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04 statistics presentation_notes

Statistics is the application of mathematical principles to the collection, analysis, and presentation of numerical data. Statisticians contribute to scientific inquiry by applying their knowledge to the design of surveys and experiments, collection and analysis of data, and interpretation of results. Key parts of statistics include mean, standard deviation, error bars, significant difference tests using t-tests, and understanding the difference between correlation and causation. The standard deviation is used to summarize the spread of variables around the mean and can be used to compare data sets.

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What is statistics? From the American Statistical Association Statistics is the scientific application of mathematical principles to the collection , analysis , and presentation of numerical data . Statisticians contribute to scientific inquiry by applying their mathematical and statistical knowledge to the design of surveys and experiments; the collection, processing, and analysis of data; and the interpretation of the results.
Why do I need to know statistics? Short answer: To complete your internal assessments correctly (lab component of your IB score—24%)
Why do I need to know statistics? Life answers: To be able to effectively conduct research To make decisions based upon collected, numerical data To be able to read journals, to make meaning of results of studies, to understand sports! To develop critical and analytic thinking skills To be an informed consumer and not be mislead by erroneous reports of statistical results
What parts of statistics do I need to know? Mean Standard deviation Error bars Significant difference with a t-test Correlation and causation
Mean The most commonly used measure of central tendency is the mean, or arithmetic average (sum of data points divided by the number of points) 
How to calculate mean on a TI-83 Push the STAT button Choose EDIT Input your data in the LISTS Each level of independent variable is a separate list with at least 5 trials for each
How to calculate mean on a TI-83 Choose CALC Choose 1-VAR Stats This will provide for you the following information on ONE of your LISTS (levels of independent variable) Mean Sum of the data points Square of the sum of the data points Sample SD (this is the one you want) Population SD Number of data points (better be at least 5) Minimum value First quartile value Median Third quartile value Maximum value
How to calculate mean in Excel Input your data into the cells Highlight all of the cells of the data you want the SD for Click the Σ drop down option Select average The average will appear below your highlighted text
Standard Deviation Standard deviation is used to summarize the spread of variables around the mean . 68% of the values of a normal distribution fall within one standard deviation of the mean (+/- 1) 95% of the values fall within 2SD 99%-100% of the values fall within 3SD
Standard Deviation Standard Deviation (SD) can be used to compare populations or sets of data . The closer the mean and the SD, the more likely the populations studied are the same or similar. A small SD indicates that the data is clustered closely around the mean value . When completing your statistics you want to aim for a small SD A large SD indicates a wider spread around the mean . This may mean that your collection techniques were flawed Smaller samples create variation due to the random factors, small samples are unreliable. Because of this, you will always aim for a 5x5 experiment 5 levels of independent variable, 5 trials (or more) of each
How to compute SD on a TI-83 THIS SHOULD HAVE BEEN COMPLETED PREVIOUSLY FOR MEAN Push the STAT button Choose EDIT Input your data in the LISTS Each level of independent variable is a separate list with at least 5 trials for each
How to compute SD on a TI-83 Choose CALC Choose 1-VAR Stats This will provide for you the following information on ONE of your LISTS (levels of independent variable) Mean Sum of the data points Square of the sum of the data points Sample SD (this is the one you want) Population SD Number of data points (better be at least 5) Minimum value First quartile value Median Third quartile value Maximum value
How to compute SD on Excel Input your data into the cells Highlight all of the cells of the data you want the SD for Click the Σ drop down option Select More functions… Choose STDEV The SD will appear as formula result in a box
Error Bars The simplest way to draw an error bar is to use the mean as the central point, and to use the distance of the measurement that is furthest from the average as the endpoints of the data bar Can also use standard deviation divided by the square root of the sample size to compute standard error and use that to make error bars You want to have a LOW standard error
Drawing Error Bars Average value Value farthest from average Calculated distance
Using error bars to explain data… If the bars show extensive overlap, it is likely that there is not a significant difference between those values
Significant Difference (t-tests) t -test compares the averages and standard deviations of two samples to see if there is a significant difference between them Find the critical value of t for the relevant number of degrees of freedom Degrees of freedom = (n 1 + n 2 ) – 2 If the calculated value is below the critical value there is no sig. diff. between the two sets of data t < critical value = no sig. diff. If the calculated value is above the critical value there is a sig. diff. between the two sets of data t > critical value = sig. diff.
Using a TI-83 to compute Sig. Diff. THIS SHOULD HAVE BEEN COMPLETED PREVIOUSLY FOR MEAN AND SD Push the STAT button Choose EDIT Input your data in the LISTS Each level of independent variable is a separate list with at least 5 trials for each
Using a TI-83 to compute Sig. Diff. Push STAT Arrow over to TESTS Typically you are going to be comparing your sets of data against each other for significant difference Arrow down to 4:2-SampTTest Choose Data, press ENTER Choose the Lists you wish to compare—do not POOL your data Choose Calculate and hit ENTER T value will be listed (use absolute value) Compare to listed critical value
How to compute Sig. Diff. on Excel Input your data into the cells Highlight all of the cells of the data you want the SD for Click the Σ drop down option Select More functions… Select the category Statistical Choose TTEST Array 1 = A1:A5 (the first cell:the last cell of the data) Array 2 = B1:B5 Tails = 2 Type = 1 Formula Result will provide the answer
Correlation and Causation An action can correlate with another (such as smoking is correlated with alcoholism) A relation existing between statistical variables which tend to vary, be associated, or occur together in a way not expected on the basis of chance alone An action or occurrence can cause another (such as smoking causes lung cancer) The act or agency which produces an effect
Correlation and Causation Typically, one can only establish correlation unless the effects are extremely notable and there is no reasonable explanation that challenges causality . Without clear reasons to accept causality, we should only accept correlation.