Chapter 8: Confidence Intervals, Effect Size, and Statistical Power
Point estimate: a summary statistic from a sample that is just one number
used as an estimate of the population parameter.
Interval estimate: based on a sample statistic and provides a range of
plausible values for the population parameter
Confidence interval: an interval estimate, based on the sample statistic, that
includes the population mean a certain percentage of the time, were we to
sample from the same population repeatedly.
Calculating confidence intervals with z Distributions
Step 1: Draw a picture of a distribution that will include the confidence interval.
Step 2: indicate the bounds of the confidence interval on the drawing.
Step 2 ^^^^ Step 2 ^^^^
Step 3: Determine the z statistics that fall at each line marking the middle 95% Step 4: Turn the z statistic back into raw means
M = - z(σ ) + M
M upper = z(σ )M+ M
Step 5: Check that the CIs make sense
Does this interval make sense?
Does the sample mean fall in the middle of the interval?
Effect size and Prep
The effect of sample size on statistical significance
Statistical significance (rejecting the null hypothesis) provides only limited
information about what is happening in any particular situation. Tell you that
2 groups are different.
Indeed, statistical significance only tells you that a difference, at the
population level, is not zero (i.e, the null hypothesis). Which is really not
When a hypothesis tests rejects or fails to reject the Ho, we say there has
been a significant effect. This does not mean there has been a substantial
The statistical significance indicates that we know this result was unlikely to
have occurred by due to random sampling/a