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# Lecture 5 - Descriptive and Inferential Statistics...

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Descriptive and Inferential Statistics Descriptive statistics The science of describing distributions of samples or populations Inferential statistics The science of using SAMPLE statistics to make INFERENCES or DECISIONS about population parameters

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Inferential Statistics Examples Quantitative Using sample mean X to calculate population mean μ Using sample stdev S to calculate population stdev σ Qualitative Hypothesis testing is most widely used inferential statistic
Inferential Statistics Examples Proving true or false Ex: Prove that mean of UCLA is 110. Mean of sample is 111. What can we say about the truth of the statement Mean=110? It might be true, but also mean of population could be 110, 109, 108. But if one asserts mean of UCLA is 70, than we can be confident that this statement is false, based on the idea that a mean of 70 for UCLA is EXTREMLEY UNLIKELY to produce sample mean of 110.

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Inferential Statistics Examples Given that it is easier to show something false than true, what are we to do? Assume that nothing is going on (NULL HYPOTHESIS) , and show that this is false. We then accept that Null is false and ALTERNATE HYPOTHESIS is true.
Inferential Statistics Examples H o: μ =100 (null hypothesis) H 1 : μ NOT =100 (alternative hypothesis)

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Inferential Statistics Examples Nondirectional test H o: μ =a H 1 : μ NOT =a Use when prior evidence is non-conclusive TWO-TAILED test
Inferential Statistics Examples Directional test H o: μ <=a H 1 : μ >a Use when prior evidence suggests μ >a ONE-TAILED test Directional test H o: μ >=a H 1 : μ <a Use when prior evidence suggests μ <a ONE-TAILED test

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Hypothesis Testing
Null is true Alternate is true

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Factors affecting error rates Alpha ( ) α Beta ( ) β Set by Experimenter Alpha ( ) α Effect Size Sample Size (N) Standard Deviation ( σ X ) Tails of Test
Hypothesis Testing Errors Type 1 errors: What happens Other researchers use this false result as information Fail to replicate

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Lecture 5 - Descriptive and Inferential Statistics...

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