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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
Estimated standard error formula
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
shape depends on?
how does it compare to z?
- Symmetrical, unimodal
- 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
- -making a Type I error
- -probability in the tail
-Define: 1, 2)
- -the percent of the total variance accounted for by the treatment
- -a ratio of variability: variability due to treatment effect/ total variability
What does r2 measure?
- -How much variability is explained by the treatment
- -How much does removing the treatment effect reduce the variability?
r2 effect size
- -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
- -sample size increases
-Too much variance is bad
- -Big differences between individual scores make it harder to see overall trends
- -bigger standard error
How can you reduce variance?
- -Decrease experimental error
- -Increase sample size to reduce standard error