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Finding the CI in t-test analysis
Is there a way to get the confidence interval on the worksheet for t-Test:
Two-Sample Assuming Unequal Variances? |
#2
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Dahliah2 -
Is there a way to get the confidence interval on the worksheet for t-Test: Two-Sample Assuming Unequal Variances? < A method is described on page 132 of my book, Data Analysis Using MS Excel: Updated for Office XP. It uses the results from Analysis ToolPak on a worksheet, working "backwards" from the reported t Stat to get the Standard Error. Use cells and cell references for the following six quantities: Observed Mean Difference = Mean2 - Mean1 (using references to cells in the ToolPak results in the row labeled "Mean") Standard Error = (Observed Mean Difference - Hypothesized Mean Difference)/(t Stat) 95% Confidence t =TINV(0.05,df) Half-Width = (95% Confidence t)*(Standard Error) Lower Limit = Observed Mean Difference - Half-Width Upper Limit = Observed Mean Difference + Half-Width - Mike www.mikemiddleton.com |
#3
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The trick with unequal variances is how to calculate standard error and
evaluate df. This is discussed at http://groups-beta.google.com/group/...a5754092189c39 This (Satterthwaite's) formula for effective df usually results in non-integer df. The Analysis ToolPak uses ROUNDDOWN(df,0), which is a conservative approximation. The TTEST worksheet function uses the estimated df directly, but that too takes some work since the TDIST function only uses integer df. t^2 is distributed as F(1,df), but FDIST also only uses integer df. You can use the identity FDIST(f,d1,d2) = BETADIST(d2/(d2+d1*f),d2/2,d1/2) which reduces in this case to TDIST(t,df) = BETADIST(df/(df+t^2),df/2,0.5) to reproduce the p-value given by TTEST, which will be smaller than the p-value given by ATP. Working backward, to get a confidence interval you would use TINV(alpha,df) = SQRT(-BETAINV(alpha,df/2,0.5)*df*(BETAINV(alpha,df/2,0.5)-1))/BETAINV(alpha,df/2,0.5) to deal with the non-integer df. Jerry Dahliah2 wrote: Is there a way to get the confidence interval on the worksheet for t-Test: Two-Sample Assuming Unequal Variances? |
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