Anova
2
What does the F crit mean? F crit mean the Critical value of the ANOVA test procedure. Here, F crit = 4.256492 What numbers represent the SST, SSE and SS Total? SST is the variation due to treatments (Between Groups Sum of squares). Here, SST = 10.5. SSE is the variation within the treatments or the random error (Within groups sum of squares) Here, SSE = 182.5 SS Total is the total sum of squares. Here, SS Total = 193 What does the P-value number mean? Here, P-value = P[ F > F crit] = 0.777455 We reject the null hypothesis if the P-value < α, the significance level. If we choose α = 0.05, then P-value > 0.05. So we do not reject the null hypothesis and conclude that average time it takes to process applications in the three offices are the same. The P-value is a probability, with a value ranging from 0 to 1. It is the answer to this question: If the populations really have the same mean overall, what is the probability that random sampling would lead to a difference between sample means as large (or larger) than you observed? Here the P-value = 0.7775 means that there is a 77.75% chance of observing a difference as large as you observed even if the population means are identical. How do the F and F crit relate to each other? What do these numbers mean? F is the value of the test statistic and F crit is the critical value. The test statistic in ANOVA is the ratio of
Transcript of Anova
What does the F crit mean?
F crit mean the Critical value of the ANOVA test procedure.Here, F crit = 4.256492
What numbers represent the SST, SSE and SS Total?
SST is the variation due to treatments (Between Groups Sum of squares).Here, SST = 10.5.SSE is the variation within the treatments or the random error (Within groups sum of squares)Here, SSE = 182.5SS Total is the total sum of squares.Here, SS Total = 193
What does the P-value number mean?
Here, P-value = P[ F > F crit] = 0.777455We reject the null hypothesis if the P-value < α, the significance level.If we choose α = 0.05, then P-value > 0.05. So we do not reject the null hypothesis and conclude that average time it takes to process applications in the three offices are the same.The P-value is a probability, with a value ranging from 0 to 1. It is the answer to this question: If the populations really have the same mean overall, what is the probability that random sampling would lead to a difference between sample means as large (or larger) than you observed?Here the P-value = 0.7775 means that there is a 77.75% chance of observing a difference as large as you observed even if the population means are identical.
How do the F and F crit relate to each other? What do these numbers mean?
F is the value of the test statistic and F crit is the critical value. The test statistic in ANOVA is the ratio of two scaled sums of squares reflecting different sources of variability. That is, F = Explained variance / Unexplained variance. The critical value is the number that the test statistic must exceed to reject the test.If F > F crit, we reject the null hypothesis and if F < F crit, we do not reject the null hypothesis.Here, F = 0.258904 < 4.256492 = F crit. So we do not reject the null hypothesis and conclude that average time it takes to process applications in the three offices are the same.
Re-run an ANOVA in Excel and determine if the average processing times between workers (employees are in rows) are the same or different.
SUMMARY
Groups Count Sum Average VarianceEmployee 1 3 43 14.33333 9.333333Employee 2 3 53 17.66667 9.333333Employee 3 3 43 14.33333 6.333333Employee 4 3 59 19.66667 40.33333
ANOVASource of Variation SS df MS F P-value F critBetween Groups 62.33333 3 20.77778 1.272109 0.347709 4.06618Within Groups 130.6667 8 16.33333
Total 193 11
Here, the P-value = 0.347709 > 0.05. So we do not reject the null hypothesis and conclude that the average processing times between workers are the same.
