Question

The One-Way ANOVA applet lets you see how the F statistic and the P-value depend on the variability of the data within groups, the sample size, and the differences among the means.

(a)

The black dots are at the means of the three groups. Move these up and down until you get a configuration that gives a P-value of about 0.01. What is the value of the F statistic?

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(b)

Now increase the variation within the groups by sliding the standard deviation bar to the right. Describe what happens to the F statistic and the P-value.

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(c)

Using between- and within-group variation, explain why the F statistic and P-value change in this way.

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The F statistic for one-way ANOVA—and its P-value—depend both on the group means (black dots in this applet) and the spread (standard deviation) and number (n) of observations within each group (colored dots). This applet allows you to see how varying the means, standard deviation, and sample size affects the F statistic and resulting P-value for an ANOVA.

Move the group means by dragging the black dots with the mouse. Increase or decrease the spread within the groups by dragging the slider at the top. Change the sample size n with the slider on the left. Watch the P-value change on the scale at the bottom as you perform all these manipulations. The value of the Fstatistic appears in red under the P-value scale. Click NEW SAMPLES to generate a new set of sample data.

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Std. Dev. = 2.66 Mean = 6.17________________________________________________6

Std. Dev. = 3.31 Mean = 5.06

Std. Dev. = 2.89 Mean = 4.24________________________________________________4

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p = 0.5 0.25 0.15 0.1 0.05 0.025 0.01 0.005 0.001

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F= 4.72

p= 0.0105

Answer 1

Answer :

(a).

• from the given data, if p-esteem is about 0.01, the F measurement worth is = 4.72

(b).

• presently increment the variety with the gatherings by sliding the standard deviation bar to one side. what befell the F measurement and P-esteem.
• on the off chance that standard deviation increment, the F measurement worth is increment and the p-estimation of the test is decline.
• this implies the mean variety between the treatment is exists.

(c).

• F test to decide if the variable between gathering means is bigger than the fluctuation of the perception inside the gathering.
• in the event that that proportion is adequately huge, you can infer that not every one of the methods are equivalent.
• this takes us back to way we dissect variety to make judgment about methods.