Confidence intervals & statistical testing Flashcards
Sampling distribution
Under random sampling, sample mean good estimate of population mean.
When sampled from Gaussian distribution, sample mean also has Gaussian distribution.
Squared standard error of the mean
Variance of the sample mean
Standard error of the mean
Square root of the sample variance
Confidence interval
An interval (based on observed data) that contains an unknown population parameter with some specified probability. Statement about the likelihood that true parameter value occurs between two bounds. NOT probability a value falls between 2 points. NOT amount of certainty that an estimate takes a certain value. NOT variability in an estimate.
Critical value
Value of a distribution that occurs with a certain level of probability. Normal distribution: -1 to 1 = 68% of density -1.96 to 1.96 = 95% of density -2.58 to 2.58 = 99% of density
α
Probability of making a mistake.
P(-c
t distribution
T = (Xbar - mu)/((s/SQRT(n))
Distribution only depends on size of sample or degrees of freedom (n-1).
Two forms of error
Type 1 error: Reject the null when it’s in fact true. Probability is equal to alpha level.
Type 2 error: Fail to reject the null when it’s in fact false. Called beta, & speak in terms of power to reject the null when it is false (1-beta).
Test for normality
Shapiro-Wilk test.
Compares the quantiles of your distribution to those of a normal distribution.
Generates a test statistic, W, & a p-value which tell us if data “normal” or not.
Hypothesis testing
z-test for the mean, test a sample mean vs. a hypothesized mean value.
p-values
p-values are probabilities.
Probability of seeing a test statistic as large ast he one we calculate, then test doesn’t negate null hypothesis.
If test statistics like ours occur very rarely, then have small p value & conclude support for research hypothesis.