midterm 2 statistics

type 1 error

rejecting the null when the null hypothesis is true

type 2 error

FAILING to reject the null when the is actually false

z score equation

x minus the mean over the standard deviation

steps for a one sample t test

1. find null hypothesis and alternative hypothesis

2. find t crit

3. find t obs

4. if |t obs| is bigger than |t crit| reject null hypothesis

steps for paired sample t test

1. find D aka mean of the DIFFERENCE of the scores

2. find the s_D aka the standard deviation of the difference of the scores

3. find tcrit

4. find t obs

5. if |t obs| > |t crit| reject the null hypothesis

what is n_D

number of pairs in paired t test

what is m_D_0

equals zero because we assume there is no change

steps in independent t test

1. null is the difference in means is equal to zero

2. find pooled variance and pooled standard deviation

3. find t crit

4. find t obs

5. if |t obs| > |t crit| reject null

what is pooled variance

weighted average of the 2 samples

when to use t-test over z-test

use t-test when you don’t know the population standard deviation

what is statistical power

probability of rejecting a false null hypothesis

what is cohen’s d

what are degrees of freedom

what is 𝛽

probability of failing to reject false null hypothesis

how to find 𝛽

which error is in the researchers control

type 1 error, because researcher sets alpha

𝑍 ∼ 𝑁(0, 1) in words

𝑋 ∼ 𝑁(132,12) in words

what is p-value

a 𝑝-value is the probability of observing a sample mean as extreme or more extreme than the one we got if the null hypothesis is true

interpreting p value

if p < a, reject null hypothesis

how to find degrees of freedom independent t test

add number of people in both groups together and subtract 2