Hypothis Testing

When you state your Hypotheses

H_{0 =} Null Hypothesis = _{NO Correlation (this option ALWAYS has an = sign. It could be = , >= or <=, but it ALWAYS has the = sign)}

_{Assume that what ever you are researching has NO EFFECT}

H_{a =} Alternative Hypothesis denoted as H_a ~or~ H_{1 = There IS a Correlation (this option is the opposite of the Null Hypothesis)}

_{Assume what you are researching HAS an Effect.}

_{Writing the Hypothesis} H_{0 has 3 options and the} H_{a has 3 options:} https://www.youtube.com/watch?v=uvwNc5dVwNM

H_{0 = mean} H_{0 <= mean} H_{0 >= mean}

H_{a not = to mean} H_{a < mean} H_{a > mean}

_{Khan Academy has 2 great videos on Hypothesis Testing.}

Small Sample Testing: https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/small-sample-hypothesis-test

_{P-values from mean & sd: https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/hypothesis-testing-and-p-values}

All of Khan's Hypothesis testing videos: Choose from these Khan Academy Hypothesis Testing Videos

• Hypothesis Testing Formula = Test Value = ((Observed value) - (Expected Value)) / Standard error

  • another Formula that can be used if the Observations are Greater Than > 30

  • Z = (X-mean) / (Standard Deviation / sqr (n observations))

To understand CONCEPTS PolyerMath - has an even better one! https://www.youtube.com/watch?v=cW16A7hXbTo

The P-value helps your Decision and Conclusion

· The probability value (p-value) of a statistical hypothesis test is the probability of getting a value of the test statistic as extreme as or more extreme than that observed by chance alone, if the null hypothesis H0, is true.

· It is the probability of wrongly rejecting the null hypothesis if it is in fact true.

· It is equal to the significance level of the test for which we would only just reject the null hypothesis. The p-value is compared with the actual significance level of our test and, if it is smaller, the result is significant. That is, if the null hypothesis were to be rejected at the 5% signficance level, this would be reported as "p < 0.05".

· Small p-values suggest that the null hypothesis is unlikely to be true. The smaller it is, the more convincing is the rejection of the null hypothesis. It indicates the strength of evidence for say, rejecting the null hypothesis H0, rather than simply concluding "Reject H0' or "Do not reject H0".