What does it mean for variances to be equal? What does it mean for variances to be equal? Is this the same as the variance to follow a normal distribution?
 A: If the variances of two random variables are equal, that means on average, the values it can take, are spread out equally from their respective means.
A: I am only a 2nd year psychology degree student, but I think the below demonstration is a likely approximation to assume equal variances. If I am not likely to be accurately correct, your explanation would be appreciated. From - Ms.J.E.Sabharwal
Example scenario (put simply):
Let’s say, a researcher hypothesised that more than 21% of public service employees currently work more than 40 hours per week. He conducted the appropriate hypothesis test and obtained a p-value of 0.143. Based on this result, he concludes that exactly 21% of public service employees currently work more than 40 hours per week.
However, if the data shows the distribution is not significantly different, p=.143, greater than alpha (α=0.05), 143≥α=0.05=Ho. We assume equal variance (measures of spread about the mean is equal) between p̂=.2 (21%) and the sample ‘n ‘ (group of p-hats). This is enough evidence not to reject the value stated in the null, H0: μ ≤ p̂=.2=21% (type 1 error – false positive). Enough evidence that 21% is the average mean of the model (expected value), Mu=p̂=.2=21%. Therefore, this example shows the point estimate is p̂=.2 (21%), suggesting it is likely the null hypothesis is: ‘On average, 21% of public service employees currently work less than 40 hours per week’, instead of the researcher's above conclusion.
I hope this helped.
