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Student's t-Test

Collection of articles on t-student test: 2-population t-test with homogeneous variance, 2-student t-test with heterogeneous variance, Paired t-test

To compare the mean value of the population with a certain value or with the mean value of other populations can be done with the z test . However, the z test can only be used if the data is normally distributed and the population variance is known .
In fact, it is rare that we can know the parameter values of a population with certainty, so we can only estimate the parameters of the population from the sample we take. Since we do not know what the population standard deviation, this value is estimated by the sample standard deviation, s, which is calculated from the sample. However, for small samples, s is not an accurate estimate for so it is no longer valid if we use it for the z test. For small sample sizes, we can approach it by using the student's t-test .

In one sample t-test we only compare a population with a certain value, but in reality cases using this type of test are very rare. Researchers, particularly in agriculture, are more concerned with cases that require comparisons between two conditions or two population averages.

Before we do the analysis, we must first consider whether the two populations come from a normal distribution, are the variances of the two populations homogeneous? This will guide us in choosing the right method and formula for conducting a t-test analysis to compare the two population mean values. In this article, we will describe the 2 population/sample t-test with heterogeneous variance .

Student's t-test for one sample is rarely applied in agricultural research. However, in some cases, the t-test of a single sample can be used to compare the average of the characteristics studied with the comparator value or the standard value. For example, a single sample t-test can be used to compare the results of a measurement of the potential yield of a rice variance planted in an area (as a newcomer variance) with the average potential yield in its home country (as a hypothetical value).

Paired t-test ( paired t-test ) is one method of testing the hypothesis where the data used is not independent which is characterized by the existence of a value relationship in each of the same samples ( pairs ).). The characteristics that are most often found in paired cases are that one individual (object of research) is subjected to 2 different treatments. Although using the same individual, the researchers still obtained 2 kinds of sample data, namely data from the first treatment and data from the second treatment. The first treatment may be in the form of control, which is not giving any treatment at all to the object of research. 

In one sample t-test we only compare a population with a certain value, but in reality cases using this type of test are very rare. Researchers, particularly in agriculture, are more concerned with cases that require comparisons between two conditions or two population averages.

Before we do the analysis, we must first consider whether the two populations come from a normal distribution, are the variance of two populations equal? This will guide us in choosing the right method and formula for conducting a t-test analysis to compare the two population mean values.