Statistics for IB Statistics for IB BiologyBiology

Syllabus Topic 1Syllabus Topic 1

1.1.1: Error Bars 1.1.1: Error Bars

• State that error bars are State that error bars are graphical representations of the graphical representations of the variability of datavariability of data– Graph Pad tutorialGraph Pad tutorial– Excel instructionsExcel instructions

                                                                                             

                                                                                             

Interpreting StatisticsInterpreting Statistics is as important as is as important as collecting the datacollecting the data

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1.1.2: Mean and Standard 1.1.2: Mean and Standard DeviationDeviation

• Calculate the mean and SD of a set Calculate the mean and SD of a set of valuesof values– Mean or Mean or μμ or x bar = or x bar = ∑∑ x x

n n – Standard Deviation or SStandard Deviation or S

– For this course we will use the sample For this course we will use the sample std. dev., NOT the population std. dev.std. dev., NOT the population std. dev.

1.1.3: Spread of Values1.1.3: Spread of Values

• The term standard deviation is The term standard deviation is used to summarize the spread of used to summarize the spread of values around the mean.values around the mean.

• Sixty-eight percent (68%)Sixty-eight percent (68%) of the of the values fall within one standard values fall within one standard deviation of the mean.deviation of the mean.– 11stst SD contains 34% of the data points SD contains 34% of the data points

on each side of mean (34+34=68)on each side of mean (34+34=68)– 22ndnd SD contains 13.5% of the data SD contains 13.5% of the data

points on each side of the meanpoints on each side of the mean– 33rdrd SD contains the remaining 2.5% of SD contains the remaining 2.5% of

the data of each side of the meanthe data of each side of the mean

Standard DeviationStandard DeviationSD=1SD=1

Graphs from: http://www.childrensmercy.org/stats/definitions/stdev.htm

SD=2SD=2

SD=3SD=3

1.1.4:Comparing Means 1.1.4:Comparing Means • Explain how the standard deviation is useful for Explain how the standard deviation is useful for

comparing the means and the spread of data comparing the means and the spread of data between two or more samplesbetween two or more samples

– What can you conclude when standard error bars do What can you conclude when standard error bars do overlap? overlap? No surprises here. When SE bars overlap, you can be No surprises here. When SE bars overlap, you can be sure the difference between the two means is not statistically sure the difference between the two means is not statistically significant .significant .

– What can you conclude when standard error bars do not What can you conclude when standard error bars do not overlap? overlap? When standard error (SE) bars do not overlap, you When standard error (SE) bars do not overlap, you cannot be sure that the difference between two means is cannot be sure that the difference between two means is statistically significant. T-test is commonly used to compare these statistically significant. T-test is commonly used to compare these groups.groups.

– What if you are comparing more than two groups? What if you are comparing more than two groups? If two SE If two SE error bars overlap, you can be sure that a post test comparing error bars overlap, you can be sure that a post test comparing those two groups will find no statistical significance. However if those two groups will find no statistical significance. However if two SE error bars do not overlap, you can't tell whether a post test two SE error bars do not overlap, you can't tell whether a post test will, or will not, find a statistically significant difference. ANOVA is will, or will not, find a statistically significant difference. ANOVA is commonly used for comparing multiple groups.commonly used for comparing multiple groups.

from - http://www.graphpad.com/articles/errorbars.htmfrom - http://www.graphpad.com/articles/errorbars.htm

Data Never Lies, it just Data Never Lies, it just needs the proper needs the proper

explanationexplanation

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1.1.5: T-tests1.1.5: T-tests

• Deduce the significance of the Deduce the significance of the difference between two sets of difference between two sets of data using calculated values for t data using calculated values for t and the appropriate tables.and the appropriate tables.– used for comparing two groups of used for comparing two groups of

data (ANOVA for 3 or more)data (ANOVA for 3 or more)– GraphPadGraphPad tutorial tutorial