Hypothesis Testing Flashcards

0
Q

Hypothesis

A

With reference to statistical inference, a statement about one or more populations.

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1
Q

Hypothesis testing

A

With reference to statistical inference, the subdivision dealing with the testing of hypotheses about one or more populations.

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2
Q

Steps in hypothesis testing

A

Stating the hypotheses.

Identifying the appropriate test statistic and its probability distribution.

Specifying the significance level.

Stating the decision rule.

Collecting the data and calculating the test statistic.

Making the statistical decision.

Making the economic or investment decision.

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3
Q

Null hypothesis

A

Definition of Null Hypothesis. The null hypothesis is the hypothesis to be tested. For example, we could hypothesize that the population mean risk premium for Canadian equities is less than or equal to zero.

The null hypothesis is a proposition that is considered true unless the sample we use to conduct the hypothesis test gives convincing evidence that the null hypothesis is false. When such evidence is present, we are led to the alternative hypothesis.

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4
Q

Alternative hypothesis

A

Definition of Alternative Hypothesis. The alternative hypothesis is the hypothesis accepted when the null hypothesis is rejected. Our alternative hypothesis is that the population mean risk premium for Canadian equities is greater than zero.

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5
Q

Formulations of hypotheses

A

Formulations of Hypotheses. We can formulate the null and alternative hypotheses in three different ways:

H0: θ = θ0 versus Ha: θ ≠ θ0 (a “not equal to” alternative hypothesis)

H0: θ ≤ θ0 versus Ha: θ > θ0 (a “greater than” alternative hypothesis)

H0: θ ≥ θ0 versus Ha: θ < θ0 (a “less than” alternative hypothesis)

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6
Q

Two sided hypotheses

A

A test in which the null hypothesis is rejected in favor of the alternative hypothesis if the evidence indicates that the population parameter is either smaller or larger than a hypothesized value.

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7
Q

One sided hypotheses

A

A test in which the null hypothesis is rejected only if the evidence indicates that the population parameter is greater than (smaller than) θ0. The alternative hypothesis also has one side.

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8
Q

Test statistic

A

Definition of Test Statistic. A test statistic is a quantity, calculated based on a sample, whose value is the basis for deciding whether or not to reject the null hypothesis.

The focal point of our statistical decision is the value of the test statistic. Frequently (in all the cases that we examine in this reading), the test statistic has the form

Equation (1) 

Test statistic=

(Sample statistic−Value of the population parameter under H0) / (Standard error of the sample statistic)

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9
Q

Statistically significant

A

A result indicating that the null hypothesis can be rejected; with reference to an estimated regression coefficient, frequently understood to mean a result indicating that the corresponding population regression coefficient is different from 0.

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10
Q

Power of a test

A

The probability of correctly rejecting the null—that is, rejecting the null hypothesis when it is false.

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11
Q

Type I error

A

The error of rejecting a true null hypothesis.

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12
Q

Type II error

A

The error of not rejecting a false null hypothesis.

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13
Q

P value

A

Definition of p-Value. The p-value is the smallest level of significance at which the null hypothesis can be rejected.

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14
Q

Parametric test

A

Any test (or procedure) concerned with parameters or whose validity depends on assumptions concerning the population generating the sample.

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15
Q

Nonparametric test

A

A test that is not concerned with a parameter, or that makes minimal assumptions about the population from which a sample comes.