2023-24-PSYC122-w17-workbook-answers

Author

Rob Davies

Published

February 26, 2024

Introduction

In Week 17, we aim to further develop skills in visualizing and testing the associations between variables in psychological data.

We do this to learn how to answer research questions like:

What person attributes predict success in understanding?
Can people accurately evaluate whether they correctly understand written health information?

These kinds of research questions can be answered using methods like the linear model.

When we do these analyses, we need to think about how we report the results:

we usually need to report information about the kind of model we specify;
and we will need to report the nature of the association estimated in our model;
we usually need to decide, is the association significant?
does the association reflect a positive or negative relationship between outcome and predictor?
and is the association we see in our sample data relatively strong or weak?

We will consolidate and extend learning on data visualization:

focusing on how we edit ggplot() code to produce professional looking plots.

Naming things

I will format dataset names like this:

study-two-general-participants.csv

I will also format variable (data column) names like this: variable

I will also format value or other data object (e.g. cell value) names like this: studyone

I will format functions and library names like this: e.g. function ggplot() or e.g. library {tidyverse}.

The data we will be using

In this activity, we use data from a second 2020 study of the response of adults from a UK national sample to written health information:

study-two-general-participants.csv

Answers

Step 1: Set-up

To begin, we set up our environment in R.

Task 1 – Run code to empty the R environment

rm(list=ls())

Task 2 – Run code to load relevant libraries

library("tidyverse")

Warning: package 'tidyr' was built under R version 4.1.1

Warning: package 'purrr' was built under R version 4.1.1

Warning: package 'stringr' was built under R version 4.1.1

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.4
✔ forcats   1.0.0     ✔ stringr   1.5.0
✔ ggplot2   3.4.4     ✔ tibble    3.2.1
✔ lubridate 1.9.2     ✔ tidyr     1.3.0
✔ purrr     1.0.1     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Step 2: Load the data

Task 3 – Read in the data file we will be using

The data file is called:

study-two-general-participants.csv

Use the read_csv() function to read the data file into R:

study.two.gen <- read_csv("study-two-general-participants.csv")

Rows: 172 Columns: 12
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (5): participant_ID, study, GENDER, EDUCATION, ETHNICITY
dbl (7): mean.acc, mean.self, AGE, SHIPLEY, HLVA, FACTOR3, QRITOTAL

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

When you read the data file in, give the data object you create a distinct name e.g. study.two.gen.

Task 4 – Inspect the data file

Use the summary() or head() functions to take a look.

head(study.two.gen)

# A tibble: 6 × 12
  participant_ID mean.acc mean.self study     AGE SHIPLEY  HLVA FACTOR3 QRITOTAL
  <chr>             <dbl>     <dbl> <chr>   <dbl>   <dbl> <dbl>   <dbl>    <dbl>
1 studytwo.1        0.411      6.07 studyt…    26      27     6      50        9
2 studytwo.10       0.607      8.5  studyt…    38      24     9      58       15
3 studytwo.100      0.875      8.93 studyt…    66      40    13      60       20
4 studytwo.101      0.964      8.5  studyt…    21      31    11      59       14
5 studytwo.102      0.714      7.07 studyt…    74      35     7      52       18
6 studytwo.103      0.768      5.07 studyt…    18      40    11      54       15
# ℹ 3 more variables: GENDER <chr>, EDUCATION <chr>, ETHNICITY <chr>

summary(study.two.gen)

 participant_ID        mean.acc        mean.self        study          
 Length:172         Min.   :0.4107   Min.   :3.786   Length:172        
 Class :character   1st Qu.:0.6786   1st Qu.:6.411   Class :character  
 Mode  :character   Median :0.7679   Median :7.321   Mode  :character  
                    Mean   :0.7596   Mean   :7.101                     
                    3rd Qu.:0.8393   3rd Qu.:7.946                     
                    Max.   :0.9821   Max.   :9.000                     
      AGE           SHIPLEY           HLVA           FACTOR3     
 Min.   :18.00   Min.   :23.00   Min.   : 3.000   Min.   :29.00  
 1st Qu.:25.00   1st Qu.:32.75   1st Qu.: 7.750   1st Qu.:47.00  
 Median :32.50   Median :36.00   Median : 9.000   Median :51.00  
 Mean   :35.37   Mean   :35.13   Mean   : 9.064   Mean   :51.24  
 3rd Qu.:44.00   3rd Qu.:39.00   3rd Qu.:11.000   3rd Qu.:56.25  
 Max.   :76.00   Max.   :40.00   Max.   :14.000   Max.   :63.00  
    QRITOTAL        GENDER           EDUCATION          ETHNICITY        
 Min.   : 6.00   Length:172         Length:172         Length:172        
 1st Qu.:12.00   Class :character   Class :character   Class :character  
 Median :14.00   Mode  :character   Mode  :character   Mode  :character  
 Mean   :13.88                                                           
 3rd Qu.:16.00                                                           
 Max.   :20.00

Even though you have done this before, you will want to do it again, here, and pay particular attention to what you see, for the numeric variables, in the information about minimum (Min.) and maximum (Max.) values.

