Confidence and Power in Statistics I

1. Confidence and Power in Statistics I Office of Research Consulting Jay Raadt, Genea Stewart, Lee Bedford, and Mehri Mizaeirafe September 26, 2019 2:00 PM

2. Outline Measures of Central Tendency Mean Median Mode Measures of Variability Range Variance Deviation Standard Deviation Populations and Samples Parameters and Statistics Statistics Descriptive Statistics Inferential Statistics Statistical Distributions Sampling Distribution Standard Error

3. Measures of Central Tendency  • How can you summarize a set of numbers with a single number? • Central tendency: the most "typical", or most common number • Mode • Median • Mean

4. Mode • Most frequently occurring number in a set of numbers (a distribution) • Mode of dataset 7,8,8,7,3,1,6,9,3,8 = 8 • Measure of central tendency for nominal (categorical) variables

5. Median: the value at which 1/2 of the ordered scores fall above and 1/2 of the scores fall below. The middle score when all scores are arranged from lowest to highest •        1 2 3 4 5                  1 2 3 4 Median= 3 Median = 2.5

6. Mean: Sum of all the scores divided by the number of scores Mean of 7,8,8,7,3,1,6,9,3,8 • ΣX = 7+8+8+7+3+1+6+9+3+8 = 60 • N = 10 • Mean = 60/10 = 6

7. The mean acts as a "fulcrum", or balancing point, for all the numbers in your set. Blocks on a board, the mean is the "fulcrum"

8. Measures of Central Tendency: Review

9. Measures of Variability • Range • Variance • Deviation • Standard Deviation

12. This means that there are people different from the mean. • This deviation is the number minus the mean • The average deviation is

13. The average deviation is always zero • Square the deviations before averaging them • Yields the Variance • Take the square root to put it back in the same metric as the original set of numbers

15. Measures of Central Tendency and Measures of Variability can be interpreted together for a more accurate depiction of data.

16. Why sampling

17. Populations and Samples • Parameters and Statistics

20. Two Types of Statistics • Descriptive • Summarize • Inferential • Conclude

21. Types of Descriptive Statistics • Measures of Central Tendency • Mean, Median, and Mode • Variability • Variance and Standard Deviation • Shape of the Distribution • Normality • Skewness • Kurtosis

22. Frequency Tables • Table that shows how many times each score is used

23. Histograms

24. Frequency Tables and Histograms

25. Shapes of Frequency Distributions • The side with fewer scores (tail) is the direction of the skew • Skewed to the left: Negative • Skewed to the right: Positive

26. Shapes of Frequency Distributions • Kurtosis • Does the curve have a steep peak or is it flat on top? • A normal (bell curved) distribution may be leptokurtic or platykurtic, but it will not be highly skewed.

27. Statistical Distributions • Sampling Distribution • Given two sample means, which do we trust more? • A set of means is called a sampling distribution of the mean

28. The mean has variance Var(x̄)=Var(x)/n, which can be proved: And we can apply it to our example:

29. Given two sample means, which do we trust more? • The standard deviation of the sampling distribution of the mean has a special name: Standard Error. • Adding and subtracting standard errors, we have a confidence interval. • E.g., a 95% confidence interval of the mean is the mean plus or minus two standard errors  • Sample Mean +/- 2 Standard Errors • Be confident: Over many random samples, 95% of the confidence intervals contain the population mean

30. 12 hours of stats in 90 minutes • Give yourself a pat on the back • Plan for retrieval practice • Plan for part 2 on October 17th • Philosophy of Research Methodology • Statistical Models • The Blob • Hypothesis Testing • Independent Samples t-Test • General Linear Model • Schedule a one-on-one appointment

31. Thank You. Jay Raadt, Genea Stewart, Lee Bedford, and Mehri Mizaeirafe coe-orc@unt.edu 940.565.4414