8: Basics of Statistical Inference Flashcards
inference
allows us to draw conclusions from data
formal inference
emphasizes substantiating our conclusions via probability calculations
probability
allows us to take chance variation into account
margin of error
how accurate we believe our guess is based on variability of the estimate, and how confident we are that the procedure will catch the true popln mean, mu
confidence interval
estimates unknown parameter with an indication of how accurate the estimate is and of how confident we are that the result is correct
confidence level
states probability that the method will give a correct answer - e.g. in the long run, 95% of your intervals will contain the true parameter value
margin of error & confidence interval equation
m = z * (std dev) / sqr rt n
CI = x-bar +/- m
margin of error of confidence interval decreases as
- confidence level C decreases
- sample size n increases
- popln std dev decreases
null hypothesis
statement being tested in a test of significance. usually, the null hypothesis is a statement of “no effect” or “no difference in the true means”
Ho = there is no difference in the true means
alternative hypothesis
Ha = the true means are not the same.
One or two-sided? whether a parameter differs from Ho in a specific direction OR either direction
P values
probability (assuming Ho true) that the test statistic would take a value as extreme or more extreme than that actually observed = P value of a test. The smaller the P-value the stronger the evidence against Ho provided by the data.
statistical significance
if the p-value is as small or smaller than alpha, we say that the data are statistically significant at level alpha
standard error
when the std dev of stat is estimated from the data, the result is called the SE of the stat. The SE of the sample mean is: SE (sample mean) = s / sq rt (n)
when we substitute the SE (s / sq rt n) for the SE of x-bar, the stat does NOT have normal distribution – it has a ___________
t distribution