Step 3: Use histograms to examine the distributions of variables

Revise: practice to strengthen skills

Task 5 – Draw histograms to examine the distributions of variables

hint: Task 5

Use ggplot() with geom_histogram().

When we create a plot, we take things step-by-step.

Here’s an example you have seen before: run the lines of code and see the result in the Plots window in R-Studio.

ggplot(data = study.two.gen, aes(x = mean.acc)) + 
  geom_histogram()

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

These are the steps, set out one at a time:

ggplot(...) you tell R you want to make a plot using the ggplot() function
ggplot(data = study.two.gen ...) you tell R you want to make a plot with the study.two.gen data
ggplot(..., aes(x = mean.acc)) you tell R that you want to make a plot with the variable mean.acc – here, you specify the aesthetic mapping, x = mean.acc
ggplot(...) + geom_histogram() you tell R you want to plot values of mean.acc as a histogram

Notice that the code works the same whether we have the different bits of code on the same line or in a series of lines.

Revise: make sure you are confident about doing these things

Task 6 – Practice editing the appearance of a histogram plot step-by-step

Start by constructing a basic histogram.

hint: Task 6 – Choose whichever numeric variable from the `study.two.gen` dataset you please

hint: Task 6 – Use the line-by-line format to break the plot code into steps

It will make it easier to read, and it will make it easier to add edits e.g.

ggplot(data = study.two.gen, aes(x = SHIPLEY)) + 
  geom_histogram()

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

We are going to revise editing:

The appearance of the bars using binwidth;
The colour of the background using theme_bw();
The appearance of the labels using `labs().

Then we are going to try some new moves:

Setting the x-axis limits to reflect the full range of possible scores on the x-axis variable;
Adding annotation – here, a vertical line – indicating the sample average for a variable.

Questions: Task 6

Q.1. Edit the appearance of the bars by specifying a binwidth value.

ggplot(data = study.two.gen, aes(x = SHIPLEY)) + 
  geom_histogram(binwidth = 2)

Q.2. Then add an edit to the appearance of the background using theme_bw().

ggplot(data = study.two.gen, aes(x = SHIPLEY)) + 
  geom_histogram(binwidth = 2) +
  theme_bw()

Q.3. Then add an edit to the appearance of the labels using labs().

ggplot(data = study.two.gen, aes(x = SHIPLEY)) + 
  geom_histogram(binwidth = 2) +
  theme_bw() +
  labs(x = "SHIPLEY", y = "frequency count")

Introduce: make some new moves

Q.4. Now add an edit by setting the x-axis limits using x.lim().

ggplot(data = study.two.gen, aes(x = SHIPLEY)) + 
  geom_histogram(binwidth = 2) +
  theme_bw() +
  labs(x = "Vocabulary (SHIPLEY)", y = "frequency count") +
  xlim(0,40)

Warning: Removed 2 rows containing missing values (`geom_bar()`).

Q.5. Then add an edit to draw a vertical line to show the mean value of the variable you are plotting.

ggplot(data = study.two.gen, aes(x = SHIPLEY)) + 
  geom_histogram(binwidth = 2) +
  theme_bw() +
  labs(x = "Vocabulary (SHIPLEY)", y = "frequency count") +
  xlim(0,40) +
  geom_vline(xintercept = mean(study.two.gen$SHIPLEY), colour = "red", size = 1.5)

Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.

Warning: Removed 2 rows containing missing values (`geom_bar()`).

