Dear Pamela,

That will depend upon your research goals. I will suggest you to start with simple descriptive statistics (mean, standard deviation, CV etc.) Then, you might want to compare groups (gender, age etc) using T and U statistics ou ANOVA. Also, Factorial Analysis (FA) is a good tool in order to reduct the number of indicators and define new variables (dimensions) based on your indicators. Thus, regression analysis might be the better statistical procedure, after the FA, to present your more relevant findings.

Good luck and best regards,

E B Abbade

Lin's CCC may be a possibility

http://en.wikipedia.org/wiki/Concordance_correlation_coefficient

you can use ANOVA to or factor analysis

Weighted mean if data are grouped according to the scale or arithmetic mean if each response is treated individually. Depending on your type of sample (if your participants do not cover the whole population) you can proceed to inferential analysis such as Z test of one sample.

When you mention 'rate', are you referring to 500 respondents across a period of time and you want to find out whether their responses change significantly (statistically speaking) across time? Assuming it is normal - which you may need to conduct a test for normality - you can use ANOVA to extract F-value as by-product from grouped responses, making sure pvalue is below 5% chance in making a type-I error. But this is provided that the sub-groups in ANOVA are also normally distributed too. You can observe the change in mean-value across time periods. ANOVA is sensitive to non-normality...

you can use ANOVA and Compare Means to or factor analysis.

You can also make use of the kappa coefficient.

Best Regards

I would suggest Factor Analysis/Principal Component Analysis.

Dear Pamela,

That will depend upon your research goals. I will suggest you to start with simple descriptive statistics (mean, standard deviation, CV etc.) Then, you might want to compare groups (gender, age etc) using T and U statistics ou ANOVA. Also, Factorial Analysis (FA) is a good tool in order to reduct the number of indicators and define new variables (dimensions) based on your indicators. Thus, regression analysis might be the better statistical procedure, after the FA, to present your more relevant findings.

Good luck and best regards,

E B Abbade

I would like to agree with most of the answers given by colleagues. Start with Cronbach Alpha to check for reliability of your instrument in terms of internal consistency. That is, were your respondents answering the same construct? Given your large sample and that you used a Likert Scale, Factor Analysis/Principal Component Analysis would be good. But again, it all depends on your research question/objectives.   

PCA could be a first approach if you are not sure to succeed in test of normality of ANOVA

Wow, you all are fabulous, I apprecia your help and will indeed use several of your suggestions. Again thank you

ANOVA

and

binomial test.

Depends on the merit of your study non-parametric tests such as chi-squared test, wilcoxon signed-rank test, etc, can be applied for analysis of Likert scale data. You may want to check this out:

http://asq.org/quality-progress/2007/07/statistics/likert-scales-and-data-analyses.html

I don't have experience with Lickert, but without knowing how you are grouping/summing, and based on your info, the safe bet here would be Kruskall-Wallis 

Is your scale data normally distributed and have you checked reliability? If both ok you could start with means for simple comparisons.

Was all of the data collected in one time period? This gives/limits options on time comparisons

what profile questions were asked? This will allow for demographic analysis (t-tests and ANOVA)

did you have clusters of Likert questions? You could collapse the clusters (reduce 3, 4, 5, 6 column clusters) and cross correlate to observe if there are cluster relationships? If this is the case perhaps you could identify a cluster as dependent and others as independent and undertake regression?

as your sample size is large you could subject all scale data to a principal component analysis or more usefully exploratory factor analysis to examine the groupings based on loadings.

all depends on initial normality and reliability checks being positive

Ordered Multinomial Logistic Modelling

Expanding on the suggestion from Robert McClelland above, you probably have several different constructs that you expect to see measured by these 61 items. 

A true Likert Scale is actually a summative scale - the sum of several 1-5 (Agree-Disagree) items. (Or 7-point agree-disagree items). Humans are fickle and inconsistent, and Agree-Disagree is a very blunt measurement, so we ask several agree-disagree questions that are all variants of the same idea. The logic is that an overstatement on one item will be compensated by an understatement on another item. Thus when the items are summed, or averaged, then we get a figure that is reasonably consistent over time for the one person, and differences are reasonably consistent between individuals. 

It's a lot easier dealing with, say, ten constructs than with 61 items.

That is, for example, items (questions) 1 through 6 may be designed to measure "Perceived work stress", and items 7 though 13 may be designed to measure "Perceived workplace harmony", items 14 through 20 relate to "Job Satisfaction", and so on. If this is the case then you would combine the relevant items to make a summed rating scale - you add them up. For this to work properly you need to be sure that all of the items in a summative scale are highly positively correlated. The usual test for this preliminary task is a Confirmatory Factor Analysis. Or Cronbach's Alpha if you are happy giving all items equal importance.

If you have no theory about what constructs align with what items (What were you thinking when you wrote the questions?) then you would check if there are any "natural" groupings of question/items, using Exploratory Factor Analysis. Again, this will help you to reduce all of those 61 items into a smaller number of different constructs.

Don't stop thinking when using any of these techniques though: If there is no logical reason for an item to be included in a scale then don't just blindly add it to the scale. With 61 items it is very likely that several items will appear to be correlated purely by chance.

These techniques assume that your data are at least Interval-scaled, but of course an agree-disagree scale is, in truth, an ordinal scale. But the techniques work fine just the same. Many years ago my evil Stats Professor made us Doctoral students run hundreds of simulations, testing the results of violating various assumptions of data in statistical analyses, and comparing results using the "correct" techniques. Summing, averaging and correlating Likert Scales is fine.

The following reference is aged, but it may serve as a primer before you move to more recent methods.

Title: A Paradigm for Developing Better Measures of Marketing Constructs

Author(s): Gilbert A. Churchill, Jr.

Source: Journal of Marketing Research, Vol. 16, No. 1 (Feb., 1979), pp. 64-73

Stable URL: http://www.jstor.org/stable/3150876

Abstract: A critical element in the evolution of a fundamental body of knowledge in marketing, as well as for improved marketing practice, is the development of better measures of the variables with which marketers work. In this article an approach is outlined by which this goal can be achieved and portions of the approach are illustrated in terms of a job satisfaction measure.

I am surprised a lot of people are suggesting to begin with things like PCA. First look at how items are distributed and the scatter plots (jittering the points so that they can be seen) of the pairwise comparisons. Some of these exploratory data analysis techniques might suggest removing an item (e.g., if it seems to be mis-understood by respondents because of a large number of missing values, if it is highly correlated with another, if it has little variation).

You should also have some ideas about how the items group together (otherwise how would you have chosen them). This will likely relate to the research goals that you have, and these will inform how you should analyze the data. Without this knowledge it would be difficult to suggest methods to use.

Thank you all for your suggestions I have chosen to do factor analysis.

Yes, I think FA or PCA would be the best option for your data.