Chapter 8 BOT3015L Data analysis and interpretationTodayPowerPoint PresentationTypes of dataSlide 5Slide 6Slide 7Slide 8Independent and dependent variablesSlide 10Types of statisticsSlide 12Mean: a type of descriptive statisticSlide 14Slide 15Standard deviation: a type of descriptive statistic.Slide 17Slide 18t-test: a type of inferential statisticSlide 20Experimental DesignHypothesis testingSlide 23We will use a t-test to interpret the gas exchange experimentSlide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Degrees of freedomSlide 33Factors influencing a difference between meansSlide 35Creating graphs in excelSlide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Now your chart should look like this:Slide 47Doing a t-testSlide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Chapter 8BOT3015LData analysis and interpretationPresentation created by Jean BurnsAll photos from Raven et al. Biology of Plants except when otherwise notedToday•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 experimentToday•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 experimentTypes of data1. Discrete: Having categories (i.e. flowers present/flowers absent, large/medium/small)Seed heteromorphism: a discrete character.Not hetermorphicHetermorphicTypes of data1. Discrete: Having categories (i.e. flowers present/flowers absent, large/medium/small)2. Continuous: Having infinite possible values (i.e. age, growth rate)Seed size: a continuous characterCommelina benghalensis seed size variationTypes of data1. Independent: Manipulated or selected with the hypothesis that it is causally linked to the dependent variable. Cause.2. Dependent: Measured as a response to the dependent variable. Effect.Independent and dependent variablesIndependent: Treatment (CO2 concentration)Dependent: Stomatal apertureAssumption: Changes in CO2 concentration will alter stomatal aperture.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 experimentTypes of statistics1. Descriptive: Summarize a set of data.2. Inferential: Draw conclusions from a data set.Types of statistics1. Descriptive: Summarize a set of data.2. Inferential: Draw conclusions from a data set.Mean: a type of descriptive statisticArithmetic meanhttp://www.steve.gb.com/science/statistics.htmlMean: a type of descriptive statisticMeasure of the central tendency of a data set.FrequencyValueMean = 2.9Standard deviation: a type of descriptive statisticStandard deviationhttp://www.steve.gb.com/science/statistics.htmlStandard deviation: a type of descriptive statistic.Measure of spread of variability in a data set.FrequencyValueStandard deviation = 0.25Standard deviation: a type of descriptive statistic.Measure of spread of variability in a data set.FrequencyValueStandard deviation = 0.58 Standard deviation = 0.41ValueTypes of statistics1. Descriptive: Summarize a set of data.2. Inferential: Draw conclusions from a data set.t-test: a type of inferential statisticUsed on continuous response variable, when you have discrete treatments (independent variables).Last week: Stomatal aperture response to lower CO2 concentration.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)Experimental DesignThe question: What are the effects of CO2 on stomatal aperture? Ambient CO2 x lowered CO2 CO2 + NaOH => NaHCO3 (sodium bicarbonate)Hypothesis testingHo: Both treatments yield the same stomatal aperture.HA1: NaOH treatment results in narrower stomatal aperture.HA2: NaOH treatment results in larger stomatal aperture.Hypothesis testingHo: Both treatments yield the same stomatal aperture.HA1: Water treatment results in larger stomatal aperture.HA2: NaOH treatment results in larger 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.We will use a t-test to interpret the gas exchange experimenthttp://www.steve.gb.com/science/statistics.htmlQuestion: is there a difference in the means between two treatments?Large overlap = not different.http://www.steve.gb.com/science/statistics.htmlQuestion: is there a difference in the means between two treatments?Large overlap = not different.http://www.steve.gb.com/science/statistics.htmlsmalllarget < ~2Question: is there a difference in the means between two treatments?Large overlap = not different.http://www.steve.gb.com/science/statistics.htmlQuestion: is there a difference in the means between two treatments?Little overlap = different.http://www.steve.gb.com/science/statistics.htmllargerlarget > ~2Question: is there a difference in the means between two treatments?Little overlap = different.http://www.steve.gb.com/science/statistics.htmlQuestion: is there a difference in the means between two treatments?Little overlap = different.http://www.steve.gb.com/science/statistics.htmllargesmallt > ~2What if the answer is not so obvious?This is why we need statistics.Degrees of freedom•DF = n1 + n2 - 2DF = 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 is a measure of a test’s power. Larger sample sizes (and DF) result in more power to detect differences between the means.t-value distributionhttp://www.psychstat.missouristate.edu/introbook/sbk25m.htmt-valuefrequency1. 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.Factors influencing a difference between means•Distance between means•Variance in each sample (Standard Deviation, SD)•T-value (means and SD)•Number of samples