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# Unit 1

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Statistics
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### Transcript

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