Q.6. Can you find information on how to define the limits on the x-axis and on the y-axis?
hint: Q.6. You can see the information in this week’s how-to but try a search online for “ggplot reference xlim”.
A.6. See ggplot reference information on setting limits here:

https://ggplot2.tidyverse.org/reference/lims.html

Q.7. Can you find information on how to a reference line?
hint: Q.7. You can see the information in this week’s how-to but try a search online for “ggplot reference vline”.
A.7. See ggplot reference information on setting limits here:

https://ggplot2.tidyverse.org/reference/geom_abline.html

Step 4: Now draw scatterplots to examine associations between variables

Consolidation: should be no surprises here

Task 7 – Create a scatterplot to examine the association between some variables

Between the outcome mean.acc and each of three numeric potential predictor variables SHIPLEY, HLVA and AGE.

hint: Task 7 – We are working with `geom_point()` and you need x and y aesthetic mappings.

hint: Task 7 – The outcome variable `mean.acc` has to be mapped to the y-axis using `...y = ...`

ggplot(data = study.two.gen, aes(x = SHIPLEY, y = mean.acc)) +
  geom_point()

ggplot(data = study.two.gen, aes(x = HLVA, y = mean.acc)) +
  geom_point()

ggplot(data = study.two.gen, aes(x = AGE, y = mean.acc)) +
  geom_point()

Revise: make sure you are confident about doing these things

Task 8 – Edit the appearance of each plot step-by-step

hint: Task 8 – You may want to use the same plot appearance choices for all plots

Because a consistent appearance is generally neater and easier for your audience to process.

hint: Task 8 – You can find links to reference information on options in the how-to guide

Use the information to make the plots pleasing in appearance to you.

hint: Task 8 – Do not be afraid to copy then paste code you re-use.

But be careful that things like axis values are sensible for each variable.

Questions: Task 8

Q.8. – First, edit the appearance of the points using alpha, size, shape, and colour:

ggplot(data = study.two.gen, aes(x = SHIPLEY, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')

ggplot(data = study.two.gen, aes(x = HLVA, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')

ggplot(data = study.two.gen, aes(x = AGE, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')

Q.9. – Then edit the colour of the background using theme_bw():

ggplot(data = study.two.gen, aes(x = SHIPLEY, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw()

ggplot(data = study.two.gen, aes(x = HLVA, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw()

ggplot(data = study.two.gen, aes(x = AGE, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw()

Q.10. – Then edit the appearance of the labels using labs():

ggplot(data = study.two.gen, aes(x = SHIPLEY, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw() +
  labs(x = "SHIPLEY", y = "mean accuracy")

ggplot(data = study.two.gen, aes(x = HLVA, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw() +
  labs(x = "HLVA", y = "mean accuracy")

ggplot(data = study.two.gen, aes(x = AGE, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw() +
  labs(x = "Age (Years)", y = "mean accuracy")

Introduce: make some new moves

Q.11. – Then set the x-axis and y-axis limits to the minimum-maximum ranges of the variables you are plotting
hint: Q.11. – For these plots the y-axis limits will be the same because the outcome stays the same
hint: Q.11. – But the x-axis limits will be different for each different predictor variable
hint: Q.11. – The minimum value will always be 0

ggplot(data = study.two.gen, aes(x = SHIPLEY, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw() +
  labs(x = "SHIPLEY", y = "mean accuracy") +
  xlim(0, 40) + ylim(0, 1)

ggplot(data = study.two.gen, aes(x = HLVA, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw() +
  labs(x = "HLVA", y = "mean accuracy") +
  xlim(0, 16) + ylim(0, 1)

ggplot(data = study.two.gen, aes(x = AGE, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  theme_bw() +
  labs(x = "Age (Years)", y = "mean accuracy") +
  xlim(0, 80) + ylim(0, 1)

Step 5: Use correlation to to answer the research questions

Revise: make sure you are confident about doing these things

One of our research questions is:

What person attributes predict success in understanding?

Task 9 – Examine the correlations between the outcome variable and predictor variables

hint: Task 9 – We use `cor.test()`

hint: Task 9 – You can look at the `how-to` guide for more advice

You need to run three separate correlations:

between mean accuracy and SHIPLEY
between mean accuracy and HLVA and
between mean accuracy and AGE

cor.test(study.two.gen$SHIPLEY, study.two.gen$mean.acc, method = "pearson",  alternative = "two.sided")


    Pearson's product-moment correlation

data:  study.two.gen$SHIPLEY and study.two.gen$mean.acc
t = 6.8493, df = 170, p-value = 1.299e-10
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.3390103 0.5746961
sample estimates:
      cor 
0.4650537

cor.test(study.two.gen$HLVA, study.two.gen$mean.acc, method = "pearson",  alternative = "two.sided")


    Pearson's product-moment correlation

data:  study.two.gen$HLVA and study.two.gen$mean.acc
t = 7.5288, df = 170, p-value = 2.866e-12
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.3787626 0.6044611
sample estimates:
      cor 
0.5000559

cor.test(study.two.gen$AGE, study.two.gen$mean.acc, method = "pearson",  alternative = "two.sided")


    Pearson's product-moment correlation

data:  study.two.gen$AGE and study.two.gen$mean.acc
t = 0.30121, df = 170, p-value = 0.7636
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.1269774  0.1721354
sample estimates:
       cor 
0.02309589

Now use the results from the correlations to answer the following questions.

