CFA 11: Hypothesis Testing Flashcards
null hypothesis
Hypothesis Testing
The null hypothesis is the hypothesis to be tested.
alternative hypothesis
Hypothesis Testing
The alternative hypothesis is the hypothesis accepted when the null hypothesis is rejected.
two-sided hypothesis test
Hypothesis Testing
We reject the null in favor of the alternative if the evidence indicates that the population parameter is either smaller or larger than Theta-not.
one-sided hypothesis test
Hypothesis Testing
We reject the null only if the evidence indicates that the population parameter is respectively greater than or less than Theta-not.
4 possible outcomes when testing null hypothesis
Hypothesis Testing
1) We reject a false null hypothesis. This is a correct decision.
2) We reject a true null hypothesis. This is called a Type 1 error.
3) We do not reject a false null hypothesis. This is called a Type 2 error.
4) We do not reject a true null hypothesis. This is a correct decision.
level of significance
Hypothesis Testing
The probability of a Type 1 error in testing a hypothesis, denoted by alpha.
power of a test
Hypothesis Testing
The probability of correctly rejecting the null - that is, the probability of rejecting the null when it is false. When more than one test statistic is available to conduct a hypothesis test, we should prefer the most powerful, all else equal.
statistically significant
Hypothesis Testing
When we test the null hypothesis and find that the calculated value of the test statistic is as extreme or more extreme than a given value or values determined by the specified level of significance.
rejection point (critical value)
Hypothesis Testing
A rejection point for a test statistic is a value with which the computed test statistic is compared to decide whether to reject or not reject the null hypothesis.
p-value
Hypothesis Testing
The p-value is the smallest level of significance at which the null hypothesis can be rejected.
t-test
Hypothesis Tests Concerning the Mean
A hypothesis test using a statistic (t-statistic) that follows a t-distribution. The t-distribution is a probability distribution defined by a single parameter known as degrees of freedom (df).
Each value of degrees of freedom defines one distribution in this family of distributions. The t-distribution is closely related to the standard normal distribution.
Like the standard normal distribution, a t-distribution is symmetrical with a mean of zero. However, the t-distribution is more spread out: It has a standard deviation greater than 1 (compared to 1 for the standard normal) and more probability for outcomes distant from the mean (it has fatter tails than the standard normal distribution). As the number of degrees of freedom increases with sample size, the spread decreases and the t-distribution approaches the standard normal distribution limit.
The t-test is robust to moderate departures the normality, except for outliers and strong skewness.
When we have large samples, departures of the underlying distribution from the normal are of increasingly less concern. The sample mean is approximately normally distributed in large samples according to the central limit theorem, whatever the distribution describing the population.
In general, a sample size of 30 or more usually can be treated as a large sample and a sample size of 29 or less is treated as a small sample.
paired observations
Hypothesis Tests Concerning the Mean
Paired observations are observations that are dependent because they have something in common. A paired comparisons test is a statistical test for differences in dependent items.
parametric test
Other Issues: Nonparametric Inference
Any test (or procedure) concerned with parameters or whose validity depends on assumptions concerning the population generating the sample.
nonparametric test
Other Issues: Nonparametric Inference
A test that is not concerned with a parameter, or that makes minimal assumptions about the population from which a sample comes.
Spearman rank correlation coefficient
Other Issues: Nonparametric Inference
A measure of correlation applied to ranked data.
