Student's t-test

Student's t-test
/tee"test'/, Statistics.
a test for determining whether or not an observed sample mean differs significantly from a hypothetical normal population mean.
[1945-50; see STUDENT'S T DISTRIBUTION]

* * *

      in statistics, a method of testing hypotheses about the mean of a small sample (sampling) drawn from a normally distributed (normal distribution) population when the population standard deviation is unknown.

      In 1908 William Sealy Gosset, an Englishman publishing under the pseudonym Student, developed the t-test and t distribution. The t distribution is a family of curves in which the number of degrees of freedom (the number of independent observations in the sample minus one) specifies a particular curve. As the sample size (and thus the degrees of freedom) increases, the t distribution approaches the bell shape of the standard normal distribution. In practice, for tests involving the mean of a sample of size greater than 30, the normal distribution is usually applied.

      It is usual first to formulate a null hypothesis, which states that there is no effective difference between the observed sample mean and the hypothesized or stated population mean—i.e., that any measured difference is due only to chance. In an agricultural study, for example, the null hypothesis could be that an application of fertilizer has had no effect on crop yield, and an experiment would be performed to test whether it has increased the harvest. In general, a t-test may be either two-sided (also termed two-tailed), stating simply that the means are not equivalent, or one-sided, specifying whether the observed mean is larger or smaller than the hypothesized mean. The test statistic t is then calculated. If the observed t-statistic is more extreme than the critical value determined by the appropriate reference distribution, the null hypothesis is rejected. The appropriate reference distribution for the t-statistic is the t distribution. The critical value depends on the significance level of the test (the probability of erroneously rejecting the null hypothesis).

      For example, suppose a researcher wishes to test the hypothesis that a sample of size n = 25 with mean x = 79 and standard deviation s = 10 was drawn at random from a population with mean μ = 75 and unknown standard deviation. Using the formula for the t-statistic,

the calculated t equals 2. For a two-sided test at a common level of significance α = 0.05, the critical values from the t distribution on 24 degrees of freedom are −2.064 and 2.064. The calculated t does not exceed these values, hence the null hypothesis cannot be rejected with 95 percent confidence. (The confidence level is 1 − α.)

      A second application of the t distribution tests the hypothesis that two independent random samples have the same mean. The t distribution can also be used to construct confidence intervals for the true mean of a population (the first application) or for the difference between two sample means (the second application). See also interval estimation.

* * *


Universalium. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Student's t-test — A t test is any statistical hypothesis test in which the test statistic follows a Student s t distribution if the null hypothesis is supported. It is most commonly applied when the test statistic would follow a normal distribution if the value of …   Wikipedia

  • Student's t-test — noun a test for statistical significance based on a fraction (t) whose numerator is drawn from a normal distribution with a mean of zero, and whose denominator is the root mean square of a number of terms drawn from the same normal distribution.… …   English new terms dictionary

  • Student's t-test — /tee test /, Statistics. a test for determining whether or not an observed sample mean differs significantly from a hypothetical normal population mean. [1945 50; see STUDENT S T DISTRIBUTION] …   Useful english dictionary

  • Student's t test — noun any statistical hypothesis test in which the test statistic has a Students t distribution if the null hypothesis is true Syn: Students t, t test See Also: Students t distribution …   Wiktionary

  • Student's t-test — noun Date: 1935 t test …   New Collegiate Dictionary

  • Student's t test — see significance Pseudonym of W. S. Gosset (1876 1937), British statistician …   Medical dictionary

  • Student's t test — see significance [Pseudonym of W. S. Gosset (1876–1937), British statistician] …   The new mediacal dictionary

  • Student's t-distribution — Probability distribution name =Student s t type =density pdf cdf parameters = u > 0 degrees of freedom (real) support =x in ( infty; +infty)! pdf =frac{Gamma(frac{ u+1}{2})} {sqrt{ upi},Gamma(frac{ u}{2})} left(1+frac{x^2}{ u} ight)^{ (frac{… …   Wikipedia

  • Student (disambiguation) — A student is a school or class attendee.Student may also mean:*The pseudonym of William Sealey Gosset *Student s t test, a statistical technique *Student s t distribution, a probability distribution * THE STUDENT S, former name of the Japanese… …   Wikipedia

  • Test anxiety — is a psychological condition in which a person experiences distress before, during, or after an exam or other assessment to such an extent that this anxiety causes poor performance or interferes with normal learning.ymptoms*Physical headaches,… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”