Question

Power

What is power and why do we care about it?

What is the difference between a type I and type II error? Which is worse?

How does alpha relate to power?

What are the factors that influence power? What’s the best way to increase the power of your test/study?

What is effect size?

One-way ANOVA

There are two sources of variation. What are they? Why do we care about them?

Why do we use ANOVA? In other words, why don’t we just use t-tests?

What are post hoc tests and why do we care about them?

What’s the distinction between a between subjects/groups ANOVA vs. within subjects/groups ANOVA?

What are the assumptions of ANOVA?

Answer 1

power

power is the measure of the strongness of the test.

if w is critical region the power=p(xvbelongs to w/H₁ is true)

type 1 error-

it is the error when we reject null hypothesis when it is true

type 2 error-

it is the error when we accept alternative hypothesis when it is false

type 1 error is more dangerous.

as we increase type 1 error ,power also increases.

power can be increased by using an appropriate critical region, or the main aim is to find the best powerful test.

effective size that which is required to get a certain level of accuracy.

ANOVA

the two sources of variation are within variation and between variation.

if we have to test the equality of mean for more than two variables then we can not use t test,in that case ANOVA is useful.

between subject is variation between treatment within subject is variation within a single treatment group,or error term.

assumptions

1) various effects are additive in nature

2)observed values are independent in nature

4) error term are normally distributed with mean 0 and constant  variance .