewed respectively as generalisations of the two sample \(t\)-tests and paired samples \(t\)-tests we discussed in the previous topic. We covered the assumptions of these different tests and the relevant post-hoc testing procedures, and also outlined the corresponding non-parametric tests.

In this computer lab, you will continue to learn how to use the statistical software jamovi, and conduct various ANOVA and the equivalent non-parametric tests using real data sets. You will also learn how to interpret and summarise jamovi output for these tests.

Learning Outcomes

These labs are designed to provide you with plenty of opportunities to practice different aspects of the statistical content covered in the lectures.

Each lab consists of core questions (with the 🌱 symbol) and extension questions (with the 🌳 symbol).

• We recommend that you aim to complete at least the core component question(s) within the scheduled lab time
• If you have time, you can work through the extension component question(s) either during the lab, or later in your own time
• We recommend that you aim to complete all questions before the next DA lecture

Having completed this lab, you will be able to conduct the following tests and calculations in jamovi:

• one-way ANOVA
• one-way repeated measures ANOVA
• ANOVA post-hoc testing
• Kruskal-Wallis test
• Friedman test

You will also be able to interpret the results of the above statistical techniques, check the assumptions of the tests, and provide clear summary statements highlighting the key statistical outputs of the models.

Before you begin, please check the following:

1. Have you attended this week’s lectures/watched the lecture recordings?
2. Have you completed this week’s DA Revision Quiz?

Please aim to complete Step 1 before starting this lab, as doing so will help you to better understand the content covered. Please aim to complete Step 2 before the next week of DA content.

1 Preparations: Wolf River Data 🌱

For the first question in this computer lab we will analyse data on the distribution of toxic substances in the Wolf River in Tennessee, USA, collected by Jaffe et al. (1982). The concentration levels of certain hydrophobic substances, which are toxic to the environment through bioaccumulation, were recorded at different depth levels in the river. These substances include Aldrin, a toxic pesticide now banned in most countries, and Hexachlorobenzene (HCB), a toxic fungicide now banned worldwide. The variables in the data include:

• Aldrin: Concentration level of Aldrin (ng/L)
• HCB: Concentration level of HCB (ng/L)
• Depth: Depth level at which recordings were taken (1 = surface, 2 = mid-depth, 3 = bottom).

Note that Depth is a fixed factor since recordings have been made at specific depth levels.

Figure 1.1: Note. From File:Wolf-river-york-tn1.jpg, by Brian Stansberry, 2009, Wikimedia Commons (https://commons.wikimedia.org/). CC BY 3.0 DEED

jamovi

a.

The Wolf River data is available in this week’s tile on LMS, in the file wolf_river.omv. Download this file now, and save it on your computer. Also open up a Word document, in which you can write down your responses and save your jamovi output as you work through the lab.

You may like to save the data and Word document to your OneDrive, so you can access them easily at a later date.

b.

Open up jamovi and load in the wolf_river.omv file.

R

a.

If you would like to analyse this Wolf River data in R, you can download either the wolf_river.omv or wolf_river.csv file in the DA Topic 3 tile on LMS. Also open up a text document (e.g. a Word document), in which you can write down your responses and save your R output as you work through the lab. Alternatively, you can simply save your R script, as the code you write is reproducible.

It is recommended that you save all your lab work, e.g. on OneDrive, so that you can access it easily at a later date.

b.

Open up RStudio, then:

• Open a new R script (Ctrl + Shift + N in Windows, or go to File -> New File -> R Script),
• Set your Working Directory to where you downloaded the Wolf River data,
• Load the data into RStudio using either the read_omv or read.csv function, as appropriate, storing the data in the object wolf_river.

You should now see wolf_river listed in the Environment section of RStudio in the top right - this means the data is loaded in RStudio, and ready for analysis!

If you get stuck at any point, just expand the Details box below.

