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STEPS FOR TESTING DIFFERENCE BETWEEN TWO MEANS

STEPS FOR TESTING DIFFERENCE BETWEEN TWO MEANS - doing a...

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STEPS FOR TESTING DIFFERENCE BETWEEN TWO MEANS: You have two sample means and you want to know if they are different, or if one is greater than the other. You want to compare them. You will need to calculate a t score for the difference between the two means and you will need to calculate degrees of freedom. Degrees of freedom are df=N 1 +N 2 -2 2 1 2 1 2 1 ) 2 ( Y Y N N S Y Y t + = You will need to know your sample standard deviation or your variance to calculate the standard error of the difference between means. If your variances are not different (one is not twice as big as the other) you will use the following formula for calculating the Standard Error. 𝑆 𝑌 1 −𝑌 2 = ( 𝑁 1 1) 𝑆 𝑌 1 2 + ( 𝑁 2 1) 𝑆 𝑌 2 2 ( 𝑁 1 + 𝑁 2 ) 2 𝑁 1 + 𝑁 2 𝑁 1 𝑁 2 If your variances ARE different you use the following formula for the standard error 𝑆 𝑌 1 −𝑌 2 = 𝑆 𝑌 1 2 𝑁 1 + 𝑆 𝑌 2 2 𝑁 2 You use the value from either of these formulas to calculate t. Once you have t (t obtained) you use the alpha level you have chosen or are given, whether you are
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Unformatted text preview: doing a one tail or two tail test and your degrees of freedom to figure out the critical value for t. So if for instance you are doing a one tail test, and your alpha level is .05, and you have df of 150. You look at Appendix C Distribution of t, across the top line for one tail tests, to 0.05, and go down to the infinity row because 150 is > 120df and you find a critical t value of 1.645. Let’s say you calculated t to be 2.6. 2.6 > than 1.645 so you can reject the null hypothesis at alpha level 0.05 for a one tail test. You can even take it further and say that we can reject it at a 0.005 alpha level for a one tail test because 2.6 > than 2.576, the critical value of t at that level. Rejecting the null hypothesis means that there is indeed a difference between the two means and since we are doing a one tail test you can say one mean is greater or less than the other....
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