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Introduction to Inferential Statistics

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Introduction to Inferential Statistics

- Comparing the Obtained & Critical Values
- If Obtained > Critical, then Reject the Ho
- Can be sure to a certain level (based on α) that the findings cannot be explained by chance
- The difference is due to something other than chance

- If Obtained < Critical, then Fail to Reject the Ho
- Cannot be sure that the findings cannot be explained by chance
- The Ho is the best explanation given the data

- Compare the obtained value and the critical value
- Obtained rxy = .393
- Critical rxy = .349

- Make Decision and State Conclusion
- .393 > .349, therefore reject the null hypothesis
- The rxy is not equal to 0.

- The relationship between the two variables (quality of marriage and quality of parent/child relationship)did occur by something other than chance.

- .393 > .349, therefore reject the null hypothesis

- Compute r2
- r2 = .154
- 15.4% of the quality of the parent/child relationship is explained by the quality of the marriage

- r2 = .154

- Interpretation
- r(27) = .393, p < .05, r2 = .154
- r = the test statistic used
- 27 = number of degrees of freedom
- .393 = the obtained value of r
- p < .05 = the probability is less than 5% that the relationship between the two variables is due to chance

- r(27) = .393, p < .05, r2 = .154
- There is a significant relationship between the two variables.

- The researcher will report the findings of the testing by supplying a statement in addition to reporting the obtained value and the p-value.
- Ex: “A study was conducted examining the relationships of 378 Chinese married couples over a 2-year period. The study revealed a significant direct relationship between the quality of marriage and the quality of the parent-child relationship, r(27) = .393, p < .05, r2 = .154.” The quality of a marriage explains 15.4% of quality of the parent-child relationship within that marriage.”