What does the F crit mean



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 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 |Variance | | | |Employee 1 |3 |43 |14.33333 |9.333333 | | | |Employee 2 |3 |53 |17.66667 |9.333333 | | | |Employee 3 |3 |43 |14.33333 |6.333333 | | | |Employee 4 |3 |59 |19.66667 |40.33333 | | | | | | | | | | | | | | | | | | | |ANOVA | | | | | | | |Source of Variation |SS |df |MS |F |P-value |F crit | |Between Groups |62.33333 |3 |20.77778 |1.272109 |0.347709 |4.06618 | |Within 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.

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