Recall that to set your Working Directory (where R looks for files), the two simplest options in RStudio are:

• Press Ctrl + Shift + H in Windows (Cmd + Shift + H in Mac), then navigate to where you saved your file (e.g. your `Downloads’ folder), or
• In the menu panel in the top right, go to Session -> Set Working Directory -> Choose Directory… (see screenshot below for reference)

Recall that to open .omv files in R, we’ll need the jmvReadWrite package installed and loaded. If you are not sure whether you have this package, copy-paste and then run the following code in your R script, one line at a time.

install.packages("jmvReadWrite") # this line installs the package we need
library(jmvReadWrite) # this line loads the package in our current session
# Note that anything after a # is called a comment in R, and isn't treated as executable code

Recall that you can use the read_omv and read.csv functions as follows:

wolf_river <- read_omv("wolf_river.omv") # or
wolf_river <- read.csv("wolf_river.csv", header = T) 

2 Wolf River ANOVA 🌱

Suppose that we are interested in determining if the concentration level of the toxic substance Aldrin in Wolf River is different at different depth levels. Having more information on this could lead to a better understanding of how best to improve the health of the river.

Over the next few steps, we will conduct a one-way ANOVA in jamovi, to determine whether there is a difference in the mean Aldrin concentration levels at different depths in Wolf River.

As you progress, copy the relevant output into your Word document.

Since we have Aldrin concentration records at three specific depth levels, it is more appropriate to use an ANOVA than a t-test here.

If you would like to refresh your memory on one-way ANOVAs, check the Topic 3A lecture.

jamovi

2.0.1

To begin, write out an appropriate null hypothesis and alternative hypothesis for this one-way ANOVA, and make sure to define any notation you introduce.

2.0.2

To begin the analysis, click on the Analyses tab, and then click on ANOVA and select One-Way ANOVA.

Since we are interested in the Aldrin values, drag the Aldrin variable across to the Dependent Variables box. To separate the Aldrin results by the different Depth specifications, drag the Depth variable across to the Grouping Variable box.

Make sure at this stage to have the Assume equal (Fisher's) box selected.

You will see that some automatic results will already appear in the Results section - the initial stage for our one-way ANOVA is already complete!

2.0.3

Before we begin interpreting the one-way ANOVA results, we should also obtain some other details.

Under the Additional Statistics heading, select Descriptives table and Descriptives plots

What do you notice about the change in the mean Aldrin levels across the different river depth levels? Based solely on the descriptives outputs, does it appear that there is a significant difference in means?

2.0.4

Identify the number of categories \(c\) and the sample size \(n\), and use these values to compute \(df_1\) and \(df_2\) for this one-way ANOVA.

Verify that your calculations are correct by checking the jamovi output.

2.0.5

Before we proceed further, we should confirm if the Fisher’s \(F\)-test version of the one-way ANOVA is appropriate to use.

Under the Assumption Checks heading, select Homogeneity test. Based on the Levene’s test result, should we use the Fisher’s or Welch’s \(F\)-test here?

2.0.6

At this stage, we should also check the ANOVA assumption of normality. We have a couple of options here, but at this stage we will keep it simple - under the Assumption Checks heading, select the Normality test and Q-Q Plot boxes, and assess the results.

2.0.7

Regardless of your previous findings, assume for the remainder of this question that the one-way ANOVA has produced a statistically significant result, and that all test assumptions have been satisfied.

The next step is to conduct a post-hoc test. Click on the Post-Hoc Tests section, and select the appropriate option under the Post-Hoc Test heading.

Which specific pairwise comparison(s) is/are statistically significant? Make sure to explain your reasoning clearly.

If our ANOVA yields a statistically significant result, our work is not yet done - we need to conduct post-hoc tests to identify the specific statistically significant difference(s).

2.0.8

Write a clear summary based on your one-way ANOVA and post-hoc test results, in the style presented in the lectures. Make sure to summarise your conclusions about the ANOVA assumptions, and to note key details such as \(p\)-values.

R

2.0.1

To begin, write out an appropriate null hypothesis and alternative hypothesis for this one-way ANOVA, and make sure to define any notation you introduce.

