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BOT3015L Data analysis and interpretation

BOT3015L Data analysis and interpretation. Presentation created by Jean Burns and Sarah Tso All photos from Raven et al. Biology of Plants except when otherwise noted. Today. Types of data Discrete, Continuous Independent, dependent Types of statistics Descriptive, Inferential

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BOT3015L Data analysis and interpretation

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  1. BOT3015LData analysis and interpretation Presentation created by Jean Burns and Sarah Tso All photos from Raven et al.Biology of Plants except when otherwise noted

  2. Today • Types of data • Discrete,Continuous • Independent, dependent • Types of statistics • Descriptive, Inferential • Creating graphs in excel • Doing a t-test or Chi Square • Lab: create graphs and do statistics for the gas exchange experiment

  3. Today • Types of data • Discrete, Continuous • Independent, dependent • Types of statistics • Descriptive, Inferential • Creating graphs in excel • Doing a t-test • Lab: create graphs and do statistics for the gas exchange experiment

  4. Types of data 1. Discrete: Having categories (i.e. flowers present/flowers absent, large/medium/small)

  5. Seed heteromorphism: a discrete character. Hetermorphic Not hetermorphic

  6. Types of data 1. Discrete: Having categories (i.e. flowers present/flowers absent, large/medium/small) 2. Continuous: Having infinite possible values (i.e. age, growth rate)

  7. Seed size: a continuous character Commelina benghalensis seed size variation

  8. Types of data • Independent: Manipulated or selected with the hypothesis that it is causally linked to the dependent variable. Cause. • Dependent: Measured as a response to the independent variable. Effect.

  9. Independent and dependent variables Independent: Treatment (CO2 concentration) Dependent: Number of open and closed stomata, or stomatal aperture Assumption: Changes in CO2 concentration will affect stomatal aperture.

  10. Today • Types of data • Discrete, Continuous • Independent, dependent • Types of statistics • Descriptive, Inferential • Creating graphs in excel • Doing a t-test • Lab: create graphs and do statistics for the gas exchange experiment

  11. Types of statistics 1. Descriptive: Summarize a set of data. 2. Inferential: Draw conclusions from a data set.

  12. Types of statistics 1. Descriptive: Summarize a set of data. 2. Inferential: Draw conclusions from a data set.

  13. Mean: a type of descriptive statistic Arithmetic mean http://www.steve.gb.com/science/statistics.html

  14. Mean: a type of descriptive statistic Mean = 2.9 Measure of the central tendency of a data set. Frequency Value

  15. Standard deviation: a type of descriptive statistic Standard deviation http://www.steve.gb.com/science/statistics.html

  16. Standard deviation: a type of descriptive statistic. Measure of spread of variability in a data set. Standard deviation = 0.25 Frequency Value

  17. Standard deviation: a type of descriptive statistic. Measure of spread of variability in a data set. Standard deviation = 0.58 Standard deviation = 0.41 Frequency Value Value

  18. Types of statistics 1. Descriptive: Summarize a set of data. 2. Inferential: Draw conclusions from a data set.

  19. Pearson’s 2: a type of inferential statistic Used on discrete response variable, when you have discrete treatments (independent variables). Example: The number of open and closed stomata in response to lower CO2 concentration.

  20. t-test: a type of inferential statistic Used on continuous response variable, when you have discrete treatments (independent variables). Example: Stomatal aperture response to lower CO2 concentration.

  21. Regression: a type of inferential statistic Used on continuous response variable, when you have continuous treatments (independent variables). Example: Stomatal aperture response to varied CO2 concentration (when the CO2 concentration is actually measured). *Talk to your TA if you want to know how to do this

  22. Observation: both internal and external factors affect stomatal aperture Question: What is the effect of CO2 concentration on stomatal aperture or the number of open and closed stomata?

  23. Experimental Design Question: What is the effect of reducing CO2 concentration on the number of open stomata? Treatment: Reduce CO2 concentration using sodium hydroxide: CO2 + NaOH => NaHCO3 (sodium bicarbonate) Control: Ambient atmospheric CO2 concentration Data: Count the number of open and closed stomata (are these data discrete or continuous?)

  24. Hypothesis testing for discrete data Pearson’s Chi Square (2): a test of association between to categorical variables. Ho: Both treatments yield an equal number of open and closed stomata. HA1: NaOH treatment results in fewer open stomata than the control. HA2: NaOH treatment results in more open stomata than the control.

  25. Step 1: Make a contingency table This is a 2 x 2 contingency table, having two columns and two rows, but it can have other dimensions.

  26. Step 2: Make a contingency table Add the row and column totals and the grand total, N.

  27. Step 3: Calculate expected values based on null hypothesis Ho: Both treatments yield an equal number of open and closed stomata. For each cell, the expected value is: Row total x column total/ N.

