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Surface Statistics

Surface Statistics . How can you tell if data sets are “good”? SEM/SD How can you tell if data from a control and an experimental groups are different from one another? SEM whiskers/p-values from t-tests How can you tell if two variables are correlated? R-values .

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Surface Statistics

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  1. Surface Statistics How can you tell if data sets are “good”? SEM/SD How can you tell if data from a control and an experimental groups are different from one another? SEM whiskers/p-values from t-tests How can you tell if two variables are correlated? R-values

  2. Does Tazac reduce tumor size in mice? • Controlled study: Attempts to determine causality • IV: • DV: • Control Group: • Experimental Group: • Hypothesis: The mice that receive Tazac will have smaller tumors than the mice that don’t receive Tazac.

  3. How good is the data? • Standard Deviation (SD) • Standard Error of the Mean (SEM)

  4. Compare the averages of Trial 1 and Trial 2.Compare the individual values that contributed to the averages in Trial 1 and Trial 2.Which set of data, Trial 1 or Trial 2, shows the most consistency/reliability? Trial 1 data points have more variation in range: 3-10 and 1-6 Trial 2 data points are more consistent and reliable: 5-7 and 2-4 The data range in Trial 2 is “tighter.”

  5. A way to communicate the “tightness” of the data points is through the STANDARD DEVIATION (SD) and/or the STANDARD ERROR OF THE MEAN (SEM). The SD and SEM describe the VARIANCE in the samples. How do the SD and SEM of Trial 1 and Trial 2 differ? And, which Trial has more variance in their samples?

  6. How to use SD and SEM • Normally, only the averages and SD or SEM are reported, not all of the data points. • Scientists use SD and SEM to determine levels of variance in a data set. • Guideline: It’s best if your SEM is less than 10% of your average

  7. Add SEM whiskers to graphs

  8. How to compare two groups of data • Eye-ball it with SEM whiskers on graphs

  9. Summary:Tightness of data points – SD and SEM • Standard deviation (SD) and standard error of the mean (SEM) • Both give an indication of the range of data values • Both given an indication of the variance in the data points • It’s best if data points in a set are consistent • Values are closer together • The tighter the data, the more reliable the data • SD or SEM indicates “tightness” of the data points

  10. Does Tazac reduce tumor size in mice? • Controlled study: Attempts to determine causality • IV: Tazac • DV: Tumor size • Control Group: Mice without Tazac • Experimental Group: Mice with Tazac • Hypothesis: The mice that receive Tazac will have smaller tumors than the mice that don’t receive Tazac.

  11. How to compare two groups of data • Eye-ball it with SEM whiskers on graphs • If the whiskers overall, there is probably not a statistically significant difference between the groups:

  12. Another way to compare two groups of data • T-Tests compare two sets of data and give an indication as to whether or not the values of the two sets of data are significantly different from one another. • T-Tests report their findings as p-values. • A p-value of less than 0.1 (or 0.05 or 0.001) means that there is a high chance (90, 95, 99%, respectively) that there is a real difference between two groups of data.

  13. p=0.17 No statistically significant difference p<0.01 Statistically significant difference

  14. Analyze this data and state a conclusion Guiding questions How do the average compare? How would you describe the data variance? Is there a statistically significant difference between these two groups? State two ways you know this. What was the… IV? DV? Control Group? Experimental Group? p<0.01

  15. Correlation ≠ Causation# of dogs and # of hospitals

  16. Is there a correlation? • Correlation is measured by R values. • If R = 1 or R = -1, then it’s a perfect correlation • If R = 0, then there is no correlation between the two variables.

  17. Are the variables of a child’s shoe size and their reading ability correlated? R = 0.93

  18. Are the variables of an adult’s shoe size correlated to reading ability? R = 0.35

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