2.0.2

To conduct a one-way ANOVA in R, we will need to use the aov function. The general format for this function is as follows:

aov(formula, data = ...)

With the formula argument, we need to specify the relationship we are checking, and our chosen variables.

In order to check the test assumptions and output, it will be helpful to assign the ANOVA results to a new object, e.g. anova_wolf. In this instance, we can use:

anova_wolf <- aov(formula = Aldrin ~ Depth, data = wolf_river)

The initial stage for our one-way ANOVA is already complete!

2.0.3

Before we begin interpreting the one-way ANOVA results, we should also obtain some other details.

Using the following code as a starting point, check the sample mean Aldrin levels across the different river depth levels - do you notice any changes?

mean(wolf_river[wolf_river$Depth == "Surface", ]$Aldrin)

Based solely on these results, does it appear that there is a significant difference in means?

2.0.4

Identify the number of categories \(c\) and the sample size \(n\), and use these values to compute \(df_1\) and \(df_2\) for this one-way ANOVA.

Verify that your calculations are correct by checking your R output, using the summary function to obtain the key details of the test:

summary(anova_wolf)

2.0.5

Before we proceed further, we should confirm if the Fisher’s \(F\)-test version of the one-way ANOVA is appropriate to use.

Therefore, we need to check the underlying assumption of homogeneity of variances, via the Levene’s test.

Recall that this can be done with the leveneTest function, which is contained within the car package, which should be pre-installed with R. So we will need to load the car package before we can use the leveneTest function.

Run the following code, one line at a time, to conduct the test:

library(car)
leveneTest(anova_wolf)

Based on the Levene’s test result, should we use the Fisher’s or Welch’s \(F\)-test here?

If we decide to use the Welch’s version here, we may need to use the oneway.test function instead of the aov function - the good news is, the argument format remains the same.

2.0.6

At this stage, we should also check the ANOVA assumption of normality. We have a couple of options here, but at this stage we will keep it simple, and check the normal Q-Q plot, and conduct the Shapiro-Wilk test.

Since we have stored all our ANOVA results in the object anova_wolf, we can now access specific components using the $ operator - if you start typing out anova_wolf$, you should see a list of options appear - we want to select the residuals option, i.e. we want to use the line of code anova_wolf$residuals to access the residuals.

Details on conducting the checks above are included below.

Remember that for ANOVA, we check the normality assumption by assessing the residuals creating during the fit of the ANOVA model, not the original data.

To create a Normal Q-Q plot, we can use the following code:

qqnorm(anova_wolf$residuals)
qqline(anova_wolf$residuals)

To conduct the Shapiro-Wilk Normality Test, we can use the built-in shapiro.test function, as follows:

shapiro.test(anova_wolf$residuals)

2.0.7

Regardless of your previous findings, assume for the remainder of this question that the one-way ANOVA has produced a statistically significant result, and that all test assumptions have been satisfied.

The next step is to conduct a post-hoc test. We have several options for this process in R. We will keep it simple though, and use the Tukey’s HSD post-hoc test, which is a solid choice in most scenarios (if we had concerns about the equal variances assumptions, the Games-Howell approach may be a better option, but this requires a further package).

Run the following R code to conduct the Tukey HSD post-hoc test:

TukeyHSD(anova_wolf)

Which specific pairwise comparison(s) is/are statistically significant? Make sure to explain your reasoning clearly.

If our ANOVA yields a statistically significant result, our work is not yet done - we need to conduct post-hoc tests to identify the specific statistically significant difference(s).

2.0.8

Write a clear summary based on your one-way ANOVA and post-hoc test results, in the style presented in the lectures. Make sure to summarise your conclusions about the ANOVA assumptions, and to note key details such as \(p\)-values.

3 Wolf River ANOVA #2 🌱

In jamovi, there are actually two ways to conduct a one-way ANOVA. You have just completed the simpler process in Question 2, using the One-Way ANOVA section.

