# Statistics help! Reporting ANOVA results!

I am new to statistics and I need some help in understanding how to report the data of some tests I am running on R, I hope this is the right place!

I have a dataset:

# A tibble: 6 x 12
Participant Pr… Group Gender   Age Spreadsheet Ro… Screen_Name Condition Reaction_Time Correct_Humorous
<chr>            <chr> <chr>  <dbl>            <dbl> <chr>       <chr>             <dbl>            <dbl>
1 CG_01            cont… F         18                2 Joke        Differen…         3156.                1
2 CG_01            cont… F         18                3 Joke        Differen…        15219.                1
3 CG_01            cont… F         18                4 Joke        Differen…         4005.                1
4 CG_01            cont… F         18                5 Joke        Differen…        30027                 0
5 CG_01            cont… F         18                6 Joke        Differen…         9811.                1
6 CG_01            cont… F         18                7 Joke        Differen…        12106.                1
# … with 3 more variables: Wrong_Related <dbl>, Wrong_Unrelated <dbl>, Answer_Type <chr>


I am trying to look at accuracy between two groups of subjects in two conditions.

So I ran a linear model

model_acc_ch <- lm(data= data4, Correct_Humorous ~ Group + Condition)

I got this result:


Call:
lm(formula = Correct_Humorous ~ Group + Condition, data = data4)

Residuals:
Min       1Q   Median       3Q      Max
-0.95739  0.04261  0.13864  0.32987  0.42590

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)               0.86136    0.01556  55.357  < 2e-16 ***
Groupdyslexia            -0.28726    0.01840 -15.613  < 2e-16 ***
ConditionSame word class  0.09603    0.01836   5.231 1.88e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3893 on 1796 degrees of freedom
Multiple R-squared:  0.1311,    Adjusted R-squared:  0.1302
F-statistic: 135.5 on 2 and 1796 DF,  p-value: < 2.2e-16


I want to write down the result, it's my first time and I don't know how to report the F values, so I ran an Anova on the model that looks like this:

Analysis of Variance Table

Response: Correct_Humorous
Df  Sum Sq Mean Sq F value    Pr(>F)
Group        1  36.931  36.931 243.676 < 2.2e-16 ***
Condition    1   4.147   4.147  27.365 1.881e-07 ***
Residuals 1796 272.196   0.152
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


I don't know what might be more significant. would it be ok if I say "Analyses of variance (ANOVAs) showed significant differences for the number of correct choices between groups [F= 243.676, p < 0.0001] and between conditions [F=27.365, p<0.0001]"?

Thank you to anyone who can help!

• You need a more precise title, something more like "Reporting ANOVA results". I would always want to see means mentioned in a report from ANOVA, because that is what the procedure compares. – Nick Cox Aug 21 at 6:47
• You did not run what is commonly called a linear mixed (effects) model – Roland Aug 21 at 10:33

As I understood, you have two binary independent variables named Group and Condition and one binary dependent variable named Correct_Humorous. You are going to need a glm with the binomial family and logit link:

fit <- glm(
Correct_Humorous ~ Group + Condition,
family = binomial(link = logit),  # logistic regression
data = data4
)

summary(fit)

fit$$rsquare <- 1 - (fit$$deviance/fit\$null.deviance)


Moreover, to find out the effect size of the independent variables on the outcome, you can calculate odds ratios (OR) with confidence intervals (CI):

install.packages("questionr")
require("questionr")
odds.ratio(fit)


In such scenarios, you need to report goodness of fit (such as AIC, $$R^{2}$$), the Estimate or OR with 95% CI and p-values of the corresponding fit.

If you have more questions or problems, you can provide a reproducible example and ask on StackOverflow.