Hypothesis Testing Flashcards
Define hypothesis, describe the steps of hypothesis testing, and describe and interpret the choice of the null alternative hypotheses.
The hypothesis testing process requires a statement of a null and alternative hypothesis, the selection of the appropriate test statistic, specification of the significance level, a decision rule, the calculation of a sample statistic, decision regarding the hypotheses based on the test, and a decision based on the test results.
The null hypothesis is what the researcher wants to reject. The alternative hypothesis is what the researcher wants to support, and it is accepted when the null hypothesis is rejected.
Compare and contrast one-tailed and two-tailed tests of hypotheses.
Explain a test statistic, Type I and Type II errors, a significance level, how significance levels are used in hypothesis testing, and the power of a test.
The test statistic is the value that a decision about a hypothesis will be based on. For a test about the value of the mean of a distribution:
A Type I error is the rejection of the null hypothesis when it is actually true, while Type II error is the failure to reject the null hypothesis when it is actually false.
The significance level can be interpreted as the probability that a test statistic will reject the null hypothesis by chance when it is actually true (i.e., the probability of a Type I error). A significance level must be specified to select the critical values for the test.
The power of a test is the probability of rejecting the null when it is false. The power of a test = 1- P(Type II error).
Explain a decision rule and the relation between confidence intervals and hypothesis tests, and determine whether a statistically significant result is also economically meaningful.
Hypothesis testing compares a computed test statistic to a critical value at a stated level of significance, which is the decision rule for the test.
A hypothesis about a population parameter is rejected when the sample statistic lies outside a confidence interval around the hypothesized value for the chosen level of significance.
Statistical significance does not necessarily imply economic significance. Even though a test statistic is significant statistically, the size of the gains to a strategy to exploit a statistically significant result may be absolutely small or simply not great enough to outweigh transaction cost.
Explain and interpret p-value as it relates to hypothesis testing.
The p-value for a hypothesis test is the smallest significant level for which the hypothesis would be rejected. For example, a p-value of 7% means the hypothesis can be rejected at the 10% significance level but cannot be rejected at the 5% significance level.
Describe how to interpret the significance of a test in the context of multiple tests.
When multiple tests are performed on different samples from a population, the p-values of each test are ranked, from lowest to highest, and compared to the adjusted critical values for each rank. When the proportion of the total number of ranked tests for which reported p-values are less than their adjusted critical values is greater than the significance level, the null hypothesis is rejected.
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning the population mean of both large and small samples when the population is normally or approximately normally distributed and the variance is (1) known or (2) unknown.
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning the equality of the population means oft at least random samples with equal assumed variances.
For two independent samples from two normally distributed populations, the difference in means can be tested with a t-statistic. When the two population variances are assumed to be equal, the denominator is based on the variance of the pooled samples.
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning the mean difference of two normally distributed populations.
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning (1) the variance of a normally distributed population and (2) equality of the variance of wot normally distributed populations bases on two independent random samples.
Compare and contrast parametric and nonparametric tests, and describe situations where each is there appropriate type of test.
Parametric tests, like the t-test, F-test, and chi-square tests, make assumptions regarding the distribution of the population from which samples are drawn. Nonparametric test either do not consider a particular population parameter or have few assumptions about the sampled population. Nonparametric test are used when the assumptions of parametric tests can’t be supported or when the data are not suitable for parametric tests.
Explain parametric and nonparametric tests of the hypothesis that the population correlation coefficient equals zero, and determine whether the hypothesis is rejected at a given level of significance.
Explain tests of independence based on contingency table data.
A contingency table can be used to test hypothesis that two characteristics (categories) of a sample of items are independent. The test statistic follows a chi-square distribution and is calculated as:
The degrees of freedom are [(r - 1)(c - 1)]. If the test statistic is greater than the critical chi-square value for a given level of significance, we reject the hypothesis that the two characteristics are independent.
