Week 6
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What is a population?
all units of interest,(which can’t all be measured)
What are samples?
subsets of units taken for analysis
What does sampling introduce?
sampling introduces uncertainty, because properties of samples differ from true population values simply by chance
What is sampling error?
chance deviations of sample values from true population values are called sampling error
What is the goal of statistics?
Estimate the values of important parameters, including: • means • proportions • variances • effects
What are the steps in hypothesis testing?
• State the hypotheses • Compute the test statistic with the data • Determine the P-value • Draw the appropriate conclusions
What is the null hypothesis(H0)?
is a specific statement about its value no effect, no difference, nothing interesting going on
What is the alternate hypothesis (HA)?
covers every other possibility some effect, some difference, something interesting going on
if data is consistent with null hypothesis what should be done?
If data are consistent with the null hypothesis, we fail to reject it we never say it’s accepted or true!
if data is inconsistent with null hypothesis what should be done?
If data are inconsistent with the null hypothesis, we reject it and say that the alternate hypothesis is supported instead
What are test statistics used for?
to see whether mismatch compatible with chance, or too extreme for chance to explain
When should a t test be used?
when hypotheses compare • a mean to a null value • two means • two paired means (e.g., before/after) • slopes or trends to null values
When should an F test or ANOVA be used?
more than two means with numerical response and categorical explanatory variable
When should χ2 (chi-squared) be used?
When hypotheses compare • frequencies or proportions to null values • frequencies or proportions
What is the p-value?
the probability of obtaining a test statistic as extreme as we did if the null hypothesis is true
What is the null distribution?
The sampling distribution of the test statistic when the null is true
What are the characteristics of the null distribution?
• values of the statistic are on the x-axis • probabilities of values are on the y-axis • probabilities depend on sample size, but decline as values get more extreme
What is the advantage and disadvantage of a one sided test?
A one-sided test is more likely to reject the null hypothesis - but we fail to reject H0 if an effect occurs in the opposite direction to HA
What is the advantage of a two-sided test?
A two-sided test can detect any effect of interest
What is a type I error?
rejecting H0 when true (a false positive)
What is a type II error?
not rejecting H0 when false (a false negative)
What is the probability of a type I error?
it has a probability of α (the significance level)
What is the probability of a type II error?
• it has a probability of beta(and 1 - beta equals power) - which depends on sample size, effect size, and precision