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Running and Interpreting a One-Way ANOVA in JASP

Minority stress theory describes how experiences with stigma, prejudice, and discrimination

connect to the physical and mental health of sexual minority people (Meyer, 2003). As societal

attitudes toward sexual minorities (e.g., gay, lesbian, and bisexual people) continues to improve,

this theory would suggest that physical and mental health outcomes for this population should

also improve. As you can see from the following Pew Research Center (2019) graph, attitudes in

favor of same-sex marriage, for example, have increased significantly since 2004. Additionally,

outcomes of three different cohorts of sexual minorities: Equality Cohort, aged 18-25 years (n =

670), Visibility Cohort, aged 34-41 years (n = 372), and Pride Cohort, aged 52-59 years (n =

476).

Meyer and colleagues (2021) examined

numerous variables, both categorical and

continuous. For the purposes of this guide, we

will be using these two continuous variables as

our dependent variables: Connection with the

LGBT community and life satisfaction. We will

need to run two One-way ANOVA’s to see if

community. Scores can range from 1-4 and are

based on a 4-point Likert scale (“agree strongly”

to “disagree strongly”). Lower scores represent

lower connection with the LGBT community.

Life satisfaction

This variable measures the degree to which participants are satisfied with their life. This variable

is measured by asking participants to rate 5-items on a7-point Likert scale (“disagree strongly” to

“agree strongly”). Lower scores represent lower life satisfaction.

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Hypotheses

We have two different dependent variables we are looking at in this example: (1) Connection

0

groups.

o Mathematical H

means for the younger, middle-aged, and older adult groups on connection with

the LGBT community; M

middle

= M

older

• Life satisfaction

o Conceptual H

0

: There are no significant group mean differences on life

satisfaction between the younger, middle-aged, and older adult groups.

• Connection with the LGBT Community

o Conceptual H

2

: There is at least one significant group mean difference on

connection with the LGBT community between the younger, middle-aged, and

older adult groups.

o Mathematical H

population means for the younger, middle-aged, and older adult groups on

connection with the LGBT community; M

.

population means for the younger, middle-aged, and older adult groups on life

satisfaction; M

younger

≠ M

middle

≠ M

older

.

JASP Analyses

In order to run analyses, the first thing we need to do is open the data set we will be working

with. To do this, open JASP and follow the steps below:

File → Open → Computer → Browse → Select the “One-Way ANOVA Practice Data Set

(Meyer et al. 2021)” JASP file wherever it is saved on your computer.

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Once the data set is open in JASP, we will change the data labels for our condition variable so

that we can see which groups are being compared when we run the omnibus and post hoc tests.

Currently the condition column has either a 1, 2, or 3 for each participant. Based on Meyer et

close the window by clicking on the X button.

Assumption Testing

There are six statistical assumptions that data must meet in order to run a one-way ANOVA.

Many of these assumptions will look familiar, as they are quite similar to those required to run an

independent measures t test – we’re just adding more groups! Assumptions 1 through 3 have to

do more with the research design, and assumptions 4 through and 6 refer to those which data

must meet in order to run the statistical test. Let’s consider whether our data meet these

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Yes. We have dependent variable(s) (‘life satisfaction’ and ‘community connectedness’) and

Yes. Our participants were assigned to one of the three possible levels of the independent

variable, and because no participant can be in more than one age group, we can assume that there

is no relationship between the observations in each group. This assumption has been met.

To check our data for Assumptions 4 and 5, we will need to utilize the Descriptives tab. When

the “Descriptive Statistics” window opens, move the dependent variables (‘life satisfaction’ and

‘community connectedness) to the “Variables” box. Then, move our factor or independent

variable (‘Cohort’) to the “Split” box so that we get plots for each group.

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3. Under “Dispersion,” select “Minimum,” “Maximum,” and “Std. deviation”

Although there are multiple ways to determine if the dependent variable is normally distributed

for each group of our independent variable, for this course we will focus on interpreting the

skewness and kurtosis statistics. We want skewness and kurtosis values at are between -2 and +2.

Looking at the values on the following output copied, we can see our skewness and kurtosis

values for the dependent variable for all of our groups are within the acceptable range of -2 and

+2 across both of our dependent variables.

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To report these results in APA format, we can write:

The scores on both life satisfaction and community connectedness were normally

we have to decide whether we want to keep the outliers, transform the outliers, or remove them.

Given that outliers are especially common in datasets with large samples (as ours is; N = 1,458),

and that we have so many, we will keep these outliers in our dataset in order to avoid removing a

significant amount of datapoints from our model (something that is generally discouraged,

Faraway, 2015). Instead, we will model how to run the analyses as normal with outliers present,

and at the end of this guide, will run the analyses with those outliers removed to examine

whether the results remained the same.

To report this using APA format, we would write:

There were no outliers identified on the life satisfaction scores; however, there were

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assessed by the inspection of a boxplot. We decided to retain these outliers given the

large sample size to avoid removing a large number of datapoints from the model.

section.

