2 Activity 2 – Between Groups (a.k.a. Independent Groups) Factorial ANOVA: Omnibus Tests in jamovi

Sex, Drugs, and Rats…

A psychologist is interested in the effect of four different dosage levels of a steroidal drug and sex on physical performance (maze running) of laboratory rats. They take 20 male and 20 female rats, and randomly assign them to one of four conditions that vary in the dosage of the drug (zero, small, moderate, large). They then measure the rats’ physical performance on a scale from 1 to 15 (with higher scores indicating better performance). The researcher reasons that different drug dosages may affect maze running ability; that male and female rats may differ in performance; and that certain drug dosages may affect maze running performance more for one sex than for the other. Based on what they know about the effect of this drug, the researcher makes the following specific hypotheses:

1. Overall, male rats will outperform female rats on maze running.
2. Overall, rats will perform better when they receive any amount of the drug than when they do not receive the drug.
3. However, a small dose will tend to lead to the best performance compared to a large dose.
4. The effect of drug dosage will differ for males compared to females. While both sexes will exhibit increased performance when they receive any amount of the drug than when they do not, the particular benefits of the small drug dosage (compared to the large dose) will be more noticeable in female rats than in male rats.

1. Before performing any analyses, decide which omnibus statistical results will address each hypothesis.

2. Examine the following table containing our data. We have added the marginal and cell totals and means to help you identify potential main/ simple effects.

Table 2.1

The Effect of Steroidal Dosage and Sex on Maze Running Performance in Rats

Go to a version of Table 2.1 formatted for accessibility.

3. Using the axes below, plot the cell means and think about what results to expect in terms of the omnibus tests (i.e., are we expecting a significant main effect of sex, main effect of drug dosage, and/ or Dosage x Sex interaction?).

We will use the rat Drug Dosage x Sex experiment to conduct a 4 x 2 between groups factorial ANOVA in jamovi. Here is the raw data that you will need to type into jamovi for this exercise:

Table 2.2

The Effect of Steroidal Dosage and Sex on Maze Running Performance in Rats

A jamovi data spreadsheet contains one line of data for each participant (in this case, rat). You’ll need three columns to enter the data – the first column will identify what level the participant is in for the sex factor (i.e., male or female), the second column will identify the participant’s level on the drug dosage factor (i.e., zero, small, moderate or large), and the third column will record the participant’s maze running performance score.

1. To specify the variables, click on the Variables tab. In the Variables tab each row represents a variable. In the first row in the Name column, type in the name of the variable with the fewest levels – Sex. Using the variable with the fewest levels first makes data entry easier (which you will see in a moment).
2. If you want to give your variable a longer name than what is allowed in the Name column, you also have the option of typing in a longer name in the Description column. We don’t really need this because we have enough space to type a descriptive name in the Name column.
3. Click on Variables > Edit in the menu ribbon to reveal where you can add details such as the level of measurement of the variable as well as values and associated labels.
   Select Nominal in the Measure type list.
   Next to the “Levels” box type click on the + and in the pop-up box, type in the first value of 1.  Then click on the + again and type in the second value of 2.
   Click in the row with the value of 1 and type in the value label male, then click in the value of 2 and type in the value label of female.
   The end result should like the screenshot below.

Figure 2.11

Sex Variable Specification in jamovi

Note. When the levels are created they are pinned and cannot be accidentally deleted.  If you type in an extra level and want to remove it, you can click the pin to unpin the level, and then toggle the ‘retain unused levels in analysis’ on and off, which should get rid of it.

4. In the second line of the Variable View, in the Name column, type in the name of the other variable – Dosage.

5. In the edit view again, specify the Measure type as Nominal. In the Levels box you want to specify the dosages of 0 (Zero), 1 (Small), 2 (Moderate), and 3 (Large). The end result should look like the screenshot below (note that the view cuts off the 3 (Large) value and label combination but it is there.

