i say this is from a 'social science' perspective because i will make use of the classical test theory model (and its assumptions) but i'm sure its much more generalizable to other areas of statistics. it really doesn't need more than understanding the basic properties of covariance algebra and i took the bulk of it from the Bollen (1989) book, although this is the univariate case (he deals mostly with the multivariate approach and the matrix algebra can get in the way of understanding things, so i worked on these slides for when i was a TA last year).

in any case, here we go!

let us define to observed scores and as:

so stands for 'true score' and for 'error' with the properties that the error has a mean of 0, a variance and some people like to say it's normally distributed (<--- not a necessary assumption but makes some things nicer later on). it is also important to keep in mind that is UNCORRELATED with , so the errors and the true score have a correlation/covariance of 0. the errors are also UNCORRELATED among themselves. in the kind of research that we do, we want to say stuff about , the true score, because that is the variable that measures the construct of interest. everything else gets in the way so we want to minimize its impact.

this leads to some basic (yet illustrative) ideas:

a similar argument can be made for and we get our first interesting result: measurement error INFLATES variances.

now, what about covariances?

uhm... interesting. it appears that, under the previously described model, measurement error has no influence in the covariances of the observed scores and

now, with these elements, we can re-express the correlation coefficient as:

so the correlation between the

and a similar development can be made for regression coefficients in the case of trying to estimate the true regression to show that the regression coefficient is attenuated and does not estimate even if the sample size grows to infinity.

now, i know the model for classical test theory sounds constricted and artificial. but then again we're social scientists so we get a free pass! :D ]]>

I am researching "The effect of review valence and brand commitment on consumer's purchase intention" for my university thesis. I conducted a 3x2(no review/positive review/negative review x brand/no brand) between subjects design experiment.There were total 6 scenarios for the experiment in which the respondents read the product specs and review for a smartphone (positive/negative) or just product specs (in the no review case). In 3 of the scenarios there was a brand for the smartphone, in the other 3 there was no brand mentioned.

I want to test my hypotheses for the no brand case - if the positive/negative review increases/decreases the purchase intention; and which has a bigger influence on purchase intension. For the brand case - if positive/negative review increases/decreases purchase intension when brand commitment is high/low.

For the purpose I collected data for the purchase probability (respondents had to choose a number from 0-100% after reading the scenarios) and I had questions measuring brand commitment on a scale 1-9 (upper/lower third are considered high/low committed - based on previous paper). Also had questions about reviews effect in general and demographics.

I have to run Analysis of variance to see the difference in means between groups. However, I am not sure

Also is it possible to analyse the first 3 groups (no brand cases) separately from the other 3 (brand cases) since I don't have to compare them based on my hypotheses. Could I run one ANOVA for the brand groups and other for the no brand groups?

My second question is how to see what is the effect of brand commitment on purchase intension (for the brand cases). How to add it in the model so I can see the interaction between review and brand.

Excuse me for the lengthy post but I wanted do describe everything (hope it is understandable), I've put headings so it could be easier to navigate.

Your help will be highly appreciated. Thank you. ]]>

Greetings,

I have a question regarding the definition of the VAR model. What follows is the basic theory behind it.

Could you please explain to me what the covariance matrix Σ is?

Thank You,

A ]]>