Test Statistics Flashcards
What is the critical value for the test statistics?
it is the threshold that her test statistic will need to surpass in order to reject the null hypothesis at a certain level of significance
What is a type I error?
When the null hypothesis is falsely rejected
What is a type II error?
When a false null hypothesis is not rejected
How is the probability of failing to reject a false null hypothesis measured?
Beta
The Probability of correctly rejecting a false null hypothesis
1 - Beta; the Power of a Test
What is the Power of a test
1 - Beta; the probability of correctly rejecting the false null hypothesis
The Rejection of a true null is measured by…?
Alpha; i.e. the level of significance
When are nonparametric tests appropriate?
- When data fails to meet distributional assumptions
- When data are given in ranks
- when the hypothesis simply doesn’t concern a parameter
Nonparametric test used for correlations of two series when one or both of the series are in ranks
The Spearman Rank Correlation Coefficient
How can samples of population variances that are not normally distributed be used for Hypothesis tests?
If the data are lognormally distributed and the log values for the data are used
When its okay to use z-statistic for a t-test
When the population standard deviation is known (and assuming it is normally distributed)
When to use t-statistic over the z-statistic
When the sample is large enough to be normally distributed, but the population standard deviation is unknown
Reason why z-statistic is easier than t-statistic
The critical values can be memorized since they are independent of the sample size and therefore do not change
What the critical values for a two-tailed z-test with 1%, 5%, and 10% significance levels?
two-tailed @ 1% level = -2.575 and 2.757
two-tailed @ 5% level = -1.96 and 1.96
two-tailed @ 10% level = -1.645 and 1.645
What are the critical values for a one-tailed z-test with 1%, 5%, and 10% significance levels?
one-tailed @ 1% = -2.33 and 2.33
one-tailed @ 5% = -1.645 and 1.645
one-tailed @ 10% = -1.28 and 1.28
What is the relationship between the t-statistic and the z-statistic as the sample size gets larger?
the t-distribution converges toward the z-distribution; therefore the t-statistic converges toward the z-statistic
When should should a pooled variance be used?
When measuring the differences between two means in independent samples.
What is the t-test for mean differences most appropriate for examining?
dependent samples, as in before and after measurements
What is the test statistic that tests the equality of two variances, and how do you calculate it?
F-statistic; Divide the two variances into each other
how do you solve for the chi square test statistic?
n-1 times the sample variance over the hypothesized variance
What does a chi-squared test examine?
chi-squared tests examine claims about a population standard deviation or, equivalently, a population variance; it is the correct distribution to use when testing a normally distributed variance
