Timeline 2013 2009 2010 2011 2012 T-Test 0 + - = 9 8 7 1 2 3 4 5 6 c Definitions Mean: an average of data points

Range: measure of the spread of data; difference between largest and smallest values

Standard Deviation: measure of how individual observations of a data set are dispersed or spread about the mean Correlation does not mean Causation Correlations suggest relationships between sets of data Error Bars Error bars are a graphic representation of variability in the data. Measurements and uncertainty Uncertainty: margin of error in a measurement When to use t-test T-test is used to determine whether or not difference between two sets of data is a significant difference. T-test compares two sets of data. Why is this useful? It tells you how many extremes are in the data.

A lot of extremes = large standard deviation

Few extremes= small standard deviation IB Objectives 1.1.1 State that error bars are a graphical representation of the variability of data.

1.1.2 Calculate the mean and standard deviation of a set of values. Students may use a scientific calculator, and are not required to know the formula.

1.1.3 State that the term standard deviation is used to summarize the spread of values around the mean.

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

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

1.1.6 Explain that the existence of a correlation does not establish that there is a causal relationship between two variables. Statistics Error bars can represent range, standard error, or standard deviation. Standard Deviation Formula: standard deviation shows how much variation or "dispersion" exists from the average (mean) Standard Error Formula Standard error represents how well the sample mean approximates the population mean where:

s= standard deviation

n= number of values For a digital measuring device: these cherries weigh For analogue measurements: Graph of Normal Distribution -dotted area represents one standard deviation from the mean in both directions

-the green crossed area represents two standard deviations from the mean 10, 11, 12, 9, 8, 7 Practice Problem! p=0.50 difference due to chance is 50%

this is not a statistically significant difference

p=0.05 difference due to change is only 5%

this is a statistically significant difference When given a calculated t-value, you can use a table of t-values.

For this you will need to know how to calculate degrees of freedom. df=sum of sample sizes of each of the two groups - 2 However correlation does not mean causation, observations without an experiment can only show a correlation. Experiments provide a test which shows cause.

In order for experiments do so, there must be independent, dependent, and carefully controlled variables. Criteria for t -test :

- Approximately normal distribution

-Sample size of at least 10

-Null Hypothesis (Ho): There is not a significant difference in the mean of two sets of data.

The t -test can be used to compare two sets of data and measure the amount of overlap.(two-tailed, unpaired t test). If the value of t is greater than the critical t value at .05, then there is a significant difference between the two sets of data, and the null hypothesis should be rejected

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# AP/IB Biology Review: Statistics

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