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zEconometrics > 5.) Hypothesis Testing > Flashcards

5.) Hypothesis Testing Flashcards

1
Q

The F-Test is …if th

A

a formal hypothesis test that is designed to deal with a null hypothesis that contains multiple hypotheses or a single hypothesis about a group of coefficients

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2
Q

The first step in the F-test is…

A

translate the particular null hypothesis in question into constraints that will be placed on the equation

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3
Q

A constrained equation can be thought of as…

A

what the equation would look like if the null hypothesis were correct

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4
Q

For a constrained equation you…

A

substitute the hypothesized values into the regression equation in order to see what would happen if the equation were constrained to agree with the null hypotest

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5
Q

In the F-test the null hypothesis always leads to a…

A

constrained equations, even if this violates our standard practice that the alternative hypothesis contains what we expect is true

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6
Q

The second step in an F-test is to…

A

estimate this constrained equation with OLS and compare the fit of this constrained equation with the fit of the unconstrained equation

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7
Q

If the fits of the constrained equation and the unconstrained equation are not significantly differerent…

A

the null hypothesis should not be rejected

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8
Q

RSS =

A

Residual sum of squares from the unconstrained equation

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9
Q

RSS(M) =

A

residual sum of squares form the constrained equation

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10
Q

M =

A

number of constraints place don the equation (usually equal to the number of betas eliminated from the unconstrained equation)

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11
Q

(N-K-1) =

A

degrees of freedom in the unconstrained equation

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12
Q

F =

A

((RSSm-RSS)/M) / (RSS/(N-K-1))

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13
Q

RSS(M) is always …

A

greater than or equal to RSS

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14
Q

Imposing constraints on the coefficients instead of allowing OLS to select their values …

A

can never decrease the summed squared residuals

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15
Q

As the difference between the constrained coefficients and the unconstrained coefficients increases…

A

the data indicate that the null hypothesis is less likely to be true

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16
Q

The decision rule to use in the F-test is …

A

to reject null hypothesis if the calculated F-value from Equation 11 is greater than the appropriate critical F-value

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17
Q

The F-statistic has two types of degrees of freedom…

A
  1. ) The degrees of freedom for the numerator of Equation 11 (M, the number of constraints implied by the null hypothesis)
  2. ) The degrees of freedom for the denominator of the F equation (N-K-1 , the degrees of freedom in the regression equation)
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18
Q

Underlying Principle here is that…

A

if the calculated F-value (or F-ratio) is greater than the critical value

19
Q

F-test of overall significance is really testing…

A

the null hypothesis that the fit of the equation isn’t significantly better than that provided by using the mean alone.

20
Q

The null hypothesis in an F-test of overall significance

A

is that all the slope coefficients in the equation equal zero simultaneously

21
Q

Our decision rule tells us to…

A

reject the null hypothesis if the calculated F-value is greater than the critical F-value

22
Q

Seasonal Dummies are…

A

dummy variables that are used to account for seasonal variation in time-series models

23
Q

To test the hypothesis of significant seasonality in the data…

A

one must test the hypothesis that all the dummies equal zero simultaneously rather than test the dummies one at a time.

24
Q

What are the two kids of errors we can make in hypothesis testing?

A

Type I: We reject a true null hypothesis.

Type II: We do not reject a false null hypothesis

25
Q

A decision rule is…

A

a method of deciding whether to rejct a null hypothesis

26
Q

A decision rule involves comparing…

A

a sample statistic with a pre-selected critical value found in talbes

27
Q

A critical value is…

A

a value that divides the “acceptance” region from the rejection region when testing a null hypothesis

28
Q

Decreasing the chance of a Type I Error means…

A

increasing the chance of a Type II Error

29
Q

A critical t-value is..

A

the value that distinguishes the “acceptance” region from the rejection region.

30
Q

The level of Type I Error in a hypothesis test is also called…

A

the level of significance of that test

31
Q

The level of significance indicates the probability of observing an…

A

estimated t-value greater than the critical t-value if the null hypothesis were correct. It measures the amount of Type I Error implied by a particular critical t-value.

32
Q

An extremely low level of significance also dramatically increases…

A

the probability of making a Type II Error

33
Q

A confidence interval is…

A

a range that contains the true value of an item a specified percentage of the time. This percentage is the level of confidence associated with the level of significance used to choose the critical t-value in the interval.

34
Q

A p-value for a t-score is…

A

the probability of observing a t-score that size or larger (in absolute value) if the null hypothesis were true.

35
Q

Graphically, the p-value is…

A

the area under the curve of the t-distribution between the actual t-score and infinity

36
Q

A p-value is a probability so…

A

it runs form 0-1. It tells us the lowest level of significance at which we could reject the null hypothesis

37
Q

The p-value decision rule is…

A

reject the null hypothesis if the p-value

38
Q

The most common use of a one-sided t-test is to determine whether a regression coefficient is…

A

significantly different from zero in the direction predicted by theory

39
Q

Using a one-sided t-test to in order to be able to control the amount of Type I Error me make, the implication is

A

Alternative Hypothesis: B > 0

Null Hypothesis: B less than or equal 0

(If positive coefficient predicted by theory)

40
Q

The Four Steps to use when working with the t-test are..

A
  1. ) Set up the Null and Alternative Hypothesis
  2. ) Choose a level of significance and therefore a critical t-value
  3. ) Run the regression and obtain an estimated t-value (or t-score)
  4. ) Apply the decision rule by comparing the calculated t-value with the critical t-value in order to reject or not reject the null hypotheses
41
Q

The kinds of circumstances that call for a two-sided test fall into two categories…

A
  1. ) Two sided tests of whether an estimated coefficient is significantly different from zero.
  2. ) Two-sided tests of whether an estimated coefficient is significantly different from a specific nonzero value
42
Q

The t-Test does not test…

A
  1. ) Theoretical Validity
  2. ) “Importance” of an independent variable
  3. ) I not intended for tests of the entire population
43
Q

the t-test tests hypotheses about…

A

individual coefficients from regression equations.

zEconometrics (16 decks)

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