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| ## page was renamed from Econometrics/TestStatistic | |
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| A '''test statistic''' is a statistic generated for hypothesis testing in statistical inference. | A '''test statistic''' is a statistic generated for hypothesis testing in [[Statistics/CausalInference|causal inference]]. |
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| == Usage == | == Description == |
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| A critical value should reflect a tolerance for Type I error. |
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| Statistical analysis can be done with '''p-values''' instead. | A '''p-value''' is the probability of achieving a test statistic assuming the null hypothesis is true. This is effectively a reformulation of the above framework: a critical level is selected (commonly 0.05; or conversely a level of significance is selected, like 95%) and ''H,,0,,'' is rejected if the p-value exceeds it. |
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| The ''intention'' of p-values is to enable readers to apply their own tolerance for Type I error as a critical value. In some cases it is more succinct to report p-values rather than annotate multiple levels of significance (e.g. 90%, 95%, and 99%). | The advantage to formulating inference through p-values is that anyone can formulate their personal tolerance for Type I error, determine the corresponding critical level, and re-evaluate the inference. In contexts where a variety of critical levels ought to be considered (e.g., at 0.1, 0.05, and 0.01 simultaneously), it can also be more succinct to report p-values than annotate each. |
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| The unfortunate fact is that many people interpret p-values as a probability that the result is correct. For example, some people see a p-value of 0.02 and incorrectly assume that there is a 98% probability that the result is correct. | The disadvantage to this formulation is that p-values are more easily misunderstood (e.g., possible to misinterpret a p-value of 0.02 as meaning there is a 98% probability that the result is correct, when it truly means that there is a 2% probability that the estimate is 0). |
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| == t-test == | == Usage == |
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| ---- | There are a variety of test statistics. Most tests are designed for application in specific contexts, when certain assumptions hold. See the below pages for usage guidance: |
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== Z-test == ---- == Chi-squared test == ---- == F-test == |
* [[Statistics/CollinearityTest|Collinearity test]] * [[Statistics/HosmerLemeshowTest|Hosmer-Lemeshow test]] * [[Statistics/KolmogorovSmirnovTest|Kolmogorov-Smirnov test]] * [[Statistics/LagrangeMultiplierTest|Lagrange multiplier test]] * [[Statistics/LikelihoodRatioTest|Likelihood-ratio test]] * [[Statistics/PearsonTest|Pearson test]] * [[Statistics/WaldTest|Wald test]] |
Test Statistic
A test statistic is a statistic generated for hypothesis testing in causal inference.
Contents
Description
A test statistic is compared to a critical value. H0 is rejected if:
A critical value should reflect a tolerance for Type I error.
P-Values
A p-value is the probability of achieving a test statistic assuming the null hypothesis is true. This is effectively a reformulation of the above framework: a critical level is selected (commonly 0.05; or conversely a level of significance is selected, like 95%) and H0 is rejected if the p-value exceeds it.
The advantage to formulating inference through p-values is that anyone can formulate their personal tolerance for Type I error, determine the corresponding critical level, and re-evaluate the inference. In contexts where a variety of critical levels ought to be considered (e.g., at 0.1, 0.05, and 0.01 simultaneously), it can also be more succinct to report p-values than annotate each.
The disadvantage to this formulation is that p-values are more easily misunderstood (e.g., possible to misinterpret a p-value of 0.02 as meaning there is a 98% probability that the result is correct, when it truly means that there is a 2% probability that the estimate is 0).
Usage
There are a variety of test statistics. Most tests are designed for application in specific contexts, when certain assumptions hold. See the below pages for usage guidance: