TOPIC 1: STATISTICAL ANALYSIS

1.1.1 State that error bars are a graphical representation of the variability of data. Error bars can be used to show either the range of the data or the standard deviation.

1.1.2 Calculate the mean and standard deviation of a set of values. You don’t need to know how to calculate standard deviation by hand! On a TI-83 Calculator: Press [STAT] and select EDIT to enter your list of numbers. Remember the list you entered them in (watch the heading over your number on the calculator screen). Press [STAT] and select CALC, then select 1-Var Stats. Enter the name of the list you used. press [ENTER] to view the results. x with a bar on top= the mean S x = the standard deviation Test yourself: Try to get the mean and standard deviation of   37.75, 38, 37, 38.5, and 37.5. You should get a mean of 37.75 and a standard deviation of 0.559. On Excel: http://www.saburchill.com/IBbiology/ICT/dataprocessing/011.html

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. (in normally distributed data)

36 51 56 62 62 63 65 69 73 83 Mean = 62 Standard deviation = 12.5 Sample IB Question The data shows the number of flowers per flower head of a random sample from a white clover (Trifolium repens) population. 36 51 56 62 62 63 65 69 73 83 Mean = 62 Standard deviation = 12.5 What statistical percentage of the population has between 49 and 75 flowers per flower head? A. 5 % B. 32 % C. 68 % D. 95 % ANSWER= C

1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples. small standard deviation= the data is clustered closely around the mean value. (i.e. less variation within the sample) large standard deviation= a wider spread around the mean. (i.e. more variation within the sample) It is also used in the t-test (which determines if there is a statistically significant difference between samples).

Example IB Question The masses of two different populations of sparrows (Passer domesticus) are shown in the table below. Population 1: mass of birds/ g Population 2: mass of birds / g 24.5 26.9 25.0 23.2 24.0 23.6 31.0 27.9 24.8 28.3 (i) Calculate the mean value of the mass of birds for population 1. (ii) With reference to the data shown, explain what is meant by the term standard deviation. No calculation is expected.

Exit Questions Explain how and why error bars are used. Explain how to calculate the mean for a set of data. What is standard deviation and how is it useful?

1.1.5 Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables. The t-test can be used to compare two sets of data and measure the amount of overlap Null hypothesis: There is no significant difference between the two sets of data. If P  > 5% (.05) then the two sets are the same (i.e. accept the null hypothesis). If P  < 5% (.05) then the two sets are different (i.e. reject the null hypothesis). For the t-test to be applied: the data must have a normal distribution The dependent variable should be a continuous variable (not categorical) a sample size of at least 10. Practice on Excel: http://web.mac.com/mindorffd/Site/ttest_files/t-test%20on%20excel.pdf

How to use a table of critical t values Use two tailed P values Look at P= 0.05 Look at degrees of freedom (i.e. the total number of values in both populations – 2) If the calculated t value is greater than the t value on the table, the results are significantly different.

Practice IB question To test how temperature affects growth, some plants were grown at 20°C and another group at 30°C . After a number of weeks, the height of the plants was measured. Explain how the t-test could be used to test the significance of the effect of temperature on plant growth.

1.1.6 Explain that the existence of a correlation does not establish that there is a causal relationship between two variables. “Correlation does not necessarily imply causation!” Correlation= an apparent relationship between variables. Causal Relationship= a relationship between variables in which changes in one variable cause changes in the other variable. Some unusual examples that are supposedly true: Ice cream sales and the number of shark attacks on swimmers are correlated. Skirt lengths and stock prices are highly correlated (as stock prices go up, skirt lengths get shorter). The number of cavities in elementary school children and vocabulary size have a strong positive correlation.

Exit Questions Explain how and why a t-test is used. What are some conditions that must be met in order to use a t-test? Explain how correlation and causation differ, giving a clear example of each in your explanation.