Over the next few steps, we will repeat the one-way ANOVA analysis from Question 2, this time using the second process.

This process will yield the same results, but provides options for the inclusion of additional details, like effect sizes.

As you progress, copy the relevant output into your Word document.

3.0.1

In the Analyses tab in the top menu bar, click on ANOVA and select ANOVA. This will open a new section, with some new choices.

To begin, drag Aldrin to the Dependent Variable box, and drag Depth across to the Fixed Factors box.

You should see some automatic results appear in the Results section.

3.0.2

Check the \(F\) and \(p\)-values in the ANOVA results, and confirm that they match the results you obtained in part 2.0.2.

3.0.3

Select the \(\eta^2\) box under the Effect Size heading, and interpret the result.

To refresh your memory on the \(\eta^2\) effect size, check slides 17-18 of the DA Topic 3B lecture.

3.0.4

When checking the ANOVA normality assumption, it can be helpful to produce a histogram of the residuals.

1. Down the bottom of the ANOVA section, click on Save, and select the Residuals box.
2. Navigate to the Exploration -> Descriptives section - you should see that you now have a new variable, Residuals, in your data set.
3. Create a histogram and Q-Q plot using the Residuals data, and verify that the Q-Q plot is identical to the one you obtained in part 2.0.6

Does the histogram of residuals support the assumption of normality?

When conducting one-way ANOVA analyses in jamovi, we recommend that you use the approach described in part 2.0.2, and supplement the results by obtaining the effect size and residuals histogram via the second approach described here.

4 Wolf River Kruskal-Wallis test 🌱

Suppose that after conducting your analysis in parts 2.0.2 and 3 you have some lingering concerns that the one-way ANOVA assumptions have been violated. Therefore, you decide to conduct a Kruskal-Wallis test, the non-parametric alternative test.

jamovi

4.0.1

To begin, write out an appropriate null hypothesis and alternative hypothesis, given we are testing Aldrin levels across different Depth levels.

4.0.2

In the Analyses tab in the top menu bar in jamovi, click on ANOVA and select One-Way ANOVA - Kruskal Wallis, under the Non-Parametric subsection.

You will see that the options available are fairly sparse, which makes the analysis process here straightforward.

To begin, just as in the previous analyses, drag Aldrin and Depth across to the appropriate boxes.

Also select DSCF pairwise comparisons.

Do not worry about selecting Effect size, as this will be a different effect size to both Cohen’s \(d\) and \(\eta^2\), and we have not covered this in the lectures.

4.0.3

Write a clear summary of the Kruskal-Wallis analysis, in the style presented in the lectures.

R

4.0.1

To begin, write out an appropriate null hypothesis and alternative hypothesis, given we are testing Aldrin levels across different Depth levels.

4.0.2

In R, we can use the kruskal.test function to conduct the Kruskal-Wallis test, and the argument format is quite similar to that of the earlier aov function, e.g.:

kw_wolf <- kruskal.test(Aldrin ~ Depth, data = wolf_river)
kw_wolf

If we find that our test result is statistically significant, we can conduct a post-hoc pairwise comparisons test using the following code:

install.packages("PMCMRplus")
library(PMCMRplus)
dscfAllPairsTest(Aldrin ~ Depth, data = wolf_river)

Note that the above code conducts the DSCF pairwise comparison, as used in the jamovi version of this question. Another good option is Dunn’s test, which requires the FSA library.

Do not worry about checking for the Effect size, as this will be a different effect size to both Cohen’s \(d\) and \(\eta^2\), and we have not covered this in the lectures.

4.0.3

Write a clear summary of the Kruskal-Wallis analysis, in the style presented in the lectures.