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To interpret the results of the Levene’s test, we need to look at the significance or probability

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To interpret the results, we want to look at the p value. In this example, you can see that our p

value is <.001, which is less than the alpha of .05. Therefore, we will reject our null hypothesis –

there are significant group mean differences on life satisfaction between the younger, middle,

and older cohorts.

Writing the basic results of the omnibus ANOVA test (F test) in APA format follows this general

format:

F(df1, df2) = F statistic, p < .05 or p > .05, η

= ω

value

different from one another regarding life satisfaction? To answer these questions, we will need to

look at the Post Hoc Analyses section.

Post Hoc Analyses: Life Satisfaction

Now that we have rejected our null hypothesis and determined there is at least one age group that

is significantly different in their level of life satisfaction, let’s conduct post hoc tests to determine

what groups are different. To do this, go back to the ANOVA test selection for the life

satisfaction outcome variable. Under “Post Hoc Tests” we will move our grouping variable

[Cohort] over using the arrow and select:

• Under Type: select ‘Standard’ and ‘Effect size’ (Note: If we had violated the

homogeneity of variances assumption, we would need to select the “Games-Howell”

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Looking at the preceding Descriptives table image, we can see the older cohort has the highest

mean level of life satisfaction (M = 4.53), the middle cohort has the second highest mean level of

(M = 4.14). We still don’t know which groups are statistically different, but we can see a trend of

the mean levels of life satisfaction increasing for each age group.

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The Games-Howell post hoc test is preferred when your data violate the homogeneity of

variances assumption. As you can see from the table above, it is set up a little differently than the

Tukey post hoc test results. The Games-Howell Post Hoc Comparisons table still tells us if the

mean differences between the groups are statistically significant; however, Cohen’s d effect size

statistics are not available for this post hoc option. [Note: If you need to report an effect size for

your post hoc comparisons, you can check the “Confidence Intervals” box under “Post Hoc

were reporting in APA format using this formula, we would write the following:

The older cohort (M = 4.53, SD = 1.71) had significantly higher levels of life satisfaction

compared to the young cohort (M = 4.14, SD = 1.52), p

Tukey

< .001. No other group

comparisons were significantly different, p

Tukey

Now that we have interpreted the statistical significance of our ANOVA Omnibus tests, let’s

consider the practical significance. Remember, a significant p value tells us that there is a

significant difference in the mean levels of community connectedness and life satisfaction

between our three age groups. The effect size tells us how meaningful the difference between the

age cohorts is for our dependent variable.

Eta-squared (η

2

) or omega-squared (ω

2

)

are both a representation of effect sizes for the omnibus

test for an ANOVA. Because we are not yet able to say that, for example, Group 1 is different

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than Group 2 for the omnibus ANOVA test, you have to estimate how much the difference is

across all the groups. Therefore, eta- and omega-squared are used to determine the amount of

variance accounted for (out of 100% variance) that the IV explains in the DV. These values are

Let’s interpret eta-squared for our variables. We obtained eta-squared values of .01 – this is a

small effect. So, although we have a statistical difference in the mean levels of community

connectedness and life satisfaction between cohorts, that difference is small (negligible, even).

This can often happen in studies that have a very large sample size. Finding a significant

difference becomes easier, even if it is really small.

Reporting in APA Format

We ran the test for both community connectedness and life satisfaction, but for simplicity, let’s

just look at the full write-up for the community connectedness analysis.

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statistics fell within the acceptable range of -2 and +2. There was homogeneity of

variances, as assessed by the Levene’s test for equality of variances (p > .05).

2

2

Tukey

Tukey

significantly different, p

> .05.

Now that the statistical jargon is out of the way – what do our results mean? We rejected the null

hypothesis for community connectedness and found differences between the younger cohort and

the middle/older cohorts. This means the younger cohort feels a stronger connection to the

LGBT community compared to the middle and older cohorts; however, given the small effect

size we obtained, this difference is may not be practically meaningful. We also rejected the null

satisfied with their life than the younger cohort.

Thinking back to Meyer and colleagues (2021) original hypothesis using minority stress theory,

they measured other variables to address their original research question. Specifically, they

levels of life satisfaction in the older cohort. Looking across all the outcomes Meyer and

colleagues analyzed, they found that younger cohorts reported more experiences with physical

violence, sexual violence, and verbal abuse. They also reported higher levels of felt stigma and

psychological distress.

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References

Meyer, I. H. (2003). Prejudice, social stress, and mental health in lesbian, gay, and bisexual

stress, distress, and suicide attempts in three cohorts of sexual minority adults: A U.S. probability

sample. PloS One, 16(3), e0246827–e0246827. https://doi.org/10.1371/journal.pone.0246827

Pew Research Center (2019). Majority of public favors same-sex marriage, but division persist.

Retrieved from https://www.pewresearch.org/politics/2019/05/14/majority-of-public-favors-

same-sex-marriage-but-divisions-persist/

The Office of Equity, Diversity, and Inclusion (2020). The Supreme Court bans employment