# Statistical analysis for two questionnaires

I am working on a research paper and I need to organize the statistical analysis part. I have two questionnaires with the same number of participants (15 cases). Basically, we asked the participants to play two different games with two different conditions.

• Imagine: Game A (under conditions 1 and 2) (questionnaire with 5 questions). Game B (under conditions 1 and 2) (questionnaire with 7 questions). And we asked them to fill out the questionnaire to estimate the overall satisfaction for each condition. I am wondering that whats could be the best statistical method here to analyze the results for each condition. Is (one/two way) ANOVA a good solution? If yes is it a good way to do it on Python? (unfortunately, I am not familiar with R and I'm kinda in rush) Here is an example of the result of the questionnaires for only one person (1 out of 15).
• can you share what you have tried? Otherwise i think it's more of a statistical question rather than programming Commented Dec 30, 2021 at 5:36
• I think the first part of my question is mainly related to statistics. I am not yet do coding, I'm curious if python is a good option rather than R?
– Wishii
Commented Dec 30, 2021 at 5:40
• You need to say what you want to compare and using what data. Compare Conditions 1 and 2? Games A and B? Presumably the comparison will be based on questionnaires with 15 ('cases' or 'questions', or with 5 or 7 questions). As is, it's a jumble of games, conditions, groups and questionnaires. //. What do questionnaires provide? (Number 'correct'? Opinions 1-5? Sores 0-100?) // Can you show a partial table with some results suitably organized? // We wouldn't provide Python or R code. Perhaps with some clue as to the experimental design, someone can recommend a statistical test or procedure. Commented Dec 30, 2021 at 6:43
• first, thank you for your help and your comments. Mainly I want to compare each condition for each game. In other words, I like to know for "Game A" which condition is the preference of the player. and for Game B again which condition is better. So basically I am not comparing these games together. For both questionnaires, each question has to be answered on a five-point Likert scale. I am adding an example image of the dataset sheet also. Commented Dec 30, 2021 at 7:24

Thanks for the revised question.

For Game A. The two conditions were scored very similarly, and you have only 7 scores.

a1 = c(4, 3.5, 3, 4, 4.5, 4, 4)
a2 = c(4,   4, 4, 3,   4, 4, 4)


A paired Wilcoxon signed rank test finds no difference between conditions. The P-value is not exact because of the ties in the data. Tests from R.

wilcox.test(a1, a2, pair=T)

Wilcoxon signed rank test
with continuity correction

data:  a1 and a2
V = 5, p-value = 1
alternative hypothesis:
true location shift is not equal to 0


Treating the scores as numerical (even though I wonder if they may be ordinal categorical choices), we find no difference (high P-value), again because the scores are so nearly the same for the two conditions.

t.test(a1, a2)\$p.val
[1] 1


For Game B. In all five categories, Condition 2 was preferred. The Wilcoxon signed rank test will not work because of ties in the differences. However, regarding data as numerical, a paired t test is significant at the 5% level (P-value $$0.012 < 0.05 = 5\%.)$$

b1 = c(4, 3, 3, 3, 4)
b2 = c(5, 4, 5, 5, 4.5)
t.test(b1, b2, pair=T)

Paired t-test

data:  b1 and b2
t = -4.3333, df = 4, p-value = 0.01232
alternative hypothesis:
true difference in means is not equal to 0
95 percent confidence interval:
-2.1329335 -0.4670665
sample estimates:
mean of the differences
-1.3