Unit 1

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