Prepare by M. Noaman Akbar

Published on: **Mar 3, 2016**

Published in:
Education

- 1. My Topic Significance of t-test
- 2. 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
- 3. What is t-test ? “A t-test is used to determine whether a set or sets of scores are from the same population.” 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.
- 4. Who invented t-test? The t-test is 107 years old. The t statistic was introduced by William Sealy Gosset Gosset published the t test in Biometrika in 1908, but was forced to use a pen name by his employer who regarded the fact that they were using statistics as a trade secret. Hence, the name Student's t-test.
- 5. 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.
- 6. significance of t-test ? A t-test’s 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.
- 7. Why we use t-test ? A test of whether the slope of a regressionline differs significantly from 0.
- 8. 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 the hsb2 data file, say we wish to test whether the mean for write is the same for males and females.
- 9. explanation Example: 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 well expect a difference between trees growing in a cold, windy location and those in a warm, protected location, but it would be difficult to predict the 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.
- 10. explanation Solution: 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 termed n1 and the number for sample 2 being termed n2) Calculate mean of each sample Calculate s 2 for each sample; call these s 1 2 and s 2 2 [Note that actually we are using S2 as an estimate of s 2 in each case] . Calculate the variance of the difference between the two means (sd2) as follows
- 11. explanation Calculate sd (the square root of sd 2) Calculate the t value as follows: Enter the t-table at (n1 + n2 -2) degrees of freedom; choose the level of significance required (normally p = 0.05) and read the tabulated t value.
- 12. application To 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.