1. DateGroup Project TaskDetails Feb 8, 9Article Analysis Due at start of class. See pgs. 139-141 Feb 15, 16In-class work day Discuss scientific writing, statistics, proposals Feb 22, 23Proposal Due at start of class Intro & methods for topic See pgs. 144-156 Mar 1, 2Start data collection Receive TA approval MarchCollect data, analyze data, write draft of paper See pgs. 157-161 for details on paper Mar 29, 30In-class work day Peer edit papers Apr 5, 6Final paper Due at start of class Apr 12, 13In-class work day Discuss presentations Apr 26, 27In-class presentations Present work to class See pgs. 164-166

2. Today we will –Perform & understand basic descriptive statistics –Understand ideas of inferential statistics (hypothesis testing) –Become familiar with three statistical tests: T-test, Chi-square, Regression –Select & perform appropriate statistical test for your group’s question –Communicate your findings in writing and in an oral presentation to your peers

3. What do they have in common?

4. Descriptive Statistics What are the characteristics of my data set? What does my sample suggest about the population? Center of data –mean, median, mode Spread of data –Variance, standard deviation, standard erro r Later we’ll discuss, Inferential Statistics - Using data to test hypotheses

5. Center of Data “central tendency”

6. Spread of Data small variance large variance

7. Spread of Data standard deviation From Wikipedia

8. Spread of Data standard deviation From Wikipedia

9. Standard Deviation vs. Standard Error Both estimate spread of data around mean Standard Deviation - Estimates variability of population around the mean Standard Error - Measures precision of sample mean standard error = standard deviation √sample size

10. Data Analysis For your group’s variables, calculate: 1) Sum 5) Standard Deviation 2) Mean 6) Standard Error 3) Median 7) Variance 4) Mode (use Data Analysis ToolPak) A)Record these measures on handout B) Write 1-2 sentences on - What do these measures tell you about your data? C) Plot data in excel, sketch on pg 88 For guidance, see p. 172-173 (stats); 191-193 (excel) (demo use of Data Analysis ToolPak)

11. Types of Data Count –Number of events –(only whole #s, no fractions) Ex: # galls with evidence of predation Continuous –Includes fractions/decimals Ex: Length of gallfly larvae Categorical –Data fall into groups Ex: Parasitoid/Predator/None (other exs: Male/Female, Juvenile/Adult, Red/Blue)

12. In ecology (as in science, in general), you need to use your data to test hypotheses. To test your hypotheses & to interpret your data you use inferential statistics

13. Three types of Tests Student’s t-test –Determine if means of two populations are considered different –For continuous data SuccessFailure Treatment 11535 Treatment 21485 Chi-Square –Determine if means of two populations are considered different –For count or frequency data Correlation/Regression –Indicates how closely two things are related to each other

14. Question: What affects rates of play in meerkats 1)Available energy 2)Size of individual 3)Sex of pups

15. Types of Data Count, Continuous or Categorical? Categorical Continuous Question 1: Does rate of play differ for provisioned & unprovisioned pups? Rate of play Provisioned vs. unprovisioned pups

16. Results Unprovisioned Provisioned (Control)(Treatment) Mean = 7.3Mean = 13.5 So these are different, Right?

17. Maybe, let’s look at the spread of the data

18. Consider Means & Variance Declaring two populations different depends on both: Means Variation For the same means, more variation = less likely means can be declared as different Use the t-test!

19. How do you calculate the t statistic?

20. Is the difference statistically significant? Calculate t-value from your datat calc Compare to “critical t-value”t critical T-value needed for significant differences If t calc > t critical, then your group means differ significantly When t calc > t critical, your p-value (significance value) is very small P-values ≤ 0.05 indicate significant differences

21. What is the p-value? The probability that the findings from study are due to chance. –For example, a p-value of.01 (p =.01) means there is a 1 in 100 chance the result occurred by chance. –The standard accepted value is 0.05 or less.

22. Provisioned pups play more TreatmentControl p < 0.05 *

23. Types of Data Count, Continuous or Categorical? Continuous Question 2: Does size of individuals affect rate of play? Rate of play Size of individuals

24. The Data Weight (kg)Rate (min/hr) 1.514.4 1.015.6 2.030.5 2.033.7 1.710.1 3.536.6

25. Larger pups play more r = 0.8 There is a positive relationship between rates of play and body weight

26. Correlation/Regression Correlations tell you if there is a relationship between 2 variables (but provide no information on causation) Correlation coefficient ranges between -1 and 1 Regression implies that one variable predicts the other

27. Correlation/Regression

28. Types of Data Count, Continuous or Categorical? Categorical Count Question 3: Does sex of individuals affect the number of play events? # of play events Sex of individuals

29. 3) Sex of the pup Study Description: Observe the frequency of play of male and female pups If sex does not determine play we would expect the probability to be 50%

30. Data SexObservedExpected Male1115 Female1915

31. Data Sex(Observed - Expected) 2 / Expected Degrees of Freedom Male(11-15) 2 /15= 1.07 1 Female(19-15) 2 /15= 1.07 Total2.14 Table pg. 189 For 1 df the critical value is 3.84 2.14< 3.84 so neither sex plays more than expected by chance

33. Data Analysis & Conclusions 1) Write your hypotheses (null & alternative) i.e., null: no difference A = B, alternative: A > B 2) Determine which test is best for testing your hypothesis t-test, Chi-square, correlation/regression 3) Perform test in Excel (see pgs. 191-193) 4) Record degrees of freedom (df) and appropriate stat output ( T-value, Chi-square value, P-value, R 2 ) 5) On pg 89, write -Statistical conclusion – Significant difference or not? How do you know? -Biological conclusion – What does the statistical conclusion mean for your hypothesis? Explain. -Reference graph in conclusion 6) Prepare a few PPT slides (<5) to explain findings to class

34. Announcements -Read Adaptation Lab (pgs. 29-40) -We’ll meet here & then go to greenhouse -Complete Article Analysis for group project -1 article per person -Different article than group members -1 article from primary literature (scientific journals) -I suggest you avoid journals Science and Nature