tailieunhanh - Ebook Handbook of biolological statistics (3rd edition): Part 2

(BQ) Part 2 book "Handbook of biolological statistics" has contents: Student’s t – test for two samples, homoscedasticity and heteroscedasticity, data transformations, one - way anova, correlation and linear regression, analysis of covariance, simple logistic regression,.and other contents. | STUDENT’S T-­‐TEST FOR TWO SAMPLES Student’s t–test for two samples Use Student’s t–test for two samples when you have one measurement variable and one nominal variable, and the nominal variable has only two values. It tests whether the means of the measurement variable are different in the two groups. Introduction There are several statistical tests that use the t-distribution and can be called a t–test. One of the most common is Student’s t–test for two samples. Other t–tests include the one-sample t–test, which compares a sample mean to a theoretical mean, and the paired t– test. Student’s t–test for two samples is mathematically identical to a one-way anova with two categories; because comparing the means of two samples is such a common experimental design, and because the t–test is familiar to many more people than anova, I treat the two-sample t–test separately. When to use it Use the two-sample t–test when you have one nominal variable and one measurement variable, and you want to compare the mean values of the measurement variable. The nominal variable must have only two values, such as “male” and “female” or “treated” and “untreated.” Null hypothesis The statistical null hypothesis is that the means of the measurement variable are equal for the two categories. How the test works The test statistic, t , is calculated using a formula that has the difference between the means in the numerator; this makes t get larger as the means get further apart. The denominator is the standard error of the difference in the means, which gets smaller as the sample variances decrease or the sample sizes increase. Thus t gets larger as the means get farther apart, the variances get smaller, or the sample sizes increase. You calculate the probability of getting the observed t value under the null hypothesis using the t-distribution. The shape of the t-distribution, and thus the probability of getting s s s s 127 HANDBOOK OF BIOLOGICAL