1. mean of sample means = population μ; μM = μ

2. Standard deviation of smaple means=average distance a sample mean is from μ; σM= σ/ sq.root n

3. Distribution of all sample means forms normal distribution

σM = Sq. root(Ε(M-μ)^2/n-1)

σM= σ/sq. root(n)

the distance a particular mean is from μ

refers to the location of a mean in a distribution of sample means

z=(M-μ)/σM

t= (M-μ)/ SM

Use to compare a mean with a population value when population variance  and standard error of the mean is not known

random sampling

independence of observations

observations sampled from a normally distributed population

homogeneity of variance (variance of sample=variance in population)

sample mean = population mean; t=0

sample mean greater than pop. mean; t>0

sample mean < pop. mean; t<0

mean difference + or - (critical t value)(estimate of the standard error of the mean)

Note: when the range includes zero, fail to reject the null hypothesis

when it doesn't, we reject the null hypothesis

d= (M-μ)/s

the larger the effect size, the greater the significance

2 population means

2 groups instead of one

ex: do males differ from females in their anxiety level?

1. Normally distributed variables

2. variances are equivalent

3. sample 1 is randomly sampled from population 1 and sample 2 is randomly sampled from population 2

t=Difference between Means/Standard error of the mean difference =variance btwn means/variance within groups (error)

df=n1+n2-2

or

df= (n1-1) + (n2-1)

if zero is within the interval, there is no significant difference

if zero is not within the interval, the difference IS significant

Sp=√((S1+S2)/2)

square root of the average of the 2 sample variances

one way analysis of variance

analyzes differences among 2 or more groups

test statistic = F

F= (variance between groups)/(variance within groups (error))

F ratio cannot be negative

examines variance btwn set of means

larger difference btwn means = larger F ratio

smaller variance within grps= larger F ratio

F = (treatment effect+individual differences+error)/(individual differences+error)

No btwn groups effect means F ratio =1

difference, F ratio > 1

variability between treatment conditions

3 sources

1. the treatment effect

2. individual differences

3. error

2 sources

1. individual differences

2. Error

1. variable is normally distributed

2. variances are equivalent

3. each sample is independent

Numerator/denominator

numerator=btwn variance # grps - 1

denominator=within grps variance (# in each grp - 1 summed across grps)

LSD; same as a t-test

planned comparisons