When the null hypothesis of equal group means is incorrect, then the numerator should be large compared to the denominator, giving a large F statistic and a small area (small p-value) to the right of the statistic under the F curve. A small F statistic will result, and the area under the F curve to the right will be large, representing a large p-value.
If the null hypothesis is correct, then the numerator should be small compared to the denominator. The F statistic is the ratio of a measure of the variation in the group means to a similar measure of the variation within the groups. The graph of the F distribution is always positive and skewed right, though the shape can be mounded or exponential depending on the combination of numerator and denominator degrees of freedom. (Why?)Ĭonclusion: With a 3% level of significance, from the sample data, the evidence is not sufficient to conclude that the mean heights of the bean plants are different. The distribution for the test is F 2,12 and the F statistic is F = 0.134ĭecision: Since α = 0.03 and the p-value = 0.8759, do not reject H 0. The dfs for the denominator = the total number of samples – the number of groups = 15 – 3 = 12 The dfs for the numerator = the number of groups – 1 = 3 – 1 = 2. Mean of the sample variances = 15.433 = s 2 pooled Then MS between = (5)(0.413) where n = 5 is the sample size (number of plants each child grew).Ĭalculate the mean of the three sample variances (Calculate the mean of 11.7, 18.3, and 16.3). Next, calculate the variance of the three group means (Calculate the variance of 24.2, 25.4, and 24.4). įirst, calculate the sample mean and sample variance of each group. Notice that each group has the same number of plants, so we will use the formula F’ =. Sampling distributions can be solved using the Sampling Distribution Calculator.This time, we will perform the calculations that lead to the F’ statistic. It is used extensively in statistical inference, such as sampling distributions. The most important continuous probability distributions is the normal probability distribution. Probabilities for discrete probability distributions can be found using the Discrete Distribution Calculator. Discrete distributions are probability distributions for discrete random variables. A closely related topic in statistics is discrete probability distributions. t-Distribution TableĬontinuous probability distributions are probability distributions for continuous random variables. So use of the t table involves matching the degrees of freedom with the area in the upper tail to get the corresponding t-value. Another difference is that the t table provides the area in the upper tail whereas the z table provides the area in the lower tail. We have a different t-distribution for each of the degrees of freedom. The main difference is that the t-distribution depends on the degrees of freedom. They both have a similar bell-shape and finding probabilities involve the use of a table. The t-distribution is similar to the standard normal distribution. For the uniform probability distribution, the probability density function is given by f(x)=$\begin $. For a continuous probability distribution, probability is calculated by taking the area under the graph of the probability density function, written f(x).