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What do we use sample means for?
To test hypotheses about population means because M approximates u

What does standard error tell us?
How well our sample mean approximates the population mean
Or how much difference we expect between our sample mean and population mean

Obtained difference between the data and hypothesis is
The standard difference between M and u

Sample variance equation
s^2
s^2=SS/df

Estimated standard error formula
Sm
sqrt(s^2/n)

When is the t statistic used?
When the population variance is unknown


As the df for a sample increases,
the better the sample variance represents the population variance and the better the sample mean represents the population mean

As as the sample variance approaches the population variance,
the more the t becomes like a z

Sampling distribution of t characteristics
Symmetry?
u?
shape depends on?
how does it compare to z?
t approximates?
 Symmetrical, unimodal
 u=0
 shape depends on sample size n
 higher tails and lower peak than z
 t approximates z distribution as n approaches infinity

If prescise df is not shown use
the critical value for the next smallest df shown

p value
Probability of
Probability of
 making a Type I error
 probability in the tail

Variance (r2)
Define: 1, 2)
Formula
 the percent of the total variance accounted for by the treatment
 a ratio of variability: variability due to treatment effect/ total variability
 r2=t2/t2+df

What does r2 measure?
1,2)
 How much variability is explained by the treatment
 How much does removing the treatment effect reduce the variability?

r2 effect size
small
medium
large

Confidence interval
Estimates?
Centered around?
Formula?
 The treated population mean from our treated sample mean
 Interval or range of values centered around a sample statistic
 See chart

T vs. z
Probability of extreme values is higher for
Critical values will be larger for
Critical values of t get closer to z as
 t
 t
 sample size increases

Too much variance is bad
Higher variance=
 Big differences between individual scores make it harder to see overall trends
 bigger standard error

How can you reduce variance?
1,2)
 Decrease experimental error
 Increase sample size to reduce standard error