Q.12. – What is r, the coefficient for the correlation between mean.acc and SHIPLEY?
A.12. – r = 0.4650537
Q.13. – Is the correlation between mean.acc and HLVA significant?
A.13. – r is significant, p < .05
Q.14. – What are the values for t and p for the significance test for the correlation between mean.acc and AGE?
A.14. – t = 0.30121, p = 0.7636
Q.15. – For which pair of outcome-predictor variables is the correlation the largest?
A.15. – The correlation is the largest between mean.acc and HLVA.
Q.16. – What is the sign or direction of each of the correlations?
A.16. – All the correlations are positive.

Step 6: Use a linear model to to answer the research questions

Introduce: Make some new moves

One of our research questions is:

What person attributes predict success in understanding?

Task 10 – Examine the relation between outcome mean accuracy (`mean.acc`)

And each of the predictors: SHIPLEY, HLVA and AGE

hint: Task 10 – Use `lm()`

hint: Task 10 – Run three separate `lm()` analyses

All with mean.acc as the outcome but each with one predictor variable

hint: Task 10 – See the `how-to` guide for example code

model <- lm(mean.acc ~ SHIPLEY, data = study.two.gen)
summary(model)


Call:
lm(formula = mean.acc ~ SHIPLEY, data = study.two.gen)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.285771 -0.076662  0.002099  0.079416  0.257793 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.308027   0.066426   4.637 7.01e-06 ***
SHIPLEY     0.012854   0.001877   6.849 1.30e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.107 on 170 degrees of freedom
Multiple R-squared:  0.2163,    Adjusted R-squared:  0.2117 
F-statistic: 46.91 on 1 and 170 DF,  p-value: 1.299e-10

model <- lm(mean.acc ~ HLVA, data = study.two.gen)
summary(model)


Call:
lm(formula = mean.acc ~ HLVA, data = study.two.gen)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.27457 -0.06777  0.01474  0.08025  0.23146 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.522016   0.032544  16.040  < 2e-16 ***
HLVA        0.026207   0.003481   7.529 2.87e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1047 on 170 degrees of freedom
Multiple R-squared:  0.2501,    Adjusted R-squared:  0.2456 
F-statistic: 56.68 on 1 and 170 DF,  p-value: 2.866e-12

model <- lm(mean.acc ~ AGE, data = study.two.gen)
summary(model)


Call:
lm(formula = mean.acc ~ AGE, data = study.two.gen)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.34684 -0.08464  0.01084  0.08323  0.21968 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.7519965  0.0267206  28.143   <2e-16 ***
AGE         0.0002136  0.0007092   0.301    0.764    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1208 on 170 degrees of freedom
Multiple R-squared:  0.0005334, Adjusted R-squared:  -0.005346 
F-statistic: 0.09073 on 1 and 170 DF,  p-value: 0.7636

Notice that we do the linear model in the steps:

model <- lm(...) fit the model using lm(...), and give the model a name, here, we call it model;
...lm(mean.acc ~ SHIPLEY...) tell R you want a model of the outcome mean.acc predicted ~ by the predictor SHIPLEY
...data = study.two) tell R that the variables you name in the formula live in the study.two dataset.
summary(model) ask R for a summary of the model you called model.

Notice that R has a general formula syntax:

outcome ~ predictor *or* y ~ x

and uses the same format across a number of different functions;
each time, the left of the tilde symbol ~ is some output or outcome;
and the right of the tilde ~ is some input or predictor or set of predictors.

Questions: Task 10

If you look at the model summary you can answer the following questions.

Q.17. What is the estimate for the coefficient of the effect of the predictor HLVA on mean.acc?
A.17. 0.026207
Q.18. Is the effect significant?
A.18. It is significant, p < .05
Q.19. What are the values for t and p for the significance test for the coefficient?
A.19. t = 7.529, p = 2.87e-12
Q.20. How would you describe in words the shape or direction of the association between HLVA and mean.acc?
A.20. The slope coefficient – and a scatterplot (draw it) – suggest that as HLVA scores increase so also do mean accuracy scores.
Q.21. How how would you describe the relations apparent between the predictor and outcome in all three models?
A.21. It is possible to see, given coefficient estimates, that the association between predictor and outcome is positive for each model: mean accuracy appears to increase for increasing values of SHIPLEY vocabulary, HLVA health literacy, and age.

