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Introduction to t statistic and correlation (Hypothesis test and t stat…
Introduction to t statistic and correlation
t stat, alternative to z stat
z score can be used to compare the difference between sample mean (M) and hypothesis population, but sometimes information about the population may not be available which make it difficult to calculate z stat and we will use t stat
t stat use information about the corresponding sample instead of the population
Degree of Freedom
Degree of freedom let us know the sample mean so we can know the sample variance and able to calculate the t stat.
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t distribution
Any sample we calculate t sat for have t distribution
t distribution is a normal distribution depending on the population, n score and degree of freedom
Hypothesis test and t stat
To calculate hypothesis test for t stat use population with unknown mean and variance, then by using null hypothesis you can determine the mean and the variance
Null Hypothesis states that population mean is unchanged so even if you start with a population with unknown means and variance, you just have to determine the mean from the null hypothesis
Hypothesis and alpha value in t stat
Correlation is between 0 and -1
Effect of size and t test
Size in hypothesis of t test is known as cohen d
Cohen d is the mean difference between the treatment sample and sample that are not treat and divide both by std
Critical Region
Critical region in t stat can be determine whether it is right tail or left tail.
Correlation and relationship between two variable
The relationship can be define by some characteristics like direction, form or strength
Person correlation
Pearson correlation is the most common use correlation and it measures the relationship between two liner variable, it uses the sum of product (that is the sum of the product of the two variable) divided by square root of the sum of the square of each variable
Correlation of two variable cannot be interpreted as proportion
And a correlation is not a cause and effect
Range of the data presented in the variable can affect the correlation greatly
An outlier in a variable can affect or alter the correlation
If there are more than two variables, then you will need partial correlation that will hold the third variable constant while calculating the correlation for the two
Effect of size in correlation especially Pearson correlation