5 Background Noise Repeated Measures ANOVA 🌱

Figure 5.1: Note. From File:Colour soundwave.svg, by KMpumlwana (WMF), 2022, Wikimedia Commons (https://commons.wikimedia.org/). CC0 1.0 DEED

In this question we will consider data provided by Walker (2008) on people’s performance of a task under various levels of background noise. The variables in the data include:

• Subject: The subject number assigned to an individual in the study
• Sex: The sex of the individual (1 = male, 2 = female)
• None: Performance with no background noise
• Low: Performance with low background noise
• Medium: Performance with medium background noise
• High: Performance with high background noise

Since we have multiple recordings for the same individual here, a one-way ANOVA is not appropriate to apply to this data. Instead, we can use a Repeated Measures ANOVA.

If you would like to refresh your memory on repeated measures ANOVAs, check the Topic 3B lecture.

jamovi

The noise data is available in this week’s tile on LMS, in the file noise_data.omv. Download this file now, and open it in jamovi.

Over the next few steps, we will conduct a one-way repeated measures ANOVA in jamovi, to determine whether there is a difference in people’s performance scores under different noise conditions.

As you progress, copy the relevant output into your Word document.

5.0.1

Write out an appropriate null hypothesis and alternative hypothesis for this one-way repeated measures ANOVA analysis.

5.0.2

As a quick initial check, create a descriptives table for the 4 noise levels in the Exploration section. What do you notice about the mean performance scores across the 4 noise levels?

5.0.3

To begin the analysis, click on the Analyses tab, and then click on ANOVA and select Repeated Measures ANOVA.

The layout here can appear a little daunting at first, but we will take it a step at a time.

5.0.3.1

In the Repeated Measures Factors box, you will see RM Factor 1, with Level 1 and Level 2 listed, and Level 3 greyed out. It is in this section that we list all the recordings settings for our data.

1. Click on RM Factor 1 and change it to Noise Level
2. Click on and replace Level 1, Level 2 etc with the 4 levels None, Low, Medium and High.
3. Drag the 4 variables across to the relevant lines in the Repeated Measures Cells box.

You should see some automatically generated results appear in the Results section.

5.0.3.2

Identify the number of categories \(k\) and the sample size \(n\), and use these values to compute \(df_1\) and \(df_2\) for this one-way repeated measures ANOVA.

Verify that your calculations are correct by checking the jamovi output.

5.0.3.3

Under the Assumptions Checks section, select Sphericity tests to conduct the Mauchly’s sphericity test, as well as the Greenhouse-Geisser and Huynh-Feldt tests simultaneously.

Based on the output, what can you conclude about the sphericity assumption? Can we use the default \(F\) test here, or do we need to apply a correction?

If you believe a correction is required, select the appropriate box under the Sphericity corrections subheading before continuing.

5.0.3.4

Select the \(\eta^2\) effect size box, and interpret the output.

5.0.4

Regardless of your previous findings, asssume that post-hoc tests are justified for this analysis.

In the Post Hoc Tests section, drag Noise Level to the right-hand-side box, and select both the Tukey and Bonferroni boxes under the Corrections subheading.

Compare the results. At the 5% level of significance, are there any pairwise comparisons which are only statistically significant according to one of these two methods?

5.0.5

Write a clear summary based on your one-way repeated measures ANOVA and post-hoc test results, in the style presented in the lectures. Make sure to discuss each of the pairwise comparisons.

R

If you would like to analyse this noise data in R, you can download either the noise_data.omv or noise_data.csv file in the DA Topic 3 tile on LMS.

Over the next few steps, we will conduct a one-way repeated measures ANOVA in R, to determine whether there is a difference in people’s performance scores under different noise conditions.

As you progress, copy the relevant output into your Word document.

5.0.1

Write out an appropriate null hypothesis and alternative hypothesis for this one-way repeated measures ANOVA analysis.

5.0.2

As a quick initial check, use the summary function to check some of the key descriptive statistics for the 4 noise levels. What do you notice about the mean performance scores across the 4 noise levels?

5.0.3

Repeated measures analyses in R are a little more complicated than our previous analyses. There are several packages we could use, and the data structure needs to be in a specific format. The process outlined below is just one of several potential options.

For this repeated measures analysis, we will use the anova_test function from the rstatix package. We will also reformat our data using the pivot_longer function from the tidyr package.