Step 7: Use a linear model to generate predictions

Introduce: make some new moves

Task 11 – We can use the model we have just fitted to plot the model predictions

hint: Task 11 – We are going to draw a scatterplot and add a line

The line will show the model predictions, given the model intercept and effect coefficient estimates.

First fit a model and get a summary: model the relationship between mean.acc and HLVA

model <- lm(mean.acc ~ HLVA, data = study.two.gen)
summary(model)


Call:
lm(formula = mean.acc ~ HLVA, data = study.two.gen)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.27457 -0.06777  0.01474  0.08025  0.23146 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.522016   0.032544  16.040  < 2e-16 ***
HLVA        0.026207   0.003481   7.529 2.87e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1047 on 170 degrees of freedom
Multiple R-squared:  0.2501,    Adjusted R-squared:  0.2456 
F-statistic: 56.68 on 1 and 170 DF,  p-value: 2.866e-12

Q.22. What is the coefficient estimate for the intercept?
A.22. 0.522016
Q.23. What is the coefficient estimate for the slope of HLVA (see earlier)?
A.23. 0.026207

Second, use the geom_point() to draw a scatterplot and geom_abline() function to draw the prediction line representing the association between this outcome and predictor

ggplot(data = study.two.gen, aes(x = HLVA, y = mean.acc)) +
  geom_point(alpha = 0.5, size = 2, colour = "blue", shape = 'square')   +
  geom_abline(intercept = 0.522016, slope = 0.026207, colour = "red", size = 1.5) +
  theme_bw() +
  labs(x = "HLVA", y = "mean accuracy") +
  xlim(0, 15) + ylim(0, 1)

You can see reference information here:

https://ggplot2.tidyverse.org/reference/geom_abline.html

Introduction

Naming things

The data we will be using

Answers

Step 1: Set-up

Task 1 – Run code to empty the R environment

Task 2 – Run code to load relevant libraries

Step 2: Load the data

Task 3 – Read in the data file we will be using

Task 4 – Inspect the data file

Step 3: Use histograms to examine the distributions of variables

Revise: practice to strengthen skills

Task 5 – Draw histograms to examine the distributions of variables

hint: Task 5

Revise: make sure you are confident about doing these things

Task 6 – Practice editing the appearance of a histogram plot step-by-step

hint: Task 6 – Choose whichever numeric variable from the study.two.gen dataset you please

hint: Task 6 – Use the line-by-line format to break the plot code into steps

Questions: Task 6

Introduce: make some new moves

Step 4: Now draw scatterplots to examine associations between variables

Consolidation: should be no surprises here

Task 7 – Create a scatterplot to examine the association between some variables

hint: Task 7 – We are working with geom_point() and you need x and y aesthetic mappings.

hint: Task 7 – The outcome variable mean.acc has to be mapped to the y-axis using ...y = ...

Revise: make sure you are confident about doing these things

Task 8 – Edit the appearance of each plot step-by-step

hint: Task 8 – You may want to use the same plot appearance choices for all plots

hint: Task 8 – You can find links to reference information on options in the how-to guide

hint: Task 8 – Do not be afraid to copy then paste code you re-use.

Questions: Task 8

Introduce: make some new moves

Step 5: Use correlation to to answer the research questions

Revise: make sure you are confident about doing these things

Task 9 – Examine the correlations between the outcome variable and predictor variables

hint: Task 9 – We use cor.test()

hint: Task 9 – You can look at the how-to guide for more advice

Step 6: Use a linear model to to answer the research questions

Introduce: Make some new moves

Task 10 – Examine the relation between outcome mean accuracy (mean.acc)

hint: Task 10 – Use lm()

hint: Task 10 – Run three separate lm() analyses

hint: Task 10 – See the how-to guide for example code

Questions: Task 10

Step 7: Use a linear model to generate predictions

Introduce: make some new moves

Task 11 – We can use the model we have just fitted to plot the model predictions

hint: Task 11 – We are going to draw a scatterplot and add a line

hint: Task 6 – Choose whichever numeric variable from the `study.two.gen` dataset you please

hint: Task 7 – We are working with `geom_point()` and you need x and y aesthetic mappings.

hint: Task 7 – The outcome variable `mean.acc` has to be mapped to the y-axis using `...y = ...`

hint: Task 9 – We use `cor.test()`

hint: Task 9 – You can look at the `how-to` guide for more advice

Task 10 – Examine the relation between outcome mean accuracy (`mean.acc`)

hint: Task 10 – Use `lm()`

hint: Task 10 – Run three separate `lm()` analyses

hint: Task 10 – See the `how-to` guide for example code