unit 1
DESCRIPTION
TRANSCRIPT
Statistical analysisYou are SOOO boring
me, right now!Yes, you are…(yawn)
Mean
• Another word for the average
• Calculated by summing the values and then dividing by the number of values obtained.
• Symbol: x
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
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)
• 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?
• 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?
• 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.
• 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?
Displaying the data
• Error bars can be added to graphs to show the standard deviation.
• This shows the spread around the mean. 41.6
45.9
Comparing the two
41.6 41.6
45.9
Normally distributed data
±1s (red), ±2s (green), ±3s (blue)
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.......
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.
Correlation
Correlation