Normality of the distributions can be tested using, for example, a Q-Q plot. This test assumes that the two populations follow normal distributions (otherwise known as Gaussian distributions). Note that this result is not inconsistent with the previous result: with bigger samples we are able to detect smaller differences between populations. If both sample sizes were increased to 20, the p-value would reduce to 0.048 (assuming the sample means and standard deviations remained the same), which we would interpret as strong evidence of a difference. Since this p-value is greater than 0.05, it would conventionally be interpreted as meaning that the data do not provide strong evidence of a difference in capillary density between individuals with and without ulcers. (All measurements are in capillaries per square mm.) Using this information, the p-value is calculated as 0.167. A control sample of 10 individuals without ulcers has mean capillary density of 34, with standard deviation 8.0. A sample of 10 patients with ulcers has mean capillary density of 29, with standard deviation 7.5. blood pressure of an individual before and after a drug is administered) then the appropriate test is the paired t-test.Ī study compares the average capillary density in the feet of individuals with and without ulcers.
If you are comparing two measurements taken on the same sampling unit (e.g. the sampled individuals) in the two groups are independent. This calculator should be used when the sampling units (e.g. The most common choice of significance level is 0.05, but other values, such as 0.1 or 0.01 are also used. 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. Therefore, the smaller the p-value, the stronger the evidence is that the two populations have different means. 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. 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. It produces a “p-value”, which can be used to decide whether there is evidence of a difference between the two population means. This test is known as an a two sample (or unpaired) t-test. 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?
Once you have a value of from data, the graph will show you the P-value for this : it is the probability-calculated taking H 0 to be true-of getting a value at least that far away from H 0 in the direction of the arrow.Use this calculator to test whether samples from two independent populations provide evidence that the populations have different means. Try changing H a to see how the arrow changes. The blue arrow shows what kinds of values of count as evidence against H 0 in favor of your alternative H a. The normal curve shows the sampling distribution of the sample mean when your null hypothesis is true. Here we're testing a hypothesis about the mean of a normal distribution whose standard deviation we know, but the concepts are essentially the same for any other type of significance test. This applet illustrates the P-value of a test of significance. Or you can specify the true population mean μ and use the GENERATE SAMPLE button to create a random sample from the population, display the observations and sample mean (note that some of the points in the sample may be too far from μ to appear in the display), and calculate the P-value.Ĭlick the "Quiz Me" button to complete the activity. If you already have a sample mean, enter this value and click UPDATE to display the sample mean on the graph and calculate the P-value. To set up the test, fill in the boxes: What null hypothesis H 0 about the mean μ do you want to test? Which alternative hypothesis H a do you have in mind, and what level of significance α do you require? What value of the standard deviation σ is known to be true? How many observations n will you have (250 or fewer)?