Psych Stats Exam 3: chapter 9

as sample deviation goes up (greater variability)

estimated standard error goes up and t goes down (less likely to fall in the critical region)

as N goes up (more accurate representation of the population)

estimated standard goes down and therefore, t goes up (more likely to fall in the critical region)

if a very small treatment effect is found alongside a decision to reject the null

the sample size may be too large

with an infinite number of degrees of freedom

the t-distribution starts to look normal

factors affecting estimated standard error

1. the size of the sample 2. the standard deviation

Assumptions of t-test

1. the values in the sample must consist of independent observations 2. the population sampled must be normal

Cohen's d effect size

.2= Small .5= Medium .8+= Large

R^2 (effect size)

0.01: small 0.09: medium 0.25: large

steps to find the t-statistic

1. take a sample out of a population 2. calculate the mean of that sample 3. subtract the population mean from the sample (M-mu) 4. Calculate the estimated standard error based on the sample std. dev. which we calculate and sq. root of n 5. divide the m-mu by the estimated standard error

estimated standard error of the mean

An estimate of the true standard error obtained by dividing the sample standard deviation by the square root of the sample size.

t-statistic formula

The numerator measures the actual difference between the sample data (M) and the population hypothesis (μ). The estimated standard error in the denominator measures how much difference is reasonable to expect between a sample mean and the population mean.

likelihood of committing a type 1 error

depends on the alpha level, you can make it less likely to reject the null by using a smaller alpha level

null hypothesis for a one-sample t-test statistic

pull out one sample from the population do something to it compare the sample mean to the population mean

as degrees of freedom decreases

t looks more and more different from z

r^2 formua

t^2/t^2+df

R^2

the % of the variance explained by the treatment

the t-distribution changes depending on

the degrees of freedom (d.f.)

difference between type 1 and type 2 error

type 1 is when a null hypothesis is rejected when it is actually true; type 2 is when a null hypothesis is accepted when it should have been rejected