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Statistical Analysis

Statistical Analysis. Topic – 1.1.1-1.1.6 Math skills requirements. Syllabus Statements. 1.1.1: State that error bars are graphical representations of the variability of data 1.1.2: calculate the mean and standard deviation of a set of values

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Statistical Analysis

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  1. Statistical Analysis Topic – 1.1.1-1.1.6 Math skills requirements

  2. Syllabus Statements • 1.1.1: State that error bars are graphical representations of the variability of data • 1.1.2: calculate the mean and standard deviation of a set of values • 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 • 1.1.4: Explain how the standard deviation is useful for comparing the means and the spread of the 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 appropriate tables • 1.1.6: Explain that the existence of a correlation does not establish a causal relationship between two variables.

  3. Error Bars • Bars on a graph only show means and can be misleading • Error bars show variability around the mean • Can be used to show range, standard deviation or standard error

  4. Means can look different

  5. But really not be

  6. In calculator Stat key Edit and enter your list(s) Stat key again Calc and 1-var stats then specify your list Which one is the mean? Which one is the standard deviation? Use the following data as an example 170, 160, 150, 175, 180, 175, 190, 165 Given a set of data can you calculate mean and stdev?

  7. The mean is 170.63 • The standard deviation is 12.37 (use the s value)

  8. So what is the Standard Deviation?

  9. Standard Deviation is just • A numerical measure of the spread of the data around the mean • The absolute number doesn’t mean a lot • Look at the number in relation to the mean • If you mean is 100 and your standard deviation is 1 then its tiny • If your mean is 1.5 and your standard deviation is 1 then that is pretty significant • Rule of thumb is if Sx/mean > .20 then its getting up there

  10. So by definition the Standard deviation marks off discrete intervals under a bell curve • In a normal distribution (bell curve) remember the 68, 95, 99.7 RULE • 68% of observations are within 1 stdev of the mean, 95% within 2 stdev, 99.7% within 3 stdev • Mean of 18 stdev of 4.5 => 68% = 13.5-22.5 • Now can compare mean and spread of 2 distributions small stdev = values tightly cluster around the mean (little variability) large stdev = values spread out around the mean (large variability)

  11. Using Standard Deviation to compare Variability around means

  12. Step 8: Does your data really show an effect? • Statistics give power to your results • Is your result just chance or is it caused by your Independent Variable (IV)? • Statistics uses probability to determine how likely it is that your results are just random • You should understand T-test, linear regression analysis

  13. Statistics: T-test • Compares the means of two populations which are normally distributed, with sample size of at least 10. • A way to tell if means of two groups are actually different from each other. (Or conversely looks at the amount of overlap between the two) • Accounts for the mean and variability of the data

  14. Two tailed unpaired T-test is expected • Not expected to calculate T • So while we usually say that if the p value is < .05 then there is a significant difference • They want you to go from a T table as follows

  15. t table with right tail probabilities To calculate the df you take the total number of samples and subtract 2 T value must exceed the value in a given cell to be that p value Think of those p values as percentages look at p = .05 column

  16. So back to our graphs • Is there an actual difference between the means? • Conduct T-test  if p < 0.05 then there is an actual • difference, otherwise its just a chance event

  17. So mean boys height was 71 • And mean girls height was 64 • And the T value was t = 0.082 • And the T critical value in the table for p=.05 was t=2.002using appropriate degrees of freedom • So our t was too small meaning that the means are NOT significantly different

  18. Statistics: Linear Regression • Is there a relationship between two variables that are measured in an experiment? • Works with scatterplots with a line of best fit e.g. Height and weight data, age and weight data • Does change in one variable predict change in another?

  19. Statistics: Linear Regression • Does change in Length predict a change in Weight? • Is there a positive or negative correlation (slope) • r = correlation coefficient – measures the strength of the linear association between 2 quantitative variables

  20. Correlation • df = number of points in scatterplot – 2 (x and y axis) • Calculate r with equation or program • Use table to determine the critical value for the number of points you are using • r must exceed that number for a significant relationship (correlation) to be present

  21. But remember • The existence of a correlation does not indicate causation • So if people with bigger hands have bigger feet that does not mean that a change in hand size causes a change in foot size • Rather they are both caused by something else…

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