Statistically Significant Relationships
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Presented this slide deck to digital analytics professionals at Columbus Web Analytics' monthly networking event. Discussed how to interpret correlation values.
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Statistically Significant Relationships
- 1. Dr. Michael A. Levin SSR : 1Columbus WAW May 2016 Statistically Significant Relationship sDr. Michael A. Levin Columbus WAW mlevin@Otterbein.e du @MichaelALevin
- 2. Dr. Michael A. Levin SSR : 2Columbus WAW May 2016 Background Confidence level Type I & II Correlation Regression Confidence interval Next step
- 3. Dr. Michael A. Levin SSR : 3Columbus WAW May 2016 Background
- 4. Dr. Michael A. Levin SSR : 4Columbus WAW May 2016 Confidence Level
- 5. Dr. Michael A. Levin SSR : 5Columbus WAW May 2016 Confidence Level
- 6. Dr. Michael A. Levin SSR : 6Columbus WAW May 2016 Type I & II Error
- 7. Dr. Michael A. Levin SSR : 7Columbus WAW May 2016 Correlation
- 8. Dr. Michael A. Levin SSR : 8Columbus WAW May 2016 Correlation - 1.0 1.00
- 9. Dr. Michael A. Levin SSR : 9Columbus WAW May 2016 Correlation - 1.0 1.00 -.2 .2
- 10. Dr. Michael A. Levin SSR : 10Columbus WAW May 2016 Correlation - 1.0 1.00 - .21 .21-.4 .4
- 11. Dr. Michael A. Levin SSR : 11Columbus WAW May 2016 Correlation - 1.0 1.00 - .41 .41-.6 .6
- 12. Dr. Michael A. Levin SSR : 12Columbus WAW May 2016 Correlation - 1.0 1.00 - .61 .61-.8 .8
- 13. Dr. Michael A. Levin SSR : 13Columbus WAW May 2016 Correlation - 1.0 1.00 - .81 .81
- 14. Dr. Michael A. Levin SSR : 14Columbus WAW May 2016 Regression π¦ = π0 + π1 π₯ π΄πππ’ππ‘ π ππππ‘ = π0 + π1 πππ§π ππ πππ’πππ π1 = π π π¦ π π₯
- 15. Dr. Michael A. Levin SSR : 15Columbus WAW May 2016 Confidence Interval
- 16. Dr. Michael A. Levin SSR : 16Columbus WAW May 2016 Confidence Intervalalpha 1- alpha Interpretation .05 .95 95 times out of 100, get a value plus or minus the beta coefficient or predicted value. .10 .90 90 times out of 100, get a value plus or minus the beta coefficient or predicted value. .15 .85 85 times out of 100, get a value plus or minus the beta coefficient or predicted
- 17. Dr. Michael A. Levin SSR : 17Columbus WAW May 2016 Next Step BOOKS Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith Statistics in Plain in English by Timothy Urdan Statistics (Dictionary) by Roger Porkess
- 18. Dr. Michael A. Levin SSR : 18Columbus WAW May 2016 Next Step Excel Websites Chandoo.org Excelcharts.com Excel-easy.com Statistics Websites analyticsdemystified.com/blo g/ danielsoper.com socialresearchmethods.net statsoft.com statwiki.kolobkreations.com
- 19. Dr. Michael A. Levin SSR : 19Columbus WAW May 2016 Next Step Youtube Gaskination How2stats Kahn Academy Twitter analysis_factor DIYmr simplystats
- 20. Dr. Michael A. Levin SSR : 20Columbus WAW May 2016 Next Step WORKSHOP Inferential Statistics on Excel Otterbein University July 15, 9 a.m. β 3 p.m. www.opeg.org
- 21. Dr. Michael A. Levin SSR : 21Columbus WAW May 2016 Statistically Significant Relationship sDr. Michael A. Levin Columbus WAW mlevin@Otterbein.e du @MichaelALevin
Editor's Notes
- Be sure or confident about the type of relationship that you want to describe.
- Be sure or confident about the type of relationship that you want to describe.
- In correlation, we are interested in the strength of the relationship as denoted by r. That is, the formula that drives the correlation value determines r, or the strength the relationship. We can interpret the r value, or correlation because we want to be thorough.
- Correlation ranges from -1 to 1. 0 means perfectly no relationship. -1 and 1 mean perfect relationships. Rare if ever will you see those values in nature.
- Any two items will correlate between -.2 and .2. Mehl calls it the crud factor.
- Ranges between .21 and .4, and -.21 and -.4, we can interpret as weak. The relationship exist but it is not the important.
- Ranges between .41 and .6, and -.41 and -.6, we can interpret as moderate. The relationship exist but it is worth paying attention to.
- Ranges between .61 and .8, and -.61 and -.8, we can interpret as strong. The relationship exist and it is powerful.
- Values above -.8 or .8 are problematic because it is a sign of autocorrelation or measuring the same thing twice.
- Regression is about prediction. It is the analytical tool that allows us to make such a determination. Mathematically, we are interested in the beta coefficient associated with independent variable. The slope of the line as shown by beta one tells how much of a change in X will predict a change in Y. If I increase the coupon size from 50 cents off to 51 cents off, how much more will a consumer spend? What drives the slope is the r or the correlation value. Hence, a strong correlation predicts a bigger change in Y than a weak correlation. If the r is not statistically significant than the IV or x variable will not be a statistically significant predictor of DV or the y variable.
- These values expressed as plus and minus the value letβs us know if 0 is in the internval because 0 indicates no relationship or r equal 0. That is, we were on a break.