The following data are the morning and evening temperatures for three Michigan c

Question

The following data are the morning and evening temperatures for three Michigan cities for four consecutive days in October. Enter the table "as is" into Excel, and use the Analysis Tool Pack to run a Two Way Analysis of Variance (with Replication). Use the entire table, including row and column titles as the data block. Print and analyze (written comment) the results. Are there significant differences between the cities? Are there significant differences from morning to evening? Are there significant interactions between locations and time of day? Overall, what can we Conclude? We are running this analysis to select a site for planting an apple orchard. Suggest a few other variables that might be of interest.

Explanation / Answer

The excel output is as follows:

Here,since the pvalue for columns is more than 0.05,we reject the null hypothesis and state that is there is significant difference between the cities.

Since,the p-value for interaction is more than 0.05,we state that there is interaction between location and time of the day.

Anova: Two-Factor With Replication SUMMARY Lansing Ann Arbour Grand Rapids Total Morning Count 4 4 4 12 Sum 175 178 169 522 Average 43.75 44.5 42.25 43.5 Variance 30.25 17.66666667 29.58333333 22.09091 Evening Count 4 4 4 12 Sum 229 238 235 702 Average 57.25 59.5 58.75 58.5 Variance 32.25 57.66666667 62.25 42.45455 Total Count 8 8 8 Sum 404 416 404 Average 50.5 52 50.5 Variance 78.85714286 96.57142857 117.1428571 ANOVA Source of Variation SS df MS F P-value F crit Sample 1350 1 1350 35.26851 1.28E-05 4.413873 Columns 12 2 6 0.156749 0.856073 3.554557 Interaction 9 2 4.5 0.117562 0.889763 3.554557 Within 689 18 38.27777778

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