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

Chapter 8BOT3015L

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

•Creating graphs in excel

•Doing a t-test

•Lab: create graphs and do statistics for the gas exchange experiment

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

Types of data

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

Seed heteromorphism: a discrete character.

Not hetermorphicHetermorphic

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)

Seed size: a continuous character

Commelina benghalensis seed size variation

Types of data

1. 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 variables

Independent: Treatment (CO2 concentration)

Dependent: Stomatal aperture

Assumption: 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 experiment

Types of statistics

1. Descriptive: Summarize a set of data.

2. Inferential: Draw conclusions from a data set.

Types of statistics

1. Descriptive: Summarize a set of data.

2. Inferential: Draw conclusions from a data set.

Mean: a type of descriptive statistic

Arithmetic mean

http://www.steve.gb.com/science/statistics.html

Mean: a type of descriptive statisticMeasure of the central tendency of a data set.

Fre

quen

cy

Value

Mean = 2.9

Standard deviation: a type of descriptive statistic

Standard deviation

http://www.steve.gb.com/science/statistics.html

Standard deviation: a type of descriptive statistic.

Measure of spread of variability in a data set.

Fre

quen

cy

Value

Standard deviation = 0.25

Standard deviation: a type of descriptive statistic.

Measure of spread of variability in a data set.

Fre

quen

cy

Value

Standard deviation = 0.58 Standard deviation = 0.41

Value

Types of statistics

1. Descriptive: Summarize a set of data.

2. Inferential: Draw conclusions from a data set.

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.

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 Design

The question: What are the effects of CO2 on stomatal aperture?

Ambient CO2 x lowered CO2

CO2 + NaOH => NaHCO3 (sodium bicarbonate)

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.

Hypothesis testing

Ho: 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 experiment

http://www.steve.gb.com/science/statistics.html

Question: is there a difference in the means between two treatments?

Large overlap = not different.http://www.steve.gb.com/science/statistics.html

Question: is there a difference in the means between two treatments?

Large overlap = not different.http://www.steve.gb.com/science/statistics.html

small

larget < ~2

Question: is there a difference in the means between two treatments?

Large overlap = not different.http://www.steve.gb.com/science/statistics.html

Question: is there a difference in the means between two treatments?

Little overlap = different.http://www.steve.gb.com/science/statistics.html

larger

larget > ~2

Question: is there a difference in the means between two treatments?

Little overlap = different.http://www.steve.gb.com/science/statistics.html

Question: is there a difference in the means between two treatments?

Little overlap = different.http://www.steve.gb.com/science/statistics.html

large

smallt > ~2

What if the answer is not so obvious?

This is why we need statistics.

Degrees of freedom

• DF = n1 + n2 - 2

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 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 distribution

http://www.psychstat.missouristate.edu/introbook/sbk25m.htm

t-value

freq

uenc

y

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.

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).

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

Creating graphs in excel1. Open excel (Start/Applications/Microsoft Excel)2. Enter the data in table format

Creating graphs in excel1. Open excel (Start/Applications/Microsoft Excel)2. Enter the data in table format3. In the cells directly under treatment data:

Creating graphs in excel1. Open excel (Start/Applications/Microsoft Excel)2. Enter the data in table format3. Calculate the mean and standard deviation

Mean: enter formula

=average(cells to calculate the mean from)

Example:

=AVERAGE(A2:A11)

Creating graphs in excel1. Open excel (Start/Applications/Microsoft Excel)2. Enter the data in table format3. Calculate the mean and standard deviation

Standard deviation: enter formula

=stdev(cells to calculate the mean from)

Example:

=STDEV(A2:A11)

Creating graphs in excel1. Open excel (Start/Applications/Microsoft Excel)2. Enter the data in table format3. Calculate the mean and standard deviation4. Select the data you wish to graph

Select these cells

Creating graphs in excel1. Open excel (Start/Applications/Microsoft Excel)2. Enter the data in table format3. Calculate the mean and standard deviation4. Select the data you wish to graph5. Click the chart button Chart Button

Creating graphs in excel1. Open excel (Start/Applications/Microsoft Excel)2. Enter the data in table format3. Calculate the mean and standard deviation4. Select the data you wish to graph5. Click the chart button6. Chose your chart options:

• Column (next)• Series/Category x-axis labels/highlight

treatment labels (next)• Titles/label axes including Units (next)• Finish

Now your chart should look like this:

Creating graphs in excel1. Open excel (Start/Applications/Microsoft Excel)2. Enter the data in table format3. Calculate the mean and standard deviation4. Select the data you wish to graph5. Click the chart button6. Chose your chart options7. 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

Now your chart should look like this:

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

Doing a t-test

1. 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)

Double click Double click

Doing a t-test1. 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

Doing a t-test1. Import the data into JMP2. Look at data distribution

• Analysis• Distribution of Y• Add Stomatal aperture (ok)

Doing a t-test1. Import the data into JMP2. Look at data distribution3. Is the distribution skewed?

Yes, data is skewed:

Doing a t-test1. Import the data into JMP2. Look at data distribution3. Is the distribution skewed?4. Transform the data

• Create a new column• Double click on the heading of the column• Add a formula• Select OK• Formula: ln(stomatal aperture)• Evaluate• Close dialog box

Doing a t-test1. Import the data into JMP2. Look at data distribution3. Is the distribution skewed?4. Transform the data5. Do the t-test on transformed data:

• Analysis• Fit Y by X• Select and add• Treatment = X• Aperture = Y• OK

Doing a t-test1. Import the data into JMP2. Look at data distribution3. Is the distribution skewed?4. Transform the data5. Do the t-test on transformed data:

• Analysis• Click arrow

Doing a t-test1. Import the data into JMP2. Look at data distribution3. Is the distribution skewed?4. Transform the data5. To the t-test on transformed data:

• Analysis• Click arrow• Select Means, ANOVA, t-test

Interpret the results of your t-test

1. T-test• T-value, larger values

indicate stronger effect

Interpret the results of your t-test

1. T-test• T-value, larger values

indicate stronger effect2. DF

• Degrees of freedom

Interpret the results of your t-test

1. T-test• T-value, larger values

indicate stronger effect2. DF

• Degrees of freedom3. Prob > t

• P-value, smaller values indicate stronger effect

• P < 0.05, significant difference between means.

Reminders

1. Submit Guard cell report next week: refer to “organization of a short report” (pages 9-10 of your lab manual.)• Titles must be descriptive• Methods must be complete• Results should include descriptions (in your own

words) not just graphs and tables (although those are also necessary).

• Discussion must demonstrate thought