# Calculating Statistical Significance and Correlation of this dataset

This may sound like a beginner's question, but forgive me for asking this because I'm definitely a beginner trying to learn about statistical analysis.

Assume, I have collected survey data from N=100 (40 males, 60 females) students about their opinion regarding two short stories. I asked them to rate from 1 (very bad) to 5 (very good) regarding Q1 and Q2 about each of the aforementioned stories. Suppose I also know the gender of the students and code them as "1" for males and "2" for females. As a result, I have an excel sheet that looks something like what's shown in the image below: As part of data exploration, the questions I could ask about this dataset are:

1. Average Q1 and Q2 ratings for each story (can split by gender) and corresponding standard deviations.
2. Which story is more often rated as favorite by all students? (i.e. the mode of the last column in the table)

Those questions above can easily be answered. But the harder ones that I need help from statistics genius here are:

1. Suppose I have the average and standard deviation values for Q1 ratings by both male and female students, which test do I use to find out if there's any significant difference between male vs. female ratings for Q1 (or is that even possible)?
2. Can I use the same technique as above (that you might suggest me to use) to calculate if there's any significant difference between Q1 ratings of Story#1 vs. Story#2?
3. Is it possible to figure out whether being most frequently rated as favorite has any significant correlation to the average rating scores of either Q1 or Q2 or both? If so, what technique do I use and is there a freely available software that might help me do the calculation?
4. Suppose I know the word length of these two stories above. What technique (and again software) do I use to see if there's any significant correlation between Message length and the story being rated as favorite (or Message length and Q1 average ratings)? You might say I only have two stories, but please just assume that the above is just a toy example, and that I have about ten stories in my real data set with ratings for Q1, Q2,..., Q5 for each story.

As a final note, I do not expect anyone to explain me in detail of how to calculate things step by step (if someone could do so, I'd be eternally grateful!). The best I'm hoping for is a link (URL) to, say, an easy-to-understand (because I'm not very smart) explanation of how to calculate your suggested method of analysis for each of the above question. Also, if I'm missing any question that is worth asking about this dataset, please let me know. :)

Any help would be greatly appreciated. Thank you!

• Your ratings are ordinally scaled. So it is inappropriate to calculate means and standard deviations. Also it is poor science to do a survey without knowing which questions this survey should answer. Maybe you should look for a statistical consultant because what you need to know is much more than what can be answered here. – Horst Grünbusch Dec 27 '14 at 13:09
• @HorstGrünbusch Thank you for the answer! I'm glad I asked this question before collecting the data. Now I understand why it doesn't make sense to treat Likert ratings as if they're interval variables. :) – user1330974 Dec 27 '14 at 19:22
• Fortunately, you can use some kind of ANOVA on the ranks of your data. Unfortunately, this procedure is not implemented in most statistical software, and the way of proper ranking depends on more insight into your research question. – Horst Grünbusch Dec 28 '14 at 16:28
• @HorstGrünbusch, are you referring to one of these tests: Wilcox signed ranked test, Kruskal-Willis test or Friedman test? Thank you. – user1330974 Dec 29 '14 at 0:36
• Yes, but here we might have a factorial structure that can't be handled by these tests. – Horst Grünbusch Dec 29 '14 at 14:52