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# Statistical analysis

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### Statistical analysis

1. 1. Statistical Analysis<br />
2. 2. Why do we need stats?<br /><ul><li>To understand results of an experiment
3. 3. Make effective conclusions
4. 4. To be informed consumers</li></li></ul><li>What does this graph show us?<br />This graph shows that people over 80 are the safest group of drivers. Drivers under 20 are safer than those between 20 and 24. Right?<br />
5. 5. The problem with that assumption is that number of accidents does not account for how much driving each of the groups do. Consider this other graph.<br /><ul><li> Mile for mile, people over 80 have the most accidents followed by those under 20. This graph suggests that up until age 44, a person’s driving improves. After that, there is a decline in safety per mile driven. Over 74, there is a huge jump in accidents per mile driven.
6. 6. Neither graph prove that age is what causes the incident of accidents. </li></li></ul><li>STANDARD DEVIATION<br /><ul><li> There is almost always variation in biological data
7. 7. This variation can be shown using a frequency distribution graph
8. 8. The mean value is in the middle of the distribution
9. 9. Mean- the average of the values (the sum of the values divided by the number of values </li></li></ul><li>Normal Distribution<br />Standard Deviation- The computed measure of how much the values vary around the mean score (above and below)<br /><ul><li> 68% of the data is within 1 SD from the mean
10. 10. 95% of the data is within 2 SD from the mean
11. 11. 99% of the data is within 3 SD from the mean</li></li></ul><li>Starter Questions<br />Which Sx represents a set of data that is very similar to the mean?<br />A. 4.5 B. 23.6 C. 0.6 D. 19.6<br />What percentage of data falls within +/-1Sx of the mean?<br />If the mean of a set of data is 55, and the SX=6 what is the value of data? +/- 1Sx +/-2Sx +/-3Sx<br />Draw a normal distribution graph. Include a mean, and the percentage of data that fall with in +/-1 Sx +/-2 Sx +/-3 Sx<br />
12. 12. <ul><li>A low standard deviation indicates that the data points tend to be very close to the mean, whereas
13. 13. A high standard deviation indicates that the data are spread out over a large range of values.</li></li></ul><li>A set of length measurements are taken with a mean of 2.5 cm and the standard deviation of 0.5cm. Which of the following is true?<br />68% of all data lie between 2.5cm and 3.5cm<br />2. 68% of all data lie between 1.5cm and 3.5cm<br />3. 95% of all data lie between 1.5cm and 3.5cm<br />4. 95% of all data lie between 2.0cm and 3.0cm<br />95% of all data lie between 1.5cm and 3.5cm<br /><ul><li>1 SD=0.5cm
14. 14. 68% of data is +/- 1SD, so 68% are between 2.0cm and 3.0cm
15. 15. 95% of data are within +/- 2SD, so 95% are between 1.5cm and 3.0cm</li></li></ul><li>Error Bars<br />2 Types of Error Bars<br /> Range of Data<br /> Standard Deviation <br />
16. 16. Starter<br />In a population of men the systolic blood pressure shows a normal distribution. The mean of the population is 125 (measured in mm and Hg) and the standard deviation is 10. If the population was 1000, how many of them have a blood pressure between 115 and 135mm Hg?<br />680 men have blood pressure between 115 and 135mm Hg.<br />If the mean is 125, and the standard deviation is 10, then +1 Sx is 135, and -1 Sx is 115, and we know that 68% of your data (in this case the men) are +/-1 Sx from the mean.<br />
17. 17. Using Excel<br /><ul><li>Create your data
18. 18. Find the mean of your data
19. 19. Calculate the Standard Deviation (Sx) of your data </li></li></ul><li><ul><li>Graph your mean
20. 20. Insert Graph (Scatter)
21. 21. Then go to layout</li></li></ul><li>In layout choose the Error Bars Tab<br />
22. 22. Choose the More Error bars Options<br />Select Custom<br />For Standard Deviation Error Bars select your Sx for both Positive and Negative Values<br />For Max/Min Error Bars select your max and your min. <br /><ul><li>Take the difference from your mean, and input that as your value</li></ul>Now Label Your Graph!<br />
23. 23. Means<br />A = 10<br />B = 20<br />
24. 24. Means<br />A = 10<br />B = 20<br />Is there a significant difference between the means?<br />
25. 25. Means<br />A = 10<br />B = 20<br />Is there a significant difference between the means?<br />
26. 26. Means<br />A = 10<br />B = 20<br />Is there a significant difference between the means?<br />Would knowing the standard deviations help?<br />What if both had “large” standard deviations?<br />
27. 27. Means<br />A = 10<br />B = 20<br />Is there a significant difference between the means?<br />Would knowing the standard deviations help?<br />What if both had “small” <br />standard deviations?<br />
28. 28. Means<br />A = 10<br />B = 20<br />Is there a significant difference between the means?<br />Would knowing the population size help?<br />What if one had a large population size and the other a small size? What if both were large or both small?<br />
29. 29. The t-test takes from both samples:<br />the means, <br />the standard deviations and <br />the population size <br />into account and will give you a t-value which you can use with a t-test table to determine if there is a statistically significant difference between the means. DO NOT learn the formula. The t-value will be given to you.<br />
30. 30. <ul><li>0.05 column is our Critical value
31. 31. α significance level
32. 32. Calculated Value of t > critical value it has is <0.05 which means there is a significant difference
33. 33. Calculated Value of t < critical value it has is >0.05 which means there is NO significant difference</li></li></ul><li>Calculate Degrees of Freedom<br />N= Population N1 + N2 -2 <br />NO<br />YES<br />
34. 34. H0 Null Hypothesis states that there is no significant difference between the two groups<br />Never want to assume there is a difference<br />The null hypothesis typically corresponds to a general or default position. For example, the null hypothesis might be that there is no relationship between two measured phenomena or that a potential treatment has no effect.<br />