1. Surface Statistics 1.How can you tell if data sets are “good”? SEM/SD 2.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 3.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 1Without TazacWith Tazac Trial 2Without TazacWith Tazac MouseTumor Size (mm 3 ) MouseTumor Size (mm 3 ) A3.002.00 A6.003.00 B10.006.00 B5.003.00 C9.005.00 C7.004.00 D2.00 D5.002.00 E6.001.00 E7.003.00 Average6.003.20 Average6.003.00 SD3.542.17 SD1.000.71 SEM1.580.97 SEM0.450.32 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. Trial 1Without TazacWith Tazac Trial 2Without TazacWith Tazac MouseTumor Size (mm 3 ) MouseTumor Size (mm 3 ) A3.002.00 A6.003.00 B10.006.00 B5.003.00 C9.005.00 C7.004.00 D2.00 D5.002.00 E6.001.00 E7.003.00 Average6.003.20 Average6.003.00 SD3.542.17 SD1.000.71 SEM1.580.97 SEM0.450.32 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 1.Normally, only the averages and SD or SEM are reported, not all of the data points. 2.Scientists use SD and SEM to determine levels of variance in a data set. 3.Guideline: It’s best if your SEM is less than 10% of your average Trial 1Without TazacWith Tazac Trial 2Without TazacWith Tazac Average6.003.20 Average6.003.00 SD3.542.17 SD1.000.71 SEM1.580.97 SEM0.450.32

7. Add SEM whiskers to graphs Trial 1Without TazacWith Tazac Trial 2Without TazacWith Tazac Average6.003.20 Average6.003.00 SD3.542.17 SD1.000.71 SEM1.580.97 SEM0.450.32

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. 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. Another way to compare two groups of data

13. Trial 1Without TazacWith Tazac Trial 2Without TazacWith Tazac Ave6.003.20 Ave6.003.00 SD3.542.17 SD1.000.71 SEM1.580.97 SEM0.450.32 T-TEST0.17 T-Test0.00059 p<0.01 Statistically significant difference p=0.17 No statistically significant difference

14. Analyze this data and state a conclusion Column1Without AuxinWith Auxin PlantHeight (mm) Average6.208.60 SD1.301.14 SEM0.580.51 T-Test0.01 p<0.01 What was the… IV? DV? Control Group? Experimental Group? 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.

15. Correlation ≠ Causation # of dogs and # of hospitals Dog population Number of hospitals 2002 4004 6005 8006 10008 9006 7005 5005 4001 3001 2001 1001 1 2001 3002 4003 5004

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? Shoe size Reading ability 44 55 67 45 54 65 44 54 66 78 89 99 78 87 97 21 32 44 21 32 44 R = 0.93

18. Are the variables of an adult’s shoe size correlated to reading ability? Shoe Size Reading Ability 59 610 79 8 99 119 1211 13 1415 11 1615 7 8 9 10 1113 1214 1312 1413 514 68 712 811 910 R = 0.35