Use the following data set to complete the ANOVA table and...

Use the following data set to complete the ANOVA table and answer the questions. Group 1 Group 2 Group 3 2 2 3 5 5 4 4 2 8 7 3 7 6 1 7 ANOVA table Source SS df MS F p-value Treatment ______ ______ ______ ______ ______ Error ______ ______ ______ Total ______ Is there a significant difference (?=0.05) between at least two of the four groups for the analysis in question 1 (above)? (circle one) YES NO Confidence interval for Group 1 (______, ______) Confidence interval for Group 2 (______, ______) Confidence interval for Group 3 (______, ______) Is Group 1 significantly different from Group 2 at the ?=0.05 level of significance YES NO Is Group 1 significantly different from Group 3 at the ?=0.05 level of significance YES NO Is Group 2 significantly different from Group 3 at the ?=0.05 level of significance YES NO

Transcript

00:01 Hello student here we have to use a given set to complete the anova table.

00:06 So here first we find out a data summary.

00:09 So here group n summation of x x bar summation of x square and standard deviation.

00:18 So here first is group 1 group 2 group 3.

00:24 So here 5 5 5 now sum of all observation in group 1 which is equals to 24 x bar is equals to 4 .8 130 and sample standard deviation 1 .92 now similarly 13 2 .6 43 and 1 .51 now 29 5 .8 187 and 2 .16 now mean of all these three groups, which is equals to 4 .4 now here first.

01:05 We calculate sum of square between groups.

01:09 So here sum of square between groups, which is calculated as summation over ironing from 1 to k ni into x i minus x bar square now, we substitute all the values and solve for it.

01:27 So here 5 into 4 .8 minus 4 .4 square plus 5 into 2 .6 minus 4 .4 square plus 5 into 5 .8 minus 4 .4 square, which is equals to 26 .8.

01:56 Now here we find out sum of square within groups or so here sum of square within group, which is calculated as summation over ironing from 1 to k ni minus 1 into si square now, we substitute the value.

02:17 So here 5 minus 1 which is equals to 4.

02:21 So here 4 into 1 .92 square similarly 4 into 1 .51 square plus 4 into 2 .16 square here sum of square within group, which is equals to 42 .8.

02:42 Now our another table is written as source of variation decrease of freedom sum of square mean sum of square f ratio and here corresponding p -value.

02:57 So your first source of variation is treatment.

03:01 Second is error total now, we have total 15 observations.

03:09 So here 15 minus 1 that is 14 degrees of freedom.

03:13 Now we have three groups.

03:15 So here 3 minus 1 2 and here 14 minus 2, which is equals to 12.

03:20 Now sum of square which we have calculated that is 26 .8 and 42 .8 now 26 .8 plus 42 .8, which is equal to 69 .6...

Question

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