One way ANOVA

In Exercise 10.2 (BPS, Chapter 10, page 505), different amount of corns were planted per acre, the yields are shown in worksheet.
In this experiment, we want to test the null hypothesis that there is no difference between mean yield of corns in five different ratio of planting. The alternative hypothesis is that there is some difference, that not all five population means are equal.
Ho:u1=u2=u3=u4=u5
Ha : Not all of u1, u2, u3, u4 and u5 are equal
We call analysis of variance F test to solve this problem.

Before proceeding with the one way ANOVA test, it's important to check to see if the assumptions of one-way ANOVA are satisfied. Specifically, the populations are normal with possibly different means and the same variance. Select Stat->Basic Statistics-> Display Descriptive Statistics to see the summarized data. Since the ratio of the largest to the smallest standard deviation is less than 2, it's safe to do one-way analysis of variance.

Select Stat->ANOVA->One-way(Unstacked), enter all 5 planting ratio in Response box as shown.
Click Graphs button to specify the boxplot graph to been drawn for these five population. From side by side boxplot we can visually check the assumptions.

After clicking OK, we get the output of ANOVA table. The columns in this table are labeled Source, DF( degree of freedom), SS(sum of squares), MS(mean square), F statistic and P-value. The P-value is 0.736, which is pretty large. So we failed to reject null hypothesis in this example.
For information purpose, the output from the test provides the mean and standard deviation for each group and plots individual 95% confidence intervals for the means.

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