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BOT3015L Data analysis and interpretation

Learn about types of data, statistics, creating graphs in excel, and conducting t-tests for gas exchange experiment results. Understand the significance of discrete and continuous data and their interpretation in experimental research.

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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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