  28. Step 4: Calculate the 2 and degrees of freedom 2 =  {(observed - expected)2/ expected} d.f. = (# of columns - 1) x (# of rows - 1) 2 = (5 - 10)2/ 10 + (15 - 10)2/10 + (15 - 10)2/10 + (5 - 10)2/ 10 = 10 d.f. = (2 - 1) x (2 - 1) = 1

  29. Step 4: Compare calculated 2 with the critical value from a Chi Square distribution table The critical value can be obtained from a table based on the degrees of freedom and the level of confidence, which is set at P = 0.05. 2 calc = 10 2 crit = 3.84, d.f. = 1 If the calculated value exceeds the critical value, you can reject your Ho

  30. Hypothesis testing for continuous data Ho: Both treatments yield the same stomatal aperture. HA1: NaOH treatment results in narrower stomatal aperture. HA2: NaOH treatment results in larger stomatal aperture.

  31. Hypothesis testing for continuous data Ho: Both treatments yield the same stomatal aperture. A t-test will distinguish between Ho and HA, then you must look at the direction of the difference to interpret the results. HA1: Water treatment results in larger stomatal aperture. HA2: NaOH treatment results in larger stomatal aperture.

  32. We will use a t-test for this example: http://www.steve.gb.com/science/statistics.html

  33. Question: is there a difference in the means between two treatments? Large overlap = not different. http://www.steve.gb.com/science/statistics.html

  34. Question: is there a difference in the means between two treatments? small t < ~2 large Large overlap = not different. http://www.steve.gb.com/science/statistics.html

  35. Question: is there a difference in the means between two treatments? Large overlap = not different. http://www.steve.gb.com/science/statistics.html

  36. Question: is there a difference in the means between two treatments? larger t > ~2 large Little overlap = different. http://www.steve.gb.com/science/statistics.html

  37. Question: is there a difference in the means between two treatments? Little overlap = different. http://www.steve.gb.com/science/statistics.html

  38. Question: is there a difference in the means between two treatments? large t > ~2 small Little overlap = different. http://www.steve.gb.com/science/statistics.html

  39. What if the answer is not so obvious? This is why we need statistics.

  40. Degrees of freedom DF = number of independent categories in a statistical test. For example, in a t-test, we are estimating 2 parameters the mean and the variance. Thus we subtract 2 from the degrees of freedom, because 2 elements are no longer independent. • DF = n1 + n2 - 2 DF is a measure of a test’s power. Larger sample sizes (and DF) result in more power to detect differences between the means.

  41. t-value distribution frequency t-value 1. Get tcrit from a table of t-values, for P = 0.05 and the correct DF. 2. If tobserved > tcrit, then the test is significant. 3. If P < 0.05, the means are different. http://www.psychstat.missouristate.edu/introbook/sbk25m.htm

  42. Factors influencing a difference between means • Distance between means • Variance in each sample (Standard Deviation, SD) • T-value (means and SD) • Number of samples (DF) • Level of error we are willing to accept to consider two means different (P-value).

  43. Today • Types of data • Discrete, Continuous • Independent, dependent • Types of statistics • Descriptive, Inferential • Creating graphs in excel • Doing a t-test • Lab: create graphs and do statistics for the gas exchange experiment

  44. Creating graphs in excel • Open excel (Start/Applications/Microsoft Excel) • Enter the data in table format

  45. Creating graphs in excel • Open excel (Start/Applications/Microsoft Excel) • Enter the data in table format • In the cells directly under treatment data:

  46. Creating graphs in excel • Open excel (Start/Applications/Microsoft Excel) • Enter the data in table format • Calculate the mean and standard deviation • Mean: enter formula • =average(cells to calculate the mean from) • Example: • =AVERAGE(A2:A11)

  47. Creating graphs in excel • Open excel (Start/Applications/Microsoft Excel) • Enter the data in table format • Calculate the mean and standard deviation • Standard deviation: enter formula • =stdev(cells to calculate the mean from) • Example: • =STDEV(A2:A11)

  48. Creating graphs in excel • Open excel (Start/Applications/Microsoft Excel) • Enter the data in table format • Calculate the mean and standard deviation • Select the data you wish to graph Select these cells

  49. Creating graphs in excel • Open excel (Start/Applications/Microsoft Excel) • Enter the data in table format • Calculate the mean and standard deviation • Select the data you wish to graph • Click the chart button or “Insert” “Chart…” Chart Button

  50. Creating graphs in excel • Open excel (Start/Applications/Microsoft Excel) • Enter the data in table format • Calculate the mean and standard deviation • Select the data you wish to graph • Click the chart button • Chose your chart options: • Column (next) • Series/Category x-axis labels/highlight treatment labels (next) • Titles/label axes including Units (next) • Finish

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