Electricity Demand and Hypothesis Tests

[Richard_R]

Hello All,

I am currently investigating domestic electricity use and whether or not the average (mean) per person use is affected by the number of people living in a household.

I have monitoring data from several hundred households with household occupancies ranging from 1 to 6 people.

My null hypothesis would be that there is no difference in the per person use of electricity for different household occupancy rates (although the per household use would obviously be higher as the occupancy rate increased in this case). The alternative hypothesis would be that there is a difference between the per person electricity use regardless of the household occupancy (at a guess the per person use is probably less as occupancy increases).

Now I know how to calculate the test statistic to test for a significant difference between TWO sample means, however in this instance I have 6 sample means! So what I would like to know is if there is a way to simultaneously test for significant differences across all 6 data sets, or do I need to compare them in pairs of data sets? (Given the number of possible pairs between the 6 data sets this could take some time...)

Any help appreciated. :)

-Rob

 

[phyzguy]

I think what you want to do is calculate:
\chi^2 = \sum_{i=1}^6{\frac{(Mean_i-Model_i)^2}{\sigma_i^2}}
where Mean(i)is the mean of your data for all of the households with i people, sigma(i) is the standard deviation of your data for all of the households with i people, and Model(i) is the prediction of your null hypothesis. Chi_Squared then tells you the probability that your null hypothesis is correct and your data happened by chance.