paired t test

Wikipedia says:


Paired samples t-tests typically consist of a sample of matched pairs of similar units, or one group of units that has been tested twice (a “repeated measures” t-test).

A typical example of the repeated measures t-test would be where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are tested again after treatment with a blood-pressure lowering medication. By comparing the same patient’s numbers before and after treatment, we are effectively using each patient as their own control.


One sample t test

The one sample t test is used to test sample data against the Null Hypothesis (H0). In this case the Null Hypothesis is whether the sample mean matches the population mean.

chi square test statistic

The Chi square compares the observed data with the Null Hypothesis.

Chi square test looks at single set of data and Null Hypothesis.

Expected = row X col total / grand total

χ2 = sum ((observed – expected) /Expected)2

χ2  and DF/degree of freedom gives the test statistic

A big difference between observed and expected results in a large test statistic (χ2) and so leads to a rejection of the Null Hypothesis (Ho)

The greater the value of the test statistic, the greater the evidence against the Null hypothesis -leads to a smaller p -value

“…The p-value is the area under the chi-square probability density function (pdf) curve to the right of the specified χ2 value…”


p value area to right

Source: di


p value is the area to the right of the test statistic. The less the number (< 0.05) the more likely to reject the Null Hypothesis







Nice video explaining it all.

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