Stats Survey Analysis?

Hi, my group recently surveyed high school students on their opinions of different sexual orientations. We categorized the students into four categories: ninth, tenth, eleventh, and twelfth. There are five possible choices: Strongly Agree, Agree, Neutral, Disagree, and Strongly Disagree. I decided to make SA worth 5 points, A worth 4 points, N worth 3 points, D worth 2 points, and SD worth 1 point. I multiplied it all out, added it up, and divided by the sample size to find the average response for each grade level. However, I don't know what tests to do to find whether there is a significant difference between genders. I tried doing a 2 Sample T Test but I don't know how to find the standard deviation out of five categories. I don't understand how a Chi-Square would work. Thanks for you time.

Stats Survey Analysis?
I work with stats a lot in my work. Not to be discouraging, but Are you in high school yourself? Or a college student without a lot of experience with stats?





I don't think you have a lot of experience with these tests (since you are not familiar with calculating standard deviations). There are a lot of statistical errors that can be made without training, and you really need one or two post secondary courses to become familiar with inferential statistics.





It would be better to look at the numbers or percentages of males and females who answered with each answer choice) (SA, A, N etc). Put the percentages into a 5x2 table, answer choice in each row and gender in the columns.





If you don't have to do stats, look over the table of percentages, and see it the percentages of males and females at each level are different.





If you decide to do a statistical test, the chi-square is more appropriate. If you have never done this test, get some advice, and use software.





The problem with averaging the answer choices for each gender is that you don't know whether the difference between SA and A, for example, is the same as the difference between N and D, and so on. If it is, a t-test may be OK, but there are other issues relating to the distribtion of data that have to be considered. There is also the possibility of using a non-parametric test based on differences in the ranking of scores between the genders.
Reply:A chi-square test for independence (A.K.A. contingency table) is the appropriate statistical test. It's not that difficult:


1. Draw a 2x4 grid with your four categories as columns and gender as rows. Enter your integer totals in the appropriate cells.


2. Find the total of each row and each column. Write the grand total in the lower right. Check -- the grand total is column totals = the row totals.


3. Find the expected value for each cell by multiplying that row total by that column total and divide each by the grand total.


4. Find the chi-square value for the table by subtracting the expected value from the cell value (your data). Square this difference and divide by the expected value. Do this for each cell.


5. Add all these values. You should have 8 values. This is your calculated chi-square value.


6. Now for the statistical test. Your critical chi-square value is found in any chi-square table in the back of a statistics book. Decide on your α-risk, say α = 0.05.


Your degrees of freedom is (rows - 1)(cols- 1) = 3. So your critical chi-square value is 7.815.


7. Compare this with your calculated chi-square value. If your calculated value is larger, then the hypothesis of independence cannot be accepted and you have significant differences.





But where are these differences, if they exist? Use some of the previous suggestions to find these. But you can now attach a statistical confidence to your results. If you're still confused, look in a statistical text under contingency table. You will find examples.
Reply:I agree with overanxious that if you're worried about a standard deviation, you might be in trouble. Also, by the way you've worded your question, I'm not sure the s.d. you're worried about is an interesting one.





Ignoring whether you will correctly be able to interpret your results, ExCEL can probably do the analysis you want with a single operation. Under tools%26gt;data analysis (an add-in if you don't see it already) %26gt; ANOVA-Single Factor, you can test for differences in means. Excel wants each of your interesting groups in a seperate column, so you'll need to organize your data.





Interesting questions to ask might be, are there differences across grades? Put each grade in a different column (labels at the top, and ask for them in the ANOVA window) and highlight the whole block of data. The F-test tests if there are any differences (it will not tell you where the significant differences are).





You could ask for differences between genders... use a column for each gender. This uses an F-test for the same hypothesis as a simple t-test with a pooled s.d. (p-values will be the same).


You could ask for differences between genders within a single grade... same thing with only part of the data.





You could ask if there are any gender differences in ANY grade... this is a two factor ANOVA table (with replication), and the data organization is a little more complicated.