In this week what was interesting in the realm of hypothesis testing is the t-test.
All areas of science make use of t-test. One of the major applications of that t-test is to provide means to research questions. In hypothesis building, it is very important to form correct and factual research questions. Along with the formation, researchers also need to have a broad idea of the possible answers to the hypothesis which can help identify the direction of the research. Sometimes referred to as “Student’s t-test,” it was named after the person who helped in the study of the distribution of the means from within a small sample way back in 1890. The student was a pseudo name of William Gosset found out that the means are normally distributed only is cases when it is possible to know the actual standard deviation in the population in case of all forms of observations that originate from a normal distribution (Witte & Witte, 2004). The sample standard deviation is used by researchers in place of standard deviation in cases where it is not possible to know the true standard deviation. This results in means no longer getting normally distributed. The use of the sample standard deviation for distribution is termed as the t distribution.
To put things into perspective, the chapter showed that researchers mostly always use samples in place of populations in medical research. Hence the true standard deviation is almost never known and therefore the sample standard deviation is almost always used. Hence to ensure that the conclusions of a research are almost always accurate, the use the t distribution is preferred to be used instead of the normal distribution. However when variable n is greater than 30, the difference between t and z is almost always very small.
According to Witte & Witte, (2004): “The formula (or critical ratio) for the t-test has the observed mean ( ) minus the hypothesized value of the population mean (?) in the numerator, and the standard error of the mean in the denominator. The symbol ? stands for the true mean in the population.”
A complex concept related to the size of sample called degrees of freedom (df) decides the precise size of the standard deviation. The number of times, the sample information is used is also related to it. When sample information is used only once for the…