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Q1: What is the t-statistical used for? What is the P-value used for? What is the difference between the use of t-statistic and p-value?
Ans: The t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error. It is used in hypothesis testing.
Let be an estimator of parameter β in some statistical model. Then a t-statistic for this parameter is any quantity of the form
Where β0 is a non-random, known constant, and is the standard error of the estimator . By default, statistical packages report t-statistic with β0 = 0 (these t-statistics are used to test the significance of corresponding regressor). However, when t-statistic is needed to test the hypothesis of the form H0: β = β0, then a non-zero β0 may be used.
Uses of t-statistical:
Most frequently, t-statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals.
The key property of the t-statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the sample parameters, and thus it can be used regardless of what these may be.
P-value & its uses:
“The level of marginal significance within a statistical hypothesis test, representing the probability of the occurrence of a given event.” The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. The smaller the p-value, the stronger the evidence is in favor of the alternative hypothesis.
Example of p-value:
Because different researchers use different levels of significance when examining a question, a reader may sometimes have difficulty comparing results from two different tests.
For example, if two studies of returns from two particular assets were done using two different significance levels, a reader could not compare the probability of returns for the two
Ans: The t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error. It is used in hypothesis testing.
Let be an estimator of parameter β in some statistical model. Then a t-statistic for this parameter is any quantity of the form
Where β0 is a non-random, known constant, and is the standard error of the estimator . By default, statistical packages report t-statistic with β0 = 0 (these t-statistics are used to test the significance of corresponding regressor). However, when t-statistic is needed to test the hypothesis of the form H0: β = β0, then a non-zero β0 may be used.
Uses of t-statistical:
Most frequently, t-statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals.
The key property of the t-statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the sample parameters, and thus it can be used regardless of what these may be.
P-value & its uses:
“The level of marginal significance within a statistical hypothesis test, representing the probability of the occurrence of a given event.” The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. The smaller the p-value, the stronger the evidence is in favor of the alternative hypothesis.
Example of p-value:
Because different researchers use different levels of significance when examining a question, a reader may sometimes have difficulty comparing results from two different tests.
For example, if two studies of returns from two particular assets were done using two different significance levels, a reader could not compare the probability of returns for the two