statistic
a characteristic that describes the sample (i.e. the mean of the sample scores)
parameter
a characteristic that describes the population (i.e. the mean of all population scores)
inferential statistics
techniques used to make generalizations about the population from which the sample was drawn; to determine the likelihood that the sample result is due to chance / error
What are the two possible interpretations that one can make about the sample result from inferential statistics?
1. The result is due to chance/error.
2. The result is not due to chance (i.e. the sample accurately reflects what is really happening in the population).
hypothesis testing
a method of using sample data to evaluate a claim about a population parameter; a method for making rational decisions about the reality of our sample results
rational
systematic and logical with a relatively high likelihood of being correct
hypothesis
statement about the population parameter
null hypothesis
the hypothesis that states the population of interest is
not unusual
; typically the null hypothesis is the opposite of what we believe
H_o: ?? = ??_0
Where...
- ?? = the unknown population mean for the population of interest (what we don't know but wish
alternative hypothesis
the hypothesis that states the opposite of the null; is what we believe (or want) to be true
NOTE: It is possible to frame the alternative in 2 different ways: in a positive/higher manner or "different"/unique manner. The different wording impels the dire
null distribution
the sampling distribution under the null hypothesis
NOTE: It is important that we make the assumption that
the null distribution is normal
(just like with any sampling distribution) in order to properly compute correct probabilities.