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The lognormal distribution, probably.
An F-statistic is a measure that is calculated from a sample. It is a ratio of two lots of sums of squares of Normal variates. The sampling distribution of this ratio follows the F distribution. The F-statistic is used to test whether the variances of two samples, or a sample and population, are the same. It is also used in the analysis of variance (ANOVA) to determine what proportion of the variance can be "explained" by regression.
In a study using 9 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
No, it can not be used. Every element has colour homogeneity.
A test statistic is used to test whether a hypothesis that you have about the underlying distribution of your data is correct or not. The test statistic could be the mean, the variance, the maximum or anything else derived from the observed data. When you know the distribution of the test statistic (under the hypothesis that you want to test) you can find out how probable it was that your test statistic had the value it did have. If this probability is very small, then you reject the hypothesis. The test statistic should be chosen so that under one hypothesis it has one outcome and under the is a summary measure based on the data. It could be the mean, the maximum, the variance or any other statistic. You use a test statistic when you are testing between two hypothesis and the test statistic is one You might think of the test statistic as a single number that summarizes the sample data. Some common test statistics are z-score and t-scores.
Computing F-ratioThe F-ratio is used to determine whether the variances in two independent samples are equal. If the F-ratio is not statistically significant, you may assume there is homogeneity of variance and employ the standard t-test for the difference of means. If the F-ratio is statistically significant, use an alternative t-test computation such as the Cochran and Cox method.
In finance, risk of investments may be measured by calculating the variance and standard deviation of the distribution of returns on those investments. Variance measures how far in either direction the amount of the returns may deviate from the mean.
If the paired differences are normal in a test of mean differences, then the distribution used for testing is the
The z-score table is the cumulative distribution for the Standard Normal Distribution. In real life very many random variables can be modelled, at least approximately, by the Normal (or Gaussian) distribution. It will have its own mean and variance but the Z transform converts it into a standard Normal distribution (mean = 0, variance = 1). The Z-distribution is then used to make statistical inferences about the data. However, there is no simple analytical method to calculate the values of the distribution function. So, it has been done and tabulated for easy reference.
Variance is used to add standard deviations when comparing two samples or populations. Variance is simply Std^2. The formula for obtaining Std is dependent on the type of sample taken\ hypothesis test performed i.e. 2-proportion pop/sample, single proportion, poussin, binomial, etc.
Whereas a t-test is used for n30, where n=sample size. n < 30 or n > 30 is not entirely arbitrary; it is intended to indicate that n must be sufficiently large to use the normal distribution. In some cases, n must be greater than 50. Note, both the t-test and the z-test can only be used if the distribution from which the sample is being drawn is a normal distribution. A z-test can be used even if the distribution is not normal (but is not severely skewed) if n>30, in which case, we can safely assume that the distribution is normal.
Both are parametric test. The t-test uses a test statistic that is related to the sample mean(s) and is used to compare that with the mean of another sample or some population. The F-test uses a test statistic that is related to the sample variance and is used to compare that with the variance of another sample or some population. Both tests require identical independently distributed random variables. This ensures that the relevant test statistics are approximately normally distributed.