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

2. You need to be able to Make a data table Make a graph – the correct type –Scatterplot or bar graph with error bars Find a Mean and Standard Deviation Do a statistical test – T-test or Linear Regression

3. I know this is a science class but… The math is still very important

4. Step 1: Construct a Data Table Title Units Significant Figures Uncertainties MAKE IT CLEAR AND USEFUL TO THE READER So What’s wrong with this table? Height (inches) FrequencyPercent 7600 7511.25 7411.25 7333.75 72810 711215 701620 692227.5 68911.25 6756.25 6622.5 6500 6411.25 6300 Total80100

5. Step 2: Make a Picture Choose the correct graph for your data Bar graph, histogram, line graph, pie chart, scatterplot, box plot Label axes, units, titles, legend, choose appropriate scale If graphing means you must include error bars

6. Excel Demo

7. Suggestions for Choice of graphs Histogram – continuous data Bar graph – comparing discrete data, comparing means (use error bars) Line graph – change over time Scatterplot – showing the relationship between two measured variables Pie chart – working with percents Box plot – displays measure of central tendency and spread

9. Step 5: Descriptive statistics: They summarize your data in a few numbers Center Arithmetic Mean = sum of all observations divided by the number of observations Variability (Spread) Standard Deviation (s) = Spread of data around the mean (How different are the values from the mean?)

10. Step 6: Descriptive Statistics Measures of Dispersion Central tendencies don’t tell the whole story. Take a look at these data sets 507560100 507570100 757575100 100758075 10075900

11. Standard Deviation Graphic

12. Step 7: Now use the Descriptive statistics to make your point 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 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)

13. A good quick check is S x / X bar > 0.20 means there is variability Variability is not inherently bad You need to decide if your variability is a result of the randomness of nature or indicates some problem (lack of reliability) in your data

14. Using Standard Deviation - Variability

15. So your Bar graphs now need 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

16. Means can look different

17. But really not be

18. Step 8: SO 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 be proficient with T-test, linear regression analysis,

19. Statistics: T-test or Linear Regression T-test If you want to see if there is there a difference between two groups. Are oceanic dolphins larger than lagoon dolphins? Are melting rates faster in the northern hemisphere than in the southern hemisphere? Linear Regression If you want to see if there is a relationship between two measured variables Is there a relationship between CO2 and Temperature? Is there a relationship between fish size and prey eaten?

20. Types of T-tests Tails – Based on your initial hypothesis –1 tailed test – one mean is greater or one mean is less –2 tailed tests – the means are different Paired – measuring the same individuals before and after – removes independence from the data

21. Statistics: T-test e.g. 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 In your labs, report df, T, p, 1 or 2 tail and significance

22. Statistics: Linear Regression Does change in Length predict a change in Weight? Is there a positive or negative correlation (slope) Strong or Weak? r = correlation coefficient – measures the strength of the linear association between 2 quantitative variables r=1 means a perfectly straight line In your labs report df, equation, calculated r value, critical r value from table

23. 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