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My TopicSignificance of t-test

introduction What is t-test Who invented t-test What kind of t is it What is t-test of significance Why we use t-test When we use t-test Examples and Explanation. Applications of t-test

What is t-test ?A t-test is used to determine whether a set or sets of scores are from the same population.At-testis anystatistical hypothesis testin which thetest statisticfollows aStudent'st-distributionif thenull hypothesisis supported.

Who invented t-test?Thet-test is 107 years old. Thetstatistic was introduced byWilliam Sealy GossetGosset published thettest in Biometrikain 1908, but was forced to use apen nameby his employer who regarded the fact that they were using statistics as a trade secret. Hence, the nameStudent'st-test.

What kind of t is it ?Single sample t we have only 1 group; want to test against a hypothetical mean.Independent samples t we have 2 means, 2 groups; no relation between groups, e.g., people randomly assigned to a single group.Dependent t we have two means. Either same people in both groups, or people are related, e.g., husband-wife, left hand-right hand, hospital patient and visitor.

significance of t-test ?

A t-tests statistical significance indicates whether or not the difference between two groups averages most likely reflects a real difference in the population from which the groups were sampled.Why we use t-test ?A test of whether the slope of aregressionlinedifferssignificantly from 0.

When we use t-test ?An independent samples t-test is used when you want to compare the means of a normally distributed interval dependent variable for two independent groups. For example, using thehsb2 data file, say we wish to test whether the mean forwriteis the same for males and females.

explanationExample:If we are analysing the heights of pine trees growing in two different locations, a suitable null hypothesis would be that there is no difference in height between the two locations. The student's t-test will tell us if the data are consistent with this or depart significantly from this expectation. [NB: the null hypothesis is simply something to test against. We might wellexpect a differencebetween trees growing in a cold, windy location and those in a warm, protected location, but it would be difficult topredictthe scale of that difference - twice as high? three times as high? So it is sensible to have a null hypothesis of "no difference" and then to see if the data depart from this.

explanationSolution:List the data for sample (or treatment) 1.List the data for sample (or treatment) 2.Record the number (n) of replicates for each sample (the number of replicates for sample 1 being termedn1and the number for sample 2 being termedn2)Calculate mean of each sampleCalculates2for each sample; call theses12ands22[Note that actually we are using S2as an estimate ofs2in each case]. Calculate the variance of the difference between the two means (sd2) as follows

explanationCalculatesd(the square root ofsd2)Calculate thetvalue as follows:

Enter thet-tableat (n1+ n2-2) degrees of freedom; choose the level of significance required (normallyp= 0.05) and read the tabulatedtvalue.

applicationTo compare the mean of a sample with population mean.To compare the mean of one sample with the mean of another independent sample.To compare between the value (reading) of one sample but in two occasions.