1. + Quantitative Analysis: Supporting Concepts EDTEC 690 – Methods of Inquiry Minjuan Wang (based on previous slides)

2. + Agenda Quick review of data Why analysis is necessary – beyond descriptive statistics The Culture data posted on BB Descriptive analysis vs. inferential analysis Review Key Concepts of Descriptive Statistics Inferential analysis concepts Types of tests – parametric and non-parametric What test should I use when? Next steps for your studies We will help you with inferential analysis using SPSS or other 2

3. + Our Special Guests: Types of Analysis Descriptive statistics Correlation Measuring a relationship between studied variables Inferential statistics Inferences from a studied sample to a population Parametric analyses Nonparametric analyses 3

4. + What is measurement? Measurement: process of assigning numbers, according to rules defined by the researcher. The numbers are assigned to events or objects, such as responses to items, or to certain observed behaviors Correspondence between event/objective/behavior and number is defined by the researcher 4

5. + Types of Measurement ScalesMeasurement Scales Nominal Categorization, no implied order (e.g., sex, eye color) Ordinal Involves order of the scores/ratings on some basis (e.g., attitude toward the government) Interval Unit interval is the same across the scale, doesn’t necessarily begin at zero (e.g., time, test score) Ratio Equal unit with a true zero point (e.g., the government expenditures; birth weight in pounds) 5

6. + Let’s Practice! GRE test Celcius temperature scale Kelvin temperature scale Football jerseys IQ tests Grade Point Average Economic status as High, Middle, or Low Number of siblings 6

7. + Descriptive Statistics

8. + Descriptive statistics A mathematical summary of the data is required Paints a picture of your data Provides the necessary background and foundation for interpretation But descriptive data falls short A frequency count, constructing histograms or a graph – they’re not enough in most research reports 8

9. + Descriptive statistics Describing a distribution of scores To provide information about its location, dispersion, and shape Mean, median mode Standard deviation Normal distribution (i.e., bell shape or skewed) 9

10. + Shapes of distribution (single variable) Distributions with like central tendency (means) but different variability Distributions with like variability but different central tendency (means) 10

11. 11 Frequency distribution--Normal Curve (Figure 12.2, p. 445) Many statistics assume the normal, bell- shaped curve distribution for scores.  50% > mean; 50% < mean  Normal curve for population (height, weight, IQ scores)  Mean=median=mode  Mean + 1SD/34.13% of the score  Mean – 1SD/34.13% of the score  Mean +/- 3SD = more than 99% of the score

12. 12 Skewed Distribution Non-symmetrical distribution  Mean, median, mode not the same Negatively skewed (Figure 12.3, p. 447)  extreme scores at the lower end  Mean < median <mode  most did well, a few poorly Positively skewed  at the higher end  Mean >median >mode  Most did poorly, a few well  Colorado Mountain: Ski to the right->skew to the right The further apart the mean and median, the more the distribution is skewed.

13. 13 Describing-Variability Standard Deviation [or dispersion] (average distance from the mean)  1 sd includes 34% above and below mean  2 sd includes 47.5% above and below mean  3 sd includes 49.9 % above and below mean  SD chart by Kathleen Barlo SD chart  URL: http://edweb.sdsu.edu/eet/Articles/standarddev/index.h tm

14. 14 Using SD in Prescribing Cereal As a practicing nutritionist, Dr. Green frequently came across patient questions like "what is the cereal that are within my diet in terms of calories and fat grams?"  Dr. Greenly uses descriptive statistics to give advise.  Launch Cereal data  Draw frequency histogram  Fruit loop calories: SD=+2 Give it to someone who is trying to lose 10 lbs?

15. 15 Predicting Height: Normal Distribution 3.5”68.0” Both Sections 3.6”68.0”Tuesday* 3.56”67.9”Monday SDMean Height From this sample of 30 adults, the average height of is 68.0 inches or 5 feet 10 inches tall and that 99% of all adults fall in between the height of ??? And ???

16. 16 Measure of relative standing Z-score  One type of standard scores  Compares scores from different tests  Convert scores to z scores, average them->final index of average performance  Z= Raw Score (X)-Mean/SD  Z score of mean = 0 Percentiles  The percentage of scores that fall at or below a given score Outliers  Example GRE

17. + Correlation (relationship between two variables) The correlation coefficient is a measure of the relationship between two variables. It can vary from -1.00 to +1.00. Zero indicates no relationship. 17

18. 18 Describing-Relationships How variables are related--need at least 2 variables Spearman rho  coefficient correlates data that are ranked Pearson r  correlates data that are interval or ratio How does foot size correlate to GRE scores?  Scores go from +1 to -1 More in “Correlational Research”

19. 19 Mini-Data Activity (After Spring break) Salary Data Culture Data When you are not heavily cognitively overloaded…..