Figure 2.12

Dosage Variable Specification in jamovi

6. Now give the third variable the name of the dependent variable – Performance. In the Edit view denote this variable as continuous. Note that there are no ‘values’ to add for this variable because it is a continuous rather than categorical variable in this study. Categorical variables always need to have their levels specified in terms of value labels, while continuous variables do not.

Figure 2.13

Performance Variable Specification in jamovi

7. Click on the Data tab in the menu ribbon to access the data entry spreadsheet. Click on the first cell. You will notice that a heavy border appears around the first active cell.
Type in the value for sex for the first participant (i.e., either a ‘1’ or a ‘2’ depending on whether they are male or female, respectively), and then use the arrow keys to move right to the next cell. Type in the value of that same participant on drug dosage. Then in the next cell to the right, type in the participant’s maze running performance score.
Use the mouse or arrows to return to the first cell of the next line to enter the second participant’s data.
If you make a mistake, simply highlight the cell where the problem is and type in the correct value. As noted, before you will see that as we type in our data using our numeric values, jamovi will display the value label that corresponds with that numeric value.

If you want to practice saving the jamovi file you can save it to your home drive folder. On the menu bar, click on the three horizontal lines at the far left.

Figure 2.14

Accessing the Main Menu in jamovi

You will then be able to select to save your jamovi file.

Figure 2.15

Saving Data Files in jamovi

If you are on your own device you can save the file to wherever you choose. If you are in a computer lab on campus navigate to your home H: drive (i.e., the one with your student number).

A Note on Assigning Value Labels

When we have categorical IVs, it doesn’t matter how you label the levels, the results will end up the same. So here we labelled sex as 1 and 2 for males and females, respectively. We could have just as easily (and correctly) assigned them -1 and 1, or 0 and 1. The numbers themselves are meaningless, they are just nominal labels. Likewise, here we assigned the dosage levels values of 0, 1, 2 and 3. However, we could have given them the values of -2, 1.5, 4 and 6. The results of the analysis would be the same. But there are certain conventions to which we generally adhere. Normally, we use whole numbers and start the coding values at 1, or 0 if there is a control group.  If there are only two groups, it is also common to code them 1, -1.

1. Select the Analyses menu.
2. Click ANOVA, then ANOVA … to open ANOVA analysis menu that allows you to specify a factorial ANOVA.
3. Select the dependent variable (i.e., Performance) and then click on the arrow button to move the DV into the Dependent Variable box.
4. Select the independent variables in turn (i.e., Sex and Dosage) and click on the arrow button to move each variable into the Fixed Factors box.
5. Select Overall model test under Model Fit and select η² and ϖ² in the Effect size check boxes
6. Click on Model drop down tab. The Sum of squares (bottom right) should be Type 3, which is the default method for partitioning the variance (decomposing sums of squares). With a balanced or orthogonal design, it doesn’t really matter which of the methods you use because the tests of the main effects and interaction are independent – all methods will yield equivalent results.

The output of the omnibus tests is displayed below.

Figure 2.16

Omnibus ANOVA Tests in jamovi 

Note that we want means, standard deviations, and confidence intervals for reporting purposes. To get these we need to run a separate descriptives procedure.

If your output above does not have the syntax, you can toggle the syntax on (as described earlier in Activity 2) by clicking on the three dots in top right-hand corner of the jamovi view and ticking ‘syntax mode’ on.

You can also adjust the number of decimal places that jamovi displays.  Head to the settings menu which is accessed via the three vertical dots on the far right of the menu ribbon. You will see you have the option to change the number of decimal places (e.g., from 3 to 2 or from 3 to 4) for numbers and (separately) for p values.

Run this twice.  Once for Sex and once for Dosage.

1. Select the Analyses menu.
2. Click Exploration, then Descriptives.
3. Select the dependent variable (i.e., Performance) and then click on the arrow button to move the DV into the Variables box.
4. Select the independent variables in turn (i.e., Sex and Dosage) and click on the arrow button to move each variable into the Split by box. Click below the output of descriptives for the first IV before doing the second IV, to look at each variable separately.
5. In the Statistics drop-down menu ensure that you have the Mean checkbox under the Central Tendency section ticked, and the Std. deviation checkbox under the Dispersion section ticked. Finally, check the Confidence interval for Mean checkbox under Mean Dispersion. You can unselect all other default selections to get a table that has only the means and standard deviations you need.

