 Principles of Systematics module 130, T-Test T-Test is used when we are interested to compare the means of two samples We have seen that we use the T-Test when we compare the means of two samples and are more than the sample size 30 We will apply the T-Test when we want to compare the means of two samples We have seen that we use the T-Test when we are interested to compare the means of two samples and are more than the sample size 30 Now, what are the assumptions for T-Test? For T-Test, the distribution of data should be normal Because T-Test is a parametric test After that, the sample should be taken randomly from the population We are going to compare the samples from the population We have seen in the T-Test that the standard deviation is necessary for the T-Test But for T-Test, the standard deviation is not necessary The standard deviation may or may not be given In both the conditions, we can apply the T-Test Now, the T-Test has two types One is the independent T-Test, which we call as two-sample T-Test And the other type is the paired T-Test Now, what is the difference between the two? Where will we apply the two-sample T-Test? And where will we apply the paired T-Test? We consider this as a different example For example, you go to a field And from that field, you randomly select 10 plants from someone And know their heights After a month, you go to the same field again And randomly select 10 plants from someone And you know their heights Now, you both want to compare the samples to their means So, which test will be applied for this? For this, two-sample T-Test will be applied Now, let's take another example You randomly select 10 plants from someone After a month, you go to the same field again And randomly select 15 plants from someone Now, the first month you selected 10 plants And the second month you selected 15 plants You also selected their means Now, you want to compare the means of both the samples Still, the two-sample T-Test will be applied This means that the two-sample T-Test For this, the sample size can be the same Like in the previous case And the sample size can be different Like we saw that the first sample was 10 And the second sample was 15 Now, let's take another example You go to the field And randomly select 15 plants from someone And randomly select 15 plants Now, you go to the same field again And after going to the same field After a month, you select the data of the same plants The data you collected before Because when you went to the first time When you collected the data of the plants You tagged them You went to the same place And you collected the data of the same plants Now, when you compare the means of these two-samples Then you will apply the T-Test Similarly, you have 10 patients You recorded their glucose level After that, after a month you gave them some medicine After giving them medicine You recorded their glucose level again You want to compare that Their glucose level Before eating the medicine And after eating the medicine There is a statistical difference Or not In this case, you will apply the Pair T-Test So, the basic difference in both the tests Is that the Pair T-Test For the Pair T-Test, it is necessary to have the same entities That is, the data you collected before And the data you collected after In this, the sample size remains the same Whereas the two-sample T-Test For the two-sample T-Test The individuals The data you collected before Is not necessary You have targeted them from the population After selecting the other products You can compare the samples of the individuals So, there is no need to have the same entities And apart from that, there is no need to have the same sample size Whereas for the Pair T-Test The sample size and entities are necessary