I want to compare the english readers in Four Zones, like Costal Andhra, Rayalaseema and Telangana based on a questionaire which contains 14 questions and from each zone 200 members selected at random
Yes, the "levels of measurement" are nominal (classification only), ordinal (preserves rank), interval (distances between scale units are identical, but the position on the number line is arbitrary--no "true zero," etc.), and ratio (numbers are essentially identical with the "real number" line, with a "true zero," etc.). ANOVA-based approaches require at least interval data for the dependent variable(s). If the survey items used Likert-type scales, it is generally safe to assume you have interval data (although this remains controversial among statisticians & researchers).
in normal and hemogenous sample, ANOVA-test compares mean of a dependent variable (English reader in your study) between more than 2 groups (4 groups in your study). However, it can not show how much differences there are between groups. Normality should be assessed only for dependent variable.
are you going to compare capability of english reader in all four zone such as Costal Andhra, Rayalaseema and Telangana or the difference between two zones such as costal andhra n Ravalaseema and so on? or what?
Reiterating as well as clarifying: the four "zones" are your independent variable. You're interested in whether there are statistical differences (reject H0) among the four zones. However, the 14 survey questions constitute 14 possible dependent variables--unless they form integrated scales providing multiple measures of one or more variables.
If the 14 survey questions are 14 dependent variables, MANOVA should be used first before using ANOVA for planned comparisons.
If the assumption of equal population variances (as indicated, can be checked using Levene) within each of the zones is valid, then ANOVA is robust to the assumption of normality.
Yes, the "levels of measurement" are nominal (classification only), ordinal (preserves rank), interval (distances between scale units are identical, but the position on the number line is arbitrary--no "true zero," etc.), and ratio (numbers are essentially identical with the "real number" line, with a "true zero," etc.). ANOVA-based approaches require at least interval data for the dependent variable(s). If the survey items used Likert-type scales, it is generally safe to assume you have interval data (although this remains controversial among statisticians & researchers).
Better use a Chi squared test for non-parametric data like yours. Questionnaires do not involve independent measurement of variables. What numbers you are getting would be ranks given by respondents. ANOVA is applied only when you are measuring something; for example blood pressure of those respondents. I am afraid using ANOVA for non-parametric data would violate the basic assumption of the test.
I also have a question. In one repeated measures ANOVA, Most of cells (or groups) of the design have passed Levene test. Can I say that the data can be analyzed by the repeated measures ANOVA? Or can I just analyze the cells that have passed Levene test?
Levene's test is for homogeneity of variances. You can perform any flavour of ANOVA with Levene's test passed / failed. It affects selection of your post-hoc test. If Levene's test returns P < 0.05, then it means variances in your sample groups are not equal and you have to select a post hoc test that does not assume equal variances, e.g. Dunnett's T3, Games Howell etc. However, if Levene's test returns P > 0.05 then it means your variances are not significantly different and you can select a post hoc test that assumes equal variances e.g. Bonferoni, Tuckey etc.