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Review of Basics Part II: Probability Distributions and Statistical Significance

This review covers probability distributions, confidence intervals, and statistical significance in inferential statistics. Learn about z-scores, standard normal distribution, sampling distribution, testing the null hypothesis, and common misconceptions. Understand the importance of confidence intervals and key statistical concepts like p-values. Explore the challenges of null hypothesis significance testing and interpreting results.

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Review of Basics Part II: Probability Distributions and Statistical Significance

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  1. REVIEW OF BASICS PART II • Probability Distributions • Confidence Intervals • Statistical Significance

  2. Probability Distributions • Probabilities are relative frequencies • Probabilities vary between 0 and 1

  3. z - SCORES • z-score: standard score measuring in units of standard deviations • standard normal distribution: normal distribution in z-score units

  4. Confidence Intervals • Range of values thought to contain the population mean • Go up and down from the sample mean • Level of confidence determines how many standard deviations to go

  5. 99% 95% 68% MEAN -3SD -2SD -1SD +1SD +2SD +3SD

  6. STATISTICAL SIGNIFICANCE • Inferential statistics are used to make inferences about populations based on samples • These inferences are based on hypothetical probability distributions

  7. Sampling Distribution • Hypothetical frequency distribution of all the sample means from a population • Sampling variation • Standard error: standard deviation of sampling distribution

  8. Testing the Null • Null Hypothesis: no difference • Assume the Null Hypothesis is true until proven other wise • Reasonable doubt standard (p < .05) • Reject or Fail to Reject the Null

  9. Confusion about p • p is the probability of a Type I error: rejecting the Ho when the Ho is true • What is the probability that you could get results this extreme if the Ho is true? • NOT the probability that the Ho is true given these results

  10. Problems with NHST • Binary decision • Does not show effect size • Null is probably never literally true

  11. Choosing Stats A measure of Body Esteem is given to the same college students before and after they watch an episode of a reality TV show. The researcher would like to determine whether there is a significant decrease in Body Esteem scores after watching the TV show.

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