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# Res 342 Week 2 DQ 2

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Week 2 DQ 2: Why is the F distribution important? How do you determine if a
significant difference exists among the groups in ANOVA? How do you determine
differences between the groups in ANOVA?
The F distribution is the ratio of two independent chi-square variables each divided by
its degree of freedom. A chi-square variable is going to inform someone how close their
expectations were to the actual value, useful for hypothesis testing for example. According to
the text, “F distribution is denoted by two sets of degrees of freedom in which there is one for
numerator and one for denominator. The numerator degrees of freedom are n1-1 and
denominator is n2-1. Notice that the degrees of freedom are subtracted by one which would be
the ratio that represents the equal variances” (Doane and Seward 2007). The shape of the
curve can vary depending upon the variables of the equation, which is a complex ratio. What
one is really looking for in the F distribution is how close the plotted values on the graph match
up.
If the F statistic is small, then it indicates that the observed variation is near the
expected variance and there is no evidence to reject the null hypothesis that all the group
means are equal. If the F statistic is large, large enough to be in the reject region for the fixed
level test then it is evidence that the variance in observations is considerably greater than
expected and thus the null hypothesis is rejected and the alternate is accepted. The alternate
hypothesis for ANOVA is that at least one of the means is different from the others.
In ANOVA, the F-statistic is determined by creating the ration MSR/MSE. This produces
a test statistic that follows an F-distribution with k-1 and n-k degrees of freedom. To determine
the differences between the groups, we can just compare the means of those particular groups.
References:
Doane D.P. & Seward L.E (2007) Applied statistic in business and economics.
Boston ,MA:Mc Graw-Hill/Irwin
Retrieved on October 30, 2010, from website:
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