Here is the table you will get when you follow this process.

Figure 2.17

Descriptive Statistics for Sex in jamovi

Figure 2.18

Descriptive Statistics for Dosage in jamovi

Note: If you save your data file again now, you will not only save your data but all the analyses you have conducted so far in this exercise. When you go to reopen this data file later on it will have all these analyses saved with it.

Look at the ANOVA table (i.e., ‘ANOVA – performance’ table on the prior page). Copy down the key bits of information here, including the SS (Type III sums of squares), df (degrees of freedom), MS (mean square), F ratios and exact p–values (Sig.).

NB: p-values are to be recorded to three decimal places, while SS, MS and F are to be taken to two. The “Overall model” corresponds to the (Corrected) Total row, and the “Residuals” row corresponds to the Error row.

Table 2.3

Omnibus ANOVA Table for Recording of Results

Note – jamovi refers to the Error row as “Residuals”. The (Corrected) Total needs to be calculated and is the sum of the Residuals row and the Overall Model row.

Go to a version of Table 2.3 formatted for accessibility.

Recall that in previous statistics courses, rather than being given the exact p-values as you are here, you were asked to work out the significance of an F–ratio for yourself. You did this by comparing the obtained F-value from your calculations to the F-critical value found in the F tables (with the appropriate df). In this, if F_obtained was greater than F_critical, then the result was statistically significant at α = .05. In contrast, if F_obt < F_crit, then the result was non-significant.

Based on F tables, the F_crit values for each omnibus test are as below:

Sex: F_{α = .05}(1, 32) = 4.18

Dosage: F_{α = .05}(3, 32) = 3.21

Dosage x Sex: F_{α = .05}(3, 32) = 3.21

Task:

Double-check that your interpretations of significance are the same using exact p-values and the comparison of F_obt to F_crit.

Write Up the Results for Step 3

Now that you have done the omnibus tests for a two-way between groups factorial ANOVA, state in words what the results mean. That is:

Explain what kind of analysis was done, stating what the IV(s) and the DV were. This includes specifying the levels of the IV(s). Recall that, by convention, we tend to use specific notation to present this information in a condensed manner. Also remember that if this is the first time you have used the term “ANOVA” in the text, this acronym needs to be introduced properly i.e., analysis of variance (ANOVA).

State the significance of the first main effect and describe its direction.

State the significance of the second main effect. NB: note that we don’t describe the direction of effect for this yet, because it involves more than two levels. Hence follow-up tests are required to determine this.

State the significance of the interaction. NB: again, we require follow-up tests to work out what is happening for the interaction before we can describe its direction of effect.

Be sure to include the relevant statistical notation after each of the above omnibus effects (i.e., F, df, p, and η² or ω²). Note that statistical notation in English/ Latin letters is to be italicised (e.g., F, p), while that in Greek (e.g., η², ω²) appears as standard text. Further, inferential statistics involving F, and the effect sizes, should be presented to two decimal places, while p-values should go to three.

Be sure to include the relevant marginal or cell means, standard deviations, and 95% confidence intervals when describing the direction of effect. However, if the direction of effect is unknown because follow-up tests are needed to determine this, then hold off presenting these Ms and SDs until you report the follow-up test findings. The number of decimals reported for descriptive statistics (such as means and standard deviations) should be determined by their precision of measurement. In this case, because they were measured as whole numbers in the experiment (i.e., scored 1-15 for maze running performance), they should be taken to only one decimal place for reporting.

*** Your write up is not complete yet. Later in this workbook we will follow-up the significant main effects with more than two levels with main effect comparisons, and we will describe the significant interaction using simple effects and simple comparisons. ***