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A mix of linear regression and analysis of variance. analysis of covariance is responsible for intergroup variance when analysis of variance is performed.
See related link. You can use Excel, if you dataset is not too big. Generally, if I have a table of data, with n columns corresponding to n variables with N observations, I can calculate the covariance of columns a and b, using excel covar function, covar(range of first data values, range of second data values) To keep things organized, you may want to name the ranges of your columns and use them as the arguments in the covar.
Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.
You need a null hypothesis first. You then calculate the probability of the observation under the conditions specified by the null hypothesis.
A sample size of one is sufficient to enable you to calculate a statistic.The sample size required for a "good" statistical estimate will depend on the variability of the characteristic being studied as well as the accuracy required in the result. A rare characteristic will require a large sample. A high degree of accuracy will also require a large sample.