I have two sets of numbers. If the mean and standard deviation for one set are near to another does it mean the sets are somewhat equal to each other?
If both were the same, both sides must equal zero and this can only happen if the data are all the same. a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean
Dear Torkan Shafighfard,
Your understanding needs more clarification and statistical testings.
Mean and Standard Deviation (SD) are the univariate measures and they are determined based on the averages. For example, Variable X = 1, 2, 3, 4 and 5, and Variable Y = 5, 4, 3, 2, and 1. Here, the mean of X = 3 & SD = 1.581. This is similar to the mean of Y = 3 and SD = 1.581. But, these two variables are strongly negatively correlated with the same Mean and SD values. Hence, If the mean and standard deviation values of one set are near to another set DOES NOT mean that the sets are somewhat equal to each other.
However, you can run a correlation analysis between the two sets. The results should be positively correlated (NOT Negatively correlated) and the correlation value should be approximating 1 and significant at the 5% level.
Otherwise, get the difference of each pair of data (D1 - x1 - Y1) and subtract it from 1 (1 - D1). Then, get the average of D1 and its SD, and do the statistical test whether D1 has 95% confidence limit to have 1 (this should be tested with its SD and standard error).
Hope this will help you. Good luck in your studies.
Regards.
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