1+Stats-objectives

= Unit 1: Statistical Analysis =

**1.1.0 Use significant figures for all calculations [this is an implied requirement]**

 * See your handbook, __Student Guide to Internal Assessment__, p. 41 onward.

**1.1.1 State that error bars are a graphical representation of the variability of the data.**

 * Note that error bars __can represent range of data -or- the standard deviation (s)__ [see Click4Biology on "Why use one or the other?"]
 * Keep in mind you will need a reasonably large sample of measurement to get an sd. Ashby (in Student Guide for Internal Assessment IBO, 2005) suggests that minimum sample size is 7, but ideally 15 or more. So if you don't have a lot of repetition or samples for one independent variable then you should probably choose error bars to represent the range of your data rather than bother with sd
 * If you choose error bars to represent range of data, __make sure they include the range of your data AND experimental error__//.// [ex. if your data range is 3 mL - 7 mL but your experimental error is ±1 mL, then the error bars should be at 2mL and 8mL.]

**1.1.2 Calculate the mean and standard deviation (s) of a set of values.**
Detailed description of what standard deviation is in IB context in detail on [|Click4Biology's statistics page]. For a clear example of the equation and how to use it, see [|Simple example of calculating standard deviation]. For procedures specific to calculators and spreadsheets on how to calculate s, see below (listed in order of importance!)

__Method 1__ (Ti-84)
 * 1) This can be done on your Ti-84 calculator. **You should learn this** because it is an objective __and__ you may be asked to perform this calculation during a test __and__ you will __only__ have your calculator.
 * [|Determine standard deviation using Ti-84]

__Method 2__ (Excel - useful when doing data processing)
 * 1) This can be done on Excel (or Google Docs). You should learn this because it is an objective and you may be asked to perform this calculation during a test and you will __only__ have your calculator.
 * [|using Excel to determine standard deviation]

__Method 3__ (useful with small set of numbers - and when you are stuck without electronics!)
 * The following is from 
 * 1) Find the normal mean: (∑n) / n
 * 2) Find the differences of each number from the mean: (x-n)
 * 3) Square these differences and add them together: ∑ [(x-n)²]
 * 4) Finally, divide by the number of terms. .../n
 * Ex. find the standard deviation of 2,3,5,6.
 * 4 is the mean
 * 4-2 = 2^2 = 4
 * 4-3 = 1^2 = 1
 * 4-5 = (-1)^2 = 1
 * 4-6 = (-2)^2 = 4
 * 4+1+1+4 = 10
 * 10/4 = 5/2
 * 5/2 is the standard deviation (s).

**1.1.3 State that the term "standard deviation" is used to summarize the spread of values around the mean and that 69% of values fall within 1 sd.**

 * Describe difference between sd of a sample (s) and sd of a population (∂)

**1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples.**

 * REFLECTION-in the testing on this unit, students could state "SD is measure of variablitity" but the could not use it in the test. The question asked students to explain how SD could be used to compare two populations and students COMPLETELY MISSED the fact that SD shows (1) the quality of measurement (ie small SD means consistent data and possibly higher precision-ie. more certainty about the value of the mean) or not, depending on the value of SD and (2) students also missed the point that in comparing two means they are probably the same if their 1 SDs overlap and probably different if even at 2 SD they do NOT overlap; again this depends also on how spread out the data was at each mean.

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

 * In answering this question, students did not notice that "comparing two groups" refers to comparing two mean values. Their answers were too ambiguous.

**1.1.6 Explain that the existence of a correlation does not establish that there is a causal relationship between two variables.**
Perhaps one of the first things to do before going further is to go to [|Click4Biology]'s Statistical Analysis page and scan over the information there. [We will refer and use a number of off-wiki resources which have been well developed by other DP Biology teachers so book mark these sites in your own browser as we come to them.]