Lecture 5

# 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 110. What can we say about the truth of the statement “Population Mean is 110?” It might be true, but also mean of population could be 111, 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 EXTREMELY UNLIKELY to produce sample mean of 110.

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Inferential Statistics: Hypothesis Testing How do we show that a statement is most likely to be false? 1) Creating a statement (i.e. null hypothesis) Example: The Mean IQ of UCLA students is 100 Ho: μ =100 2) Creating a distribution of outcomes given that hypothesis Example: A mean distribution ( σ X =10 , ,N=25)
Inferential Statistics: Hypothesis Testing 3) Determine outcomes that we consider “Unlikely” Example:

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4) Evaluate if our experimental result is one of those unlikely outcomes Example: (Sample Mean=105)
5) Two possible outcomes Reject Null Hypothesis Fail to Reject Null Hypothesis

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5) Two possible outcomes Reject Null Hypothesis Fail to Reject Null Hypothesis
Inferential Statistics: Hypothesis Testing If we reject the null

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Lecture 5 - Descriptive and Inferential Statistics...

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