1. Descriptive Statistics Used to describe a data set –Mean, minimum, maximum Usually include information on data variability (error) –Standard deviation –Variance –95% Confidence interval

2. = x-x Frog Weight  Error Measurement Mean

3. MEAN ± CONFIDENCE INTERVAL When a population is sampled, a mean value is determined and serves as the point-estimate for that population. However, we cannot expect our estimate to be the exact mean value for the population. Instead of relying on a single point-estimate, we estimate a range of values, centered around the point-estimate, that probably includes the true population mean. That range of values is called the confidence interval.

4. Confidence Interval Confidence Interval: consists of two numbers (high and low) computed from a sample that identifies the range for an interval estimate of a parameter. y ± (t  /0.05 )[(  ) / (  n)] 28.17 ± 2.29 24.89    30.46 Affects the width of the confidence interval Variance Go to Excel

5. Variance =  (x-x) 2 N-1  i= x N N Mean = x = Standard Deviation =  (x-x) 2 N-1  Go to Excel Mean = 169/6 = 28.17 Min = 25 Max = 32 Sum MSE = 40.83 Variance = 40.83 / 5 = 8.16 Std. Dev. =  40.83/5 = 2.86

6. Frequency Distribution Most Common Least Common Go to Excel Gambusia Data

7. Hypothesis Testing –Null versus Alternative Hypothesis Simple: –Null: Two means are not different –Alternative: Two means are not similar A test statistic based on a predetermined probability (usually 0.05) is used to reject or accept the null hypothesis  < 0.05 then there is a significant difference  > 0.05 then there is NO significant difference

8. Single Sample t-test Boudreaux tells everyone that his bass pond has bass that average 8 pounds His neighbor, Alphonse, doesn’t believe him. Who is right?

9. Single Sample t-test Used to compare the mean of a sample to a known number Assumes that subjects are randomly drawn from a population and the distribution of the mean being tested is normal Basically, does the confidence interval include the number of interest?

10. Simple as Creating a Confidence Interval N = 10 Range = 3.3 – 8.9 Mean = 5.79 Var(  )= 2.599 t  /0.05 = 1.82 y ± (t  /0.05 )[(  ) / (  n)] 5.79 ± (1.82)(2.599)/(3.16)= 5.79 ± 1.497 = 4.29  5.79  7.29 8 is not included in the range- Boudreaux is wrong!

11. Are Two Populations The Same? Boudreaux: ‘My pond is better than yours, cher’! Alphonse: ‘Mais non! I’ve got much bigger fish in my pond’! How can the truth be determined?

12. Two Sample t-test Simple comparison of a specific attribute between two populations If the attributes between the two populations are equal, then the difference between the two should be zero This is the underlying principle of a t-test Resulting p-value = 0.956, so the populations are not significantly different

13. When to use a paired t-test: If repetitive measurements are taken on the same individual unit (pond, tree, fish, batch, cohort, etc.). The second sample is the same as the first after some treatment has been applied

14. Paired t-test Cedar Apple Rust: Rusty leaves on apple trees. Is there a year to year difference? Depends on which test you use! Go to Excel