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Definition: The Chi-Square Distribution, denoted as χ2 is related to the standard normal distribution such as, if the independent normal variable, let’s say Z assumes the standard normal distribution, then the square of this normal variable Z2 has the chi-square distribution with ‘K’ degrees of freedom. Here, K is the sum of the independent squared normal variables. The … [Read more...] about Chi-Square Distribution

Definition: The F-distribution depends on the degrees of freedom and is usually defined as the ratio of variances of two populations normally distributed and therefore it is also called as Variance Ratio Distribution. Properties of F-Distribution There are several properties of F-distribution which are explained below: The F-distribution is positively skewed and with the … [Read more...] about Properties of F-Distribution

Definition: The F-Distribution is also called as Variance Ratio Distribution as it usually defines the ratio of the variances of the two normally distributed populations. The F-distribution got its name after the name of R.A. Fisher, who studied this test for the first time in 1924. Symbolically, the quantity is distributed as F-distribution with ν1 =n1-1 and ν2 = n2-1 … [Read more...] about F-Distribution

Definition: The t-distribution is a probability distribution method wherein the hypothesis of the mean of a small sample is tested, which is drawn from the systematic population whose standard deviation is unknown. It is a statistical measure used to compare the observed data with the data expected to be obtained from a specific hypothesis. Applications of t-distribution The … [Read more...] about Applications of t-Distribution

Definition: The t-Distribution, also known as Student’s t-Distribution is the probability distribution that estimates the population parameters when the sample size is small and the population standard deviation is unknown. It resembles the normal distribution and as the sample size increases the t-distribution looks more normally distributed with the values of means and … [Read more...] about t-Distribution

Definition: The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary. In other words, the degrees of freedom, in general, can be defined as the total number of observations minus the number of independent constraints imposed on the observations. The degrees of freedom are calculated for the following statistical tests … [Read more...] about Degrees of Freedom

Definition: The Hypothesis is an assumption which is tested to check whether the inference drawn from the sample of data stand true for the entire population or not. Hypothesis Testing Procedure The following steps are followed in hypothesis testing: Set up a Hypothesis: The first step is to establish the hypothesis to be tested. The statistical hypothesis is an … [Read more...] about Hypothesis Testing Procedure

Definition: The Hypothesis Testing is a statistical test used to determine whether the hypothesis assumed for the sample of data stands true for the entire population or not. Simply, the hypothesis is an assumption which is tested to determine the relationship between two data sets. In hypothesis testing, two opposing hypotheses about a population are formed Viz. Null … [Read more...] about Hypothesis Testing

Definition: The Sampling Distribution of Standard Deviation estimates the standard deviation of the samples that approximates closely to the population standard deviation, in case the population standard deviation is not easily known. Thus, the sample standard deviation (S) can be used in the place of population standard deviation (σ). Symbolically, S= standard error of the … [Read more...] about Sampling Distribution of Standard Deviation

Definition: The Sampling Distribution of Proportion measures the proportion of success, i.e. a chance of occurrence of certain events, by dividing the number of successes i.e. chances by the sample size ’n’. Thus, the sample proportion is defined as p = x/n. The sampling distribution of proportion obeys the binomial probability law if the random sample of ‘n’ is obtained … [Read more...] about Sampling Distribution of Proportion