More statistics notes!

Syllabus notes! (The number corresponds to the actual IB numbered syllabus.) Put the number down from the syllabus and then paraphrase the information into your own words…

1.1.1 State that error bars are a graphicalrepresentation of the variability ofdata.1.1.2 Be able to calculate the mean and standarddeviation of a set of values. 1.1.3 State that the term standard deviation is used to summarize the spread of values around the mean, and that 68% of the values fall within one standard deviation of the mean.

Review1.1.4: Explain how the standard deviation is

useful for comparing the means and the spread of data between two or more samples.

Today’s lesson:

1.1.5: Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables.

1.1.5 T test notes:

T tests are used to compare means of 2 sets of data.

• Big difference? You have a big T score!

• Little difference between the two means? You have a little t score.

• You do not have to calculate the t test. You need to look at a table and determine whether a t score is significant. *Note example that is coming*

Terms to know in t-test

• P = probability… this is the probability that something occurs on its own randomly.– We care about the data when P = .05 or less

• Occurs on its own 5% of the time.• 95% sure that our treatment matter.

• Ho = Null hypothesis… this is the hypothesis that both groups are the SAME. Or that the treatment doesn’t matter.

Example:• Lets say that you tested two groups of runners.

One group ran with running shoes, the other ran barefoot.

• You calculated the mean, and performed the t-test… you found that the t-test number given was 2.7

• You had 10 runners in each group… so your degree of freedom =10+10 -2 =18…

• If the number is big, the results are valid… YOU REJECT THE NULL HYPOTHESIS

Rest of topic 11.1.6 Explain that the existence of a correlation

does not establish that there is a causal relationship between two variables.

Correlation often shows a casual relationship between two variables such as height and weight.

• If you do a scatter plot with a line of best fit, you have a correlation if the slope is 1 or -1.

• Taller people tend to be heavier and so we can see a correlation in these two sets of data.

• However, some variables may show correlation when in fact there is no casual relationship between them. The results may be correlated by chance. This means that even the correlation is a useful tool for studying data, it is not always reliable.

• Like: murder and ice cream consumption increase in August…doesn’t mean ice cream causes murder!)

• 1.1.7 Be able to calculate the percentage increase or decrease.

• Example (from the 08 test): Calculate the percentage increase in the occurrence of diabetes in women who were classified as very obese (2.8%) compared to those classified as overweight (0.6%)

• Find amount of change (2.2) • divide difference by original (2.2 / 0.6)• Multiply answer (3.6) by 100 to convert to a

percent 360% increase

You can use this website to calculate a t test:

http://www.graphpad.com/quickcalcs/ttest1.cfm