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How to calculate the degrees of freedom for t-distribution?
n-1
Does t-distribution rely on degree of freedom?
Yes. The parameters of the t distribution are mean, variance and the degree of freedom. The degree of freedom is equal to n-1, where n is the sample size. As a rule of thumb, above a sample size of 100, the degrees of freedom will be insignificant and can be ignored, by using the normal distribution. Some textbooks state that above 30, the degrees of freedom can be ignored.
What is Chi-square Probability Distribution?
Given Z~N(0,1), Z^2 follows χ_1^2 Chi-square Probability Distribution with one degree of freedom Given Z_i~N(0,1), ∑_(i=1)^ν▒Z_i^2 follows χ_ν^2 Chi-square Probability Distribution with ν degree of freedom Given E_ij=n×p_ij=(r_i×c_j)/n, U=∑_(∀i,j)▒(O_ij-E_ij )^2/E_ij follows χ_((r-1)(c-1))^2 Chi-square Probability Distribution with ν=(r-1)(c-1) degree of freedom Given E_i=n×p_i, U=∑_(i=1)^m▒(O_i-E_j )^2/E_i follows χ_(m-1)^2 Chi-square Probability Distribution with ν=m-1 degree of freedom
What does when the sample size and degrees of freedom is sufficiently large the difference between a t distribution and the normal distribution becomes negligible mean?
The t-distribution and the normal distribution are not exactly the same. The t-distribution is approximately normal, but since the sample size is so small, it is not exact. But n increases (sample size), degrees of freedom also increase (remember, df = n - 1) and the distribution of t becomes closer and closer to a normal distribution. Check out this picture for a visual explanation: http://www.uwsp.edu/PSYCH/stat/10/Image87.gif
How do you find the confidence intervals?
See: http://en.wikipedia.org/wiki/Confidence_interval Includes a worked out example for the confidence interval of the mean of a distribution. In general, confidence intervals are calculated from the sampling distribution of a statistic. If "n" independent random variables are summed (as in the calculation of a mean), then their sampling distribution will be the t distribution with n-1 degrees of freedom.
How to calculate the degrees of freedom for t-distribution?
n-1
How do you find the degrees of freedom when using the t distribution to estimate or test the mean of a sample from a single population?
If the sample consisted of n observations, then the degrees of freedom is (n-1).
Does t-distribution rely on degree of freedom?
Yes. The parameters of the t distribution are mean, variance and the degree of freedom. The degree of freedom is equal to n-1, where n is the sample size. As a rule of thumb, above a sample size of 100, the degrees of freedom will be insignificant and can be ignored, by using the normal distribution. Some textbooks state that above 30, the degrees of freedom can be ignored.
What is Chi-square Probability Distribution?
Given Z~N(0,1), Z^2 follows χ_1^2 Chi-square Probability Distribution with one degree of freedom Given Z_i~N(0,1), ∑_(i=1)^ν▒Z_i^2 follows χ_ν^2 Chi-square Probability Distribution with ν degree of freedom Given E_ij=n×p_ij=(r_i×c_j)/n, U=∑_(∀i,j)▒(O_ij-E_ij )^2/E_ij follows χ_((r-1)(c-1))^2 Chi-square Probability Distribution with ν=(r-1)(c-1) degree of freedom Given E_i=n×p_i, U=∑_(i=1)^m▒(O_i-E_j )^2/E_i follows χ_(m-1)^2 Chi-square Probability Distribution with ν=m-1 degree of freedom
What does when the sample size and degrees of freedom is sufficiently large the difference between a t distribution and the normal distribution becomes negligible mean?
The t-distribution and the normal distribution are not exactly the same. The t-distribution is approximately normal, but since the sample size is so small, it is not exact. But n increases (sample size), degrees of freedom also increase (remember, df = n - 1) and the distribution of t becomes closer and closer to a normal distribution. Check out this picture for a visual explanation: http://www.uwsp.edu/PSYCH/stat/10/Image87.gif
How do you find the confidence intervals?
See: http://en.wikipedia.org/wiki/Confidence_interval Includes a worked out example for the confidence interval of the mean of a distribution. In general, confidence intervals are calculated from the sampling distribution of a statistic. If "n" independent random variables are summed (as in the calculation of a mean), then their sampling distribution will be the t distribution with n-1 degrees of freedom.
How do you explain F-statistic?
If X and Y have Gaussian (Normal) distributions, then the ratio ofthe mean of m variables distributed as X2 andthe mean of n variables distributed as Y2 hasan F distribution with m and n degrees of freedom.
How chi square distribution is extension of normal distribution?
Given "n" random variables, normally distributed, and the squared values of these RV are summed, the resultant random variable is chi-squared distributed, with degrees of freedom, k = n-1. As k goes to infinity, the resulant RV becomes normally distributed. See link.
Properties of Chi-square distribution?
It is a continuous distribution. Its domain is the positive real numbers. It is a member of the exponential family of distributions. It is characterised by one parameter. It has additive properties in terms of the defining parameter. Finally, although this is a property of the standard normal distribution, not the chi-square, it explains the importance of the chi-square distribution in hypothesis testing: If Z1, Z2, ..., Zn are n independent standard Normal variables, then the sum of their squares has a chi-square distribution with n degrees of freedom.
How do you calculate degrees of freedom for a correlation?
To calculate the degrees of freedom for a correlation, you have to subtract 2 from the total number of pairs of observations. If we denote degrees of freedom by df, and the total number of pairs of observations by N, then: Degrees of freedom, df=N-2. For instance, if you observed height and weight in 100 subjects, you have 100 pairs of observations since each observation of height and weight constitutes one pair. If you want to calcualte the correlation for these two variables (height and weight), your degrees of freedom would be calculated as follows: N=100 df=N-2 Therefore, df=100-2=98 The degrees of freedom are a function of the parameters; you subtract the amount of parameters free to vary from the n to get the df, so logically in a correlation we should subtract 2 from n, as we are looking at a correlation between 2 variables.
Degree of freedom in classical mechanics?
In classical mechanics, the degree of freedom of a system refers to the number of independent parameters needed to describe the configuration of the system completely. It is essentially the number of ways a system can move or change its state. For example, a particle moving in one dimension has one degree of freedom, while a point mass moving in three dimensions has three degrees of freedom.
Why is it impossible to compute a T statistic for a sample that has only one score?
A T test is used to find the probability of a scenario given a specific average and the number of degrees of freedom. You are free to use as few degrees of freedom as you wish, but you must have at least 1 degree of freedom. The formula to find the degrees of freedom is "n-1" or the population sample size minus 1. The minus 1 is because of the fact that the first n is not a degree of freedom because it is not an independent data source from the original, as it is the original. Degrees of freedom are another way of saying, "Additional data sources after the first". A T test requires there be at least 1 degree of freedom, so there is no variability to test for.
