![]() In t.test(), you can set this with paired option. In unpaired data sets, the sample size between two sets may not be the same. Hence, the two data set size must be the same. Paired data sets means that if X1,X2,…,Xn are the first data set and Y1,Y2,…Yn are the second one, then Xi corresponds to Yi. You may have paired or unpaired data sets. You may have different types of data sets. The above example uses unpaired data sets with unequal variances. Note that Welch’s t-test is a t-test with unequal variances. ![]() The output also produces estimates of the sample means, the mean and the degree of freedom of the t-distribution. The maximum difference of the mean can be as low as -3.37 and as high as 0.21. Here you should accept the null hypothesis that the two means are equal because the p-value is larger than 0.05. ![]() T = -1.8608, df = 17.776, p-value = 0.0794Īlternative hypothesis: true difference in means is not equal to 0īased on the result, you can say: at 95% confidence level, there is no significant difference (p-value = 0.0794) of the two means. Can we confidently say that the two groups have different means? For instances, at 95% level of confidence, the significant level is 5% and the p-value is reported as p plot(extra ~ group, data = sleep)Ī quick grasp to the plot we see that there is naturally an overlap but the mean (half of the rectangle height) is different. The p-value is always compared with the significance level of the test. The t-test will also produce the p-value, which is the probability of wrongly rejecting the null hypothesis. Since we test the difference between the two means, the confidence interval in this case specifies the range of values within which the difference may lie. In a hypothesis test, we want to reject or accept the null hypothesis with some confidence interval. This means that the alternative hypothesis for the test is that the difference of the mean is not equal to zero. In t-test, the null hypothesis is that the mean of the two samples is equal. The basic idea behind t-test is the inference problem from a small sample size data set to test whether its sample mean may have large deviation from the true population mean.Ī very common problem you will encounter is having two data sets and you want to test whether the two sets are coming from the same (assuming) normal distributions. Gossett who hid his name due to his position as a worker in a brewery company) is a simple yet very useful statistical test. Student’s t-test or t-test (the real name is W.S.
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