Explain why the F-ratio is expected to be near 1.00 when the no hypothesis is tr

Question

Explain why the F-ratio is expected to be near 1.00 when the no hypothesis is true.
A researcher reports and F ratio with DF equals 2, 27 from an independent measures research study. How many treatment conditions are compared with the study? What is the total number of participants in the study? Please show work.
Why should you use ANOVA Instead of several T tests to evaluate mean differences when in an experiment consists of three or more treatment conditions?

Explain why the F-ratio is expected to be near 1.00 when the no hypothesis is true.
A researcher reports and F ratio with DF equals 2, 27 from an independent measures research study. How many treatment conditions are compared with the study? What is the total number of participants in the study? Please show work.
Why should you use ANOVA Instead of several T tests to evaluate mean differences when in an experiment consists of three or more treatment conditions?


A researcher reports and F ratio with DF equals 2, 27 from an independent measures research study. How many treatment conditions are compared with the study? What is the total number of participants in the study? Please show work.
Why should you use ANOVA Instead of several T tests to evaluate mean differences when in an experiment consists of three or more treatment conditions?

Explanation / Answer

Solution:-

a)

When there is no treatment effect the numerator and denominator of F ratio are both measuring the same sources of variability so in this case the F ratio is balanced and should have a value of near 1.00. Therefore there is no hypothesis true.

b) The number of treatments is 3 and total number of participants in the study is 30.

Df1 = k - 1

k - 1 = 2

k = 3

Df2 = n - k

n - k = 27

n = 30

c) Every time you conduct a t-test there is a chance that you will make a Type I error. This error is usually 5%. By running two t-tests on the same data you will have increased your chance of "making a mistake" to 10%. As we increase the number of test Type I error also increases. As such, three t-tests would be 15% (actually, 14.3%) and so on. These are unacceptable errors. An ANOVA controls for these errors so that the Type I error remains at 5% and you can be more confident for any statistically significant result.

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