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Applied Statistical Analysis

Learn statistical terms like central tendency, variability, descriptive statistics, and inferential statistics. Explore sample vs. population, hypothesis testing, scales of measurement, reliability, validity, and correlation vs. experimentation. Practice computing mean, median, mode, range, and standard deviation. Enhance clarity in data interpretation.

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Applied Statistical Analysis

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  1. Applied Statistical Analysis EDUC 6050 Week 3 Finding clarity using data

  2. Today Review Statistical Terminology Central Tendency Variability

  3. Reading Questions from Chapter 1

  4. Reading Quick, Quiet, Qualifying Quiz

  5. Reading What is the difference between a sample and a population? What are descriptive statistics? True or False. Inferential statistics help us use our sample to understand the population. True or False. Independent Variables are also known as outcomes. Hypothesis tests inform us about the ___________ of our findings.

  6. Reading • True or False. Hypothesis testing informs us about the population. • What is the difference between qualitative and quantitative? • Is a nominal variable more qualitative or quantitative? • What information does a bar chart provide? What about a histogram? • How satisfied are you with your answers?

  7. Review: Vocabulary of Statistics Population Sample

  8. Review: Vocabulary of Statistics Descriptive Statistics Describing the data that you have (your sample) Inferential Statistics Understanding what your data say about the population

  9. Review: Vocabulary of Statistics Independent Variables Dependent Variables “outcomes” or “DV” These are the variables that we think are caused by an independent variable “predictors” or “IV” These are the variables that we think are causing or influencing the outcome

  10. Review: Vocabulary of Statistics Hypothesis Testing (Inferential Statistics) “Null Hypothesis Significance Testing” Gives us an idea about what the population may look like based on our sample (accounts for sampling error) = “significance”

  11. Review: Vocabulary of Statistics Hypothesis Testing (Inferential Statistics) “Null Hypothesis Significance Testing” Effect Sizes “Magnitude of the effect” Tells us how big the effect is = “meaningfulness”

  12. Review: Scales of Measurement 4 General Types (see pg. 11)

  13. Review: Scales of Measurement 4 General Types (see pg. 11) Increasing degree of information

  14. Review: Scales of Measurement These lie on a spectrum from qualitative to quantitative NominalOrdinalIntervalRatio QualitativeQuantitative

  15. Review: Plots

  16. Break Time

  17. Reliability and Validity Reliability: the consistency of the measure Validity: does it measure what we think it measures?

  18. Reliability and Validity Reliability: the consistency of the measure Validity: does it measure what we think it measures? Not Reliable Not Valid Reliable Not Valid Not Reliable Valid Reliable Valid

  19. Reliability and Validity Reliability Compare with factor analyses (not covered in the class) Validity Compare with correlations with things that should correlate or shouldn’t Often based on theory

  20. Correlation and Experimentation Correlation observational, no treatment/intervention Experimentation treatment/intervention (best if groups are randomized) What are the pro’s and con’s of each?

  21. Correlation and Experimentation Depends on the field how often each are used Possible, but difficult, to convince of causation with correlational (observational) data Correlation does not imply causation AND Correlation does not imply it isn’t causal

  22. Central Tendency What does this mean? Mean Median Mode “arithmetic average” Sum of scores divided by number of scores “the middle score” The number where half of the scores are above and half are below “most common score” The most common score

  23. Central Tendency Outliers = points far from the other points

  24. Central Tendency See Figure 2.2 (page 42)

  25. Computing the Mean Sum of scores Number of scores

  26. Computing the Median Order the values from lowest to highest Find the middle value If two are in the middle, take the average of those two

  27. Computing the Mode Find the value that is the most common

  28. Mean, Median, and Mode for Age? Mean, Median, and Mode for Degree?

  29. Mean, Median, and Mode for Age? Mean = 213/8 = 26.6 Median = 21 21 22 25 28 29 33 34 = 26.5 Mode = 21 Mean, Median, and Mode for Degree? Mean = ... Median = ... Mode = MS

  30. The distribution of jump heights Median Mode Mean What about the spread of the data?

  31. The distribution of jump heights This is what variability is all about Median Mode Mean What about the spread of the data?

  32. Variability “spread”

  33. Variability

  34. Computing Range Two approaches: Max – Min “[Min] to [Max]”

  35. Computing Standard Deviation Essentially it is the deviation from the mean (X – M)

  36. Other Stuff about Standard Deviation There is a population standard deviation denoted but is usually unknown Our SD is an estimate of the population standard deviation

  37. Variability What is the range of Age? What is the range of Grade?

  38. Variability What is the range of Age? Range = 34 – 21 = 13 = 21 to 34 What is the range of Grade? Range = A to C

  39. Review The figure to the right is reliable/unreliable and valid/invalid. When should you use the mean? What about the median? What does the standard deviation tell us? Can we obtain a standard deviation with nominal data?

  40. Another look at Jamovi Plots Central Tendency Variability

  41. Questions?

  42. Next week: Statistics terminology continued (hypothesis testing, descriptive and inferential statistics, effect sizes, confidence intervals, Type I and II errors) Chapters 4, 5, and 6 in Book Statistical Organizer due

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