- Two Sample T-test For Means
- Two Sample T Test Definition
This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-Test, execute the following steps. First, perform an F. Step7v15.1 wincc advaced download.
Use this calculator to test whether samples from two independent populations provide evidence that the populations have different means. For example, based on blood pressures measurements taken from a sample of women and a sample of men, can we conclude that women and men have different mean blood pressures?
Two Sample T-test For Means
This test is known as an a two sample (or unpaired) t-test. It produces a “p-value”, which can be used to decide whether there is evidence of a difference between the two population means.
- The version of a t-test examined in this chapter will assess the significance of the difference between the means of two such samples, providing: (i) that the two samples are randomly drawn from normally distributed populations; and (ii) that the measures of which the two samples are composed are equal-interval.
- Two-Sample t-Test. A two-sample t-test is used to test the difference (d 0) between two population means. A common application is to determine whether the means are equal. Here is how to use the test. Define hypotheses. The table below shows three sets of null and alternative hypotheses.
The p-value is the probability that the difference between the sample means is at least as large as what has been observed, under the assumption that the population means are equal. The smaller the p-value, the more surprised we would be by the observed difference in sample means if there really was no difference between the population means. Therefore, the smaller the p-value, the stronger the evidence is that the two populations have different means.
Typically a threshold (known as the significance level) is chosen, and a p-value less than the threshold is interpreted as indicating evidence of a difference between the population means. The most common choice of significance level is 0.05, but other values, such as 0.1 or 0.01 are also used.
Two Sample T Test Definition
This calculator should be used when the sampling units (e.g. the sampled individuals) in the two groups are independent. If you are comparing two measurements taken on the same sampling unit (e.g. blood pressure of an individual before and after a drug is administered) then the appropriate test is the paired t-test.
- [Instructor] 'Kaito growstomatoes in two separate fields. 'When the tomatoes are ready to be picked, 'he is curious as to whetherthe sizes of his tomato plants 'differ between the two fields. 'He takes a random sampleof plants from each field 'and measures the heights of the plants. 'Here is a summary of the results:' So what I want you todo, is pause this video, and conduct a two sample T test here. And let's assume thatall of the conditions for inference are met,the random condition, the normal condition, andthe independent condition. And let's assume that we are working with a significance level of 0.05. So pause the video, and conductthe two sample T test here, to see whether there's evidence that the sizes of tomato plantsdiffer between the fields. Alright, now let's workthrough this together. So like always, let's firstconstruct our null hypothesis. And that's going to be the situation where there is no differencebetween the mean sizes, so that would be thatthe mean size in field A is equal to the mean size in field B. Now what about our alternative hypothesis? Well, he wants to see whetherthe sizes of his tomato plants differ between the two fields. He's not saying whetherA is bigger than B, or whether B is bigger than A, and so his alternative hypothesis would be around his suspicion, that the mean of A is notequal to the mean of B, that they differ. And to do this two sample T test now, we assume the null hypothesis. We assume our null hypothesis, and remember we're assuming that all of our conditions for inference are met. And then we wanna calculate a T statistic based on this sample data that we have. And our T statistic is going to be equal to the differencesbetween the sample means, all of that over our estimate of the standard deviationof the sampling distribution of the difference of the sample means. This will be the sample standard deviation from sample A squared, overthe sample size from A, plus the sample standard deviation from the B sample squared,over the sample size from B. And let's see, we haveall the numbers here to calculate it. This numerator is going tobe equal to 1.3 minus 1.6, 1.3 minus 1.6, all of that over the square root of, let's see, the standard deviation, thesample standard deviation from the sample from field A is 0.5. If you square that, you're gonna get 0.25, and then that's going tobe over the sample size from field A, over 22, plus 0.3 squared, so that is, 0.3 squared is 0.09, all of that over thesample size from field B, all of that over 24. The numerator is just gonna be -.3, divided by the square root of .25 divided by 22, plus .09 divided by 24, and that gets us -2.44. Approximately -2.44. And so if you thinkabout a T distribution, and we'll use our calculatorto figure out this probability, so this is a T distributionright over here, this would be the assumedmean of our T distribution. And so we got a result that is, we got a T statistic of -2.44, so we're right overhere, so this is -2.44. And so we wanna saywhat is the probability from this T distributionof getting something at least this extreme? So it would be this area, andit would also be this area, if we got 2.44 above the mean,it would also be this area. And so what I could do is,I'm gonna use my calculator to figure out thisprobability right over here, and then I'm just gonnamultiply that by two, to get this one as well. So the probability of getting a T value, I guess I could saywhere its absolute value is greater than or equal to 2.44, is going to be approximately equal to, I'm going to go to second, distribution, I'm going to go to thecumulative distribution function for our T distribution, click that. And since I wanna think aboutthis tail probability here that I'm just gonna multiply by two, the lower bound is a veryvery very negative number, and you could view that asfunctionally negative infinity. The upper bound is -2.44. - 2.44. And now what's our degrees of freedom? Well if we take the conservative approach, it'll be the smaller ofthe two samples minus one. Well the smaller of the two samples is 22, and so 22 minus one is 21. So put 21 in there. Two.. 21. And now I can paste, and I getthat number right over there, and if I multiply that bytwo, 'cause this just gives me the probability of gettingsomething lower than that, but I also wanna thinkabout the probability of getting something 2.44or more above the mean of our T distribution. So times two, is going to beequal to approximately 0.024. So approximately 0.024. And what I wanna do then is compare this to my significance level. And you can see very clearly,this right over here, this is equal to our P value. Our P value in this situation, our P value in thissituation is clearly less than our significance level. And because of that, we said hey, assuming the null hypothesis is true, we got something that'sa pretty low probability below our threshold, sowe are going to reject our null hypothesis, whichtells us that there is, so this suggests, this suggests the alternative hypothesis, that there is indeed adifference between the sizes of the tomato plants in the two fields.