Question

Homework8 Name and types DUE: April ANOVA theory 17, 2019 1) Why can we not do a series of t-tests when comparing more than two groups? 2) For an ANOVA, in English, what is the null hypothesis? The alternative? What would it mean to reject the null? How is this different than when we reject the null in a t test? 3) If I told you I ran a three-way MANCOVA, what could you tell me about my design and why? 4) If my design had two factors and a covariate, what would be the analysis I should run?

Answer 1

1)

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%. The formula for determining the new error rate for multiple t-tests is not as simple as multiplying 5% by the number of tests.

However, if you are only making a few multiple comparisons, the results are very similar if you do. 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 that any statistically significant result you find is not just running lots of tests

2)

A hypothesis test that is used to compare the means of two populations is called t-test. A statistical technique that is used to compare the means of more than two populations is known as Analysis of Variance or ANOVA.

In T-test, The null hypothesis takes the form of H₀: µ(x) = µ(y) against alternative hypothesis H1: µ(x) ≠ µ(y), wherein µ(x) and µ(y) represent the population means. The degree of freedom of t-test is n1 + n2 – 2

The null hypothesis takes the form of H₀: all population means are the same and alternative hypothesis H1: at least one population mean is different.

3)

Three-way MANCOVA has generally one primary aim: to understand whether the effect of one independent variable on the dependent variables (collectively) is dependent on the value of the other independent variable. This is called an "interaction effect". However, if no interaction effect is present (usually assessed as to whether the interaction effect is statistically significant), you would normally be interested in the "main effects" of each independent variable instead. This is somewhat akin to assessing the effect that an independent variable has on the dependent variables collectively when "ignoring" the value of the other independent variable.