To begin, run the following code, line by line:

install.packages("rstatix"); install.packages("tidyr")
library(rstatix); library(tidyr)

5.0.3.1

Then, read in your noise data and store it in the object noise.

Next, we will reformat our noise data to be in long format, which means we have one row of data per observation (originally, our data was in wide format, with one row of data per individual subject):

long_noise <- pivot_longer(noise,
                           cols = c("None", "Low", "Medium", "High"),
                           names_to = "Noise_Level",
                           values_to = "Outcome")

Take some time to check the code, the output, and the original noise data, to make sure you understand what has changed.

5.0.3.2

Now, we can conduct the repeated measures ANOVA using the following code:

rm_model <- anova_test(long_noise, dv = Outcome, wid = Subject, within = Noise_Level)

Here, dv is out dependent variable, i.e. our outcome, wid is our participant ID, and within is our within-subject factor (in this case, the noise level values recorded for each individual).

5.0.3.3

One benefit of using this anova_test function compared to some of the alternatives out there is that it conducts the Mauchly’s Sphericity test automatically, as well as the Greenhouse-Geisser and Huynh-Feldt tests - just run rm_model to see all the output.

Based on the output, what can you conclude about the sphericity assumption? Can we use the default \(F\) test here, or do we need to apply a correction?

Applying corrections here gets a little more complicated, and further packages are required, so for the time being, we will not cover continuity correction adjustments in R.

5.0.3.4

The ges output is the generalised \(\eta^2\) effect size. Check your rm_model output, and interpret this effect size result.

5.0.4

Regardless of your previous findings, asssume that post-hoc tests are justified for this analysis.

To conduct post-hoc pairwise comparisons, we will use the Bonferroni approach, via the following code:

posthoc <- pairwise_t_test(data = long_noise,
                           formula = Outcome ~ Noise_Level,
                           paired = TRUE,
                           p.adjust.method = "bonferroni"
                           )

At the 5% level of significance, are there any pairwise comparisons which are statistically significant?

5.0.5

Write a clear summary based on your one-way repeated measures ANOVA and post-hoc test results, in the style presented in the lectures. Make sure to discuss each of the pairwise comparisons.

6 Background Noise Friedman Test 🌱

jamovi

Suppose that a non-parametric test is more appropriate for your analysis of the noise_data.omv data set. Using Analyze > Nonparametric Tests > Related Samples, carry out a Friedman test to compare the performance scores across the four noise levels.

6.0.1

To begin, write out an appropriate null hypothesis and alternative hypothesis, given we are testing performance scores across different noise levels.

6.0.2

In the Analyses tab in the top menu bar in jamovi, click on ANOVA and select Repeated Measures ANOVA - Friedman, under the Non-Parametric subsection.

You will see that the options available are fairly sparse, which makes the analysis process here straightforward.

To begin, drag the 4 noise variables across to the Measures box.

Also select the Pairwise comparisons (Durbin-Conover), Descriptives and Descriptive plot - medians boxes.

6.0.3

Write a clear summary of the Friedman analysis, in the style presented in the lectures.

R

To conduct a Friedman test in R to compare the performance scores across the four noise levels, we can take the following approach, using the long_noise data we created earlier.

6.0.1

To begin, write out an appropriate null hypothesis and alternative hypothesis, given we are testing performance scores across different noise levels.

6.0.2

We will use the friedman_test function, which is from the rstatix package, meaning that we don’t need to install or load any additional packages. Run the following code to conduct the test:

friedman_noise <- friedman_test(long_noise, Outcome ~ Noise_Level | Subject)

While the Durbin-Conover test isn’t available within the rstatix package, we can use a similar test, namely pair-wise Wilcoxon tests, for our post-hoc checks:

pairwise_wilcox_test(
                     data = long_noise,
                     formula = Outcome ~ Noise_Level,
                     paired = TRUE,
                     p.adjust.method = "bonferroni"
                     )

6.0.3

Write a clear summary of the Friedman analysis, in the style presented in the lectures.

