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Empirical Methods > Hypothesis Testing > Flashcards

Hypothesis Testing Flashcards

Testing of Hypotheses

1
Q

The F-Test is…

A

a formal hypothesis test thats 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 hypothesis

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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 different…

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

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 is…

A

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 kinds of errors we can make in hypothesis testing?

A

Type 1: We reject a true null hypothesis

Type 2: We do not reject a false null hypothesis

25
Q

A decision rule is…

A

a method of deciding whether to reject a null hypothesis

26
Q

A decision rule involves comparing…

A

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

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 1 Error means…

A

increasing the chance of a Type 2 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 1 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 a…

A

estimated t-value greater than the critical t-value if the null hypothesis were correct. It measures the amount of Type 1 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 2 Error

33
Q

A confidence interval is…

A

a range that contains the true value of an item in 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 from 0-1. It tells us the lowest level of significance at which we could reject the null hypothesis

37
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

38
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 hypothesis

39
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

40
Q

The t-Test does not test…

A

1) Theoretical Validity
2) “importance” of an independent variabel
3) is not intended for tests of the entire population

41
Q

The t-test tests hypotheses about…

A

individual coefficients from regression equations.

Empirical Methods (6 decks)

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