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Chapter 8 BOT3015L Data analysis and interpretation

Chapter 8 BOT3015L Data analysis and interpretation. Presentation created by Jean Burns 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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Chapter 8 BOT3015L Data analysis and interpretation

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  1. Chapter 8BOT3015LData analysis and interpretation Presentation created by Jean Burns 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 • 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 dependent variable. Effect.

  9. Independent and dependent variables Independent: Treatment (CO2 concentration) Dependent: Stomatal aperture Assumption: Changes in CO2 concentration will alter 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. t-test: a type of inferential statistic Used on continuous response variable, when you have discrete treatments (independent variables). Last week: Stomatal aperture response to lower CO2 concentration.

  20. What internal and external factors likely affect stomatal aperture? What are the effects of CO2 on stomatal aperture? Why do we want to know? How is this important? About 1700 gallons of water are required to grow food for one adult in the US per day! (From 1993 National Geographic)

  21. Experimental Design The question: What are the effects of CO2 on stomatal aperture? Ambient CO2 x lowered CO2 CO2 + NaOH => NaHCO3 (sodium bicarbonate)

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

  23. Hypothesis testing 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.

  24. We will use a t-test to interpret the gas exchange experiment http://www.steve.gb.com/science/statistics.html

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

  26. 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

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

  28. 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

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

  30. 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

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

  32. 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.

  33. 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

  34. 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).

  35. 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

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

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

  38. 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)

  39. 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)

  40. 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

  41. 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 Chart Button

  42. 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

  43. Now your chart should look like this:

  44. 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 • Add error bars to your chart: • Double click on the bar • Y-error bars (at the top) • Go to Custom • Select the cells with the standard deviation

  45. Now your chart should look like this:

  46. 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

  47. Double click Doing a t-test Double click • Import the data into JMP • Open JMP • Create two columns: Independent and dependent variables (double click on column heading area) • Create 50 rows (double click on row heading area) • Copy and paste data from JMP (select column heading and rows to paste into)

  48. Doing a t-test • Import the data into JMP • Open JMP • Create two columns: Independent and dependent variables • Copy and paste data from JMP • Make Treatment a nominal variable (double click on column heading, change data type to character) • Or, use dummy variable, shown here

  49. Doing a t-test • Import the data into JMP • Look at data distribution • Analysis • Distribution of Y • Add Stomatal aperture (ok)

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