Here our dependent and independent variables are discrete there fore we can use CHI SQUARE to check the good ness of fit
By doing this test we will understand the difference between actual observed ratings and the future expectation (of ratings/liking) on the same aspects & deviation and through p value we will be able to determine weather or not we should trust; that the appeared deviation between expected and actual is just because of change and not because of some additional influence.
Chi-square test is only meant to test the probability of independence of a distribution of data. It will NOT tell you any details about the relationship between them.
It is also important that you have enough data to perform a viable Chi-square test. If the estimated data in any given cell is below 5, then there is not enough data to perform a Chi-square test. In a case like this, you should research some other techniques for smaller data sets: for example, there is a correction for the Chi-square test to use with small data sets, called the Yates correction. There are also tests written specifically for smaller data sets, like the Fisher Exact Test.
Just for clarity
You have 2 factors with 2 levels each and one response that will contain numbers in from 1 to 7
Factor one =
color the two levels between that are
red,
blue
Factor two =
type of website the two levels between that are
service,
outlet
above given are your independent variable x
NOW 4 dependent variables are
(1) preference,
(2) trust,
(3) purchasing_intention and
(4) price_fairness
all four will have responses that is ratings form 1 -7
The calculative results can come even through the analysis of rating between 1 to 7
Say for example in order to take a decision we will EITHER put one of the color for some kind of preference, [say] OR not put that color
Thus we have only accept or reject
For clarity I have taken a fictitious data [please see the attachments] then analyzed them on your stated requirements
Say 204 people responded with rating on RED & 183 people responded with ratings on BLUE
In part A I will deal with yes or no kind of feed back then in part B I will also show the results as rating scale 1 to 7 . You may use your data either way.
PART A
I wanted to convert the 1-7 scale ratings in two point rating i.e. accept reject there fore
For count of rater accepted I have added all the rating those were between 1 to 3 (3 columns)
For count of rater rejected I have added all the rating those were between 5 to 7 (3 columns)
For those who rated 4 in the scale of 1 to 7 have no specific meaning of acceptance or rejection to the type of webpage so I should omit that column BUT the total of the count of ratings should be uniform through out color wise.
Remember you have asked for ratings on the basis of color and form different set of populations
Also as per the rule of chi square to relay on the results of calculations you cannot omit the ratings so column 4 cannot be omitted.
In order to keep the end count of total rating uniform I have divided the count of ratings under column 4 in to two and added half of it to accepted col and half to rejected col.
Now the end count of voter will remain same
Please see attachment of data for clarity, in excel color scheme combination and corresponding count/number to scheme is given.
For calculation I have used minitab. The output is given in text file . These outputs have corresponding count/number wise calculated results for ACTUAL / EXPECTED AND DEVIATION.
For ex corresponding count/number 3 stands for red::service:
urchasing_intention
The given data in excel is a random generation of data in excel there fore they are similar with less deviations
In real time data you may get huge deviation also.
Please see the attachments
Lets take example of one of the outputs in file A - CHI SQUARE for all ratings clasified in accepted rejected
We take the scheme no. 1.
The observed/actual rating (say) for accepted = 107 when what you can expect is 102.33
The observed actual rating (say) for rejected = 97 when what you can expect is 101.67
Also the chi sqr output for deviation i.e. (deviation sqr)/ expected rating [(107 - 102.33)^2/102.33] = 0.213
This is < 0.6 thus not reliable for making any decision weather this color scheme 1 will bring any attention etc.
We can also use this number 0.213 to find P value in chi square table.
Incase p value come to be less than 0.05 then we say that there are less than 5% chances that there is no external influence on the deviation between observed vs expected (ideal) i.e. we can estimate the viewer’s preference for future through expected observation value. i.e. 102.33 (count of votes of acceptance)
Because the chance is less than 5% we cannot rely ; there are 95% chances that there exist external influence and that in future we will not get acceptance of 102.33 people out of 204 voters
State your conclusion in terms of your hypothesis.
In the file Part A - CHI SQUARE for all ratings clasified in accepted rejected see the final P value this also states that you cannot rely much on complete set of feed back. But remember this observation is due to non randomness of system generated data and not actual feed back.
a. If the p value for the calculated is p >0.05, accept your hypothesis. 'The deviation is small enough that chance alone accounts for it. In our example P-Value = 0.172, means that there is a 17.2% probability that any deviation from expected is due to chance only and no external factor is acting for this deviation. This is within the range of acceptable deviation. Thus you can relay on the choice of color and scheme
This was just and example data in real time you may have chance to get P value <0.05
b. Suppose If the p value for the calculated isp <0.05, reject your hypothesis, and conclude that some factor other than chance is operating for the deviation to be so great. For example, p value of 0.01 means that there is only a 1% chance that this deviation is due to chance alone. Therefore, other factors must be involved influencing the deviation thus you cannot relay.
PART B [just for understanding]
Calculated for complete ratings 1 to 7
Please see the file for calculation out put Part B - CHI SQUARE for all 7 ratings
You can use this site to calculate your values
Use the site to calculate statistical results
http://graphpad.com/quickcalcs/chisquared1.cfm