If you have made it to this stage by the end of the lab, that’s great! This was quite a long lab. Completing the core questions will prepare you well for upcoming assessments. The following extension questions will help consolidate and extend your understanding of the material.

7 Pea Plant Data 🌳

Recall that in DA Computer Lab 1 we introduced a raw, messy data set on dwarf pea plant seedlings, which had been collected as part of an experiment in an LTU BIO1AP lab class in 2022. Figure 7.2 below contains this data.

Previously, we produced descriptive statistics and some initial plots of this data, and then conducted some \(t\)-tests on this data in DA Computer Lab 2. However, using the two sample \(t\)-tests, we were limited to comparing two groups at once. Now, using the ANOVA procedures we have learnt, we can compare all three groups of seedlings at once.

Figure 7.1: Note. From File:Leaves of Pisum sativum (2).JPG, by Chmee2, 2011, Wikimedia Commons (https://commons.wikimedia.org/). CC BY 3.0 DEED

Background Information

To recap, in this experiment dwarf pea plant (Pisum sativum) seedlings were exposed to different concentrations of gibberellic acid (GA), in order to study the effect of GA application on plant growth. These dwarf pea plants are naturally deficient in GA, due to a mutation of a gene in the pathway for biosynthesis of GA. Therefore it is of interest to determine if application of GA to the seedlings has an impact.

For the experiment, each pea plant seedling was assigned to one of three groups, and then carefully sprayed:

• C: a control group, were sprayed with water
• TA: a treatment group, were sprayed with a 25mg/L solution of GA
• TB: a treatment group, were sprayed with a 50mg/L solution of GA

The height of the seedlings was then recorded at a later date. The pea plant data in Figure 7.2 has pea plant height (in mm) recordings, for the three treatments, across 7 different benches.

Note that the number of seedlings (1 to 6) in each of the three groups varied between benches, and that some recordings were crossed or scribbled out (perhaps due to the seedling being damaged or dying).

Figure 7.2: Pea Plant Raw Data

7.1

In DA Computer Lab 1 or DA Computer Lab 2 you should have created a data file in jamovi containing the cleaned pea plant data. If for whatever reason you do not have this data file saved, you can find a copy of the data in this week’s tile on LMS, in the file pea_plant_seedlings_data.omv.

7.2

Suppose that we are interested in comparing the growth of the seedlings in the three different groups. Using an appropriate ANOVA method, test in jamovi if there is a difference in the mean height, at time of measurement, of the pea plant seedlings in the different groups (C, TA, TB).

Write a clear summary statement, and make sure to copy the relevant jamovi output to your Word document.

Assume that this mean value is for seedlings which have been growing for the same amount of time as the seedlings in the the BIO1AP experiment had been, when their data was recorded in Figure 7.2.

Make sure you check any relevant test assumptions before concluding your test.

7.3

Do you think it would be worthwhile to also conduct an ANOVA across the different lab benches? Discuss this with other students and/or your lab demonstrator.

8 Wolf River HCB ANOVA 🌳

Conduct an appropriate analysis of the HCB variable in the wolf_river.omv data set.

Well done! That concludes the DA Topic 3 jamovi computer lab.

Before you finish up, make sure to save both your Word document and your pea plant jamovi file to your OneDrive, for future reference.

References

Jaffe, P. R., Parker, F. L., and Wilson, D. J. (1982). Distribution of toxic substances in rivers. Journal of the Environmental Engineering Division, 108(4), 639-649.

Walker, I. (2008). Repeated-measures/split-plot ANOVA: noisedata [Data file]. https://web.archive.org/web/20210506222824/https://people.bath.ac.uk/pssiw/stats2/page16/page16.html

These notes have been prepared by Rupert Kuveke and other members of the Department of Mathematical and Physical Sciences. The copyright for the material in these notes resides with the authors named above, with the Department of Mathematical and Physical Sciences and with the Department of Environment and Genetics and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License BY-NC-ND.