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# Unit 1

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### Unit 1

1. 1. Statistical analysis<br />You are SOOO boring me, right now!<br />Yes, you are…(yawn)<br />
2. 2. Mean<br />Another word for the average<br />Calculated by summing the values and then dividing by the number of values obtained.<br />Symbol: x<br />
3. 3. Displaying the data<br />Error bars can be added to graphs to show the range of data.<br />This shows the highest and lowest values of the data.<br />41.6<br />
4. 4. Standard deviation<br />Measures the spread of data around the mean.<br />Formula: s = √(x - x )2 <br />BUT you do not need to remember it. <br />You must be able to calculate it on your calculators (or spreadsheet in the lab)<br />
5. 5. The standard deviation measures how spread out your values are. <br />If the standard deviation is small, the values are close together. <br />If the standard deviation is large, the values are spread out. <br />It is measured in the same units as the original data.<br />What does the standard deviation measure?<br />
6. 6. Calculate the mean of 100, 200, 300, 400, 500.<br />Now let's imagine you had the values 298, 299, 300, 301, 302. Calculate the mean of these numbers.<br />Although the two means are the same, the original data are very different.<br />Why is it useful?<br />
7. 7. The standard deviation of 100, 200, 300, 400, 500 is 141.4<br />The standard deviation of 298, 299, 300, 301, 302 is 1.414. <br />So the standard deviation of the first set of values is 100 times as big - these data are 100 times more spread out.<br />The standard deviation will reflect this difference. <br />
8. 8. Although the standard deviation tells you about how spread out the values are, it doesn't actually tell you about the size of them. <br />For example, the data 1,2,3,4,5 have the same standard deviation as the data 298,299, 300,301,302<br />Why do I need both the mean and standard deviation?<br />
9. 9. Displaying the data<br />Error bars can be added to graphs to show the standard deviation.<br />This shows the spread around the mean.<br />45.9<br />41.6<br />
10. 10. Comparing the two<br />45.9<br />41.6<br />41.6<br />
11. 11. Normally distributed data<br />
12. 12. ±1s (red), ±2s (green), ±3s (blue) <br />
13. 13. T-test<br />A common form of data analysis is to compare two sets of data to see if they are the same or different<br />Null hypothesis: there is NO significant difference between.......<br />
14. 14. T-test<br />Calculate a value for “t”<br />Compare value to a critical value (0.05 column)<br />If “t” is equal to or higher than the critical value we can reject the null hypothesis.<br />
15. 15. Correlation<br />
16. 16. Correlation<br />