Statistical Analysis

1
Statistical Analysis
2
Intro to Statistics

• What are Statistics?
• A tool for analyzing and making inferences from a
  dataset
• Shorthand way of comparing scientific data
• A way to make conclusions based on quantitative
  information

3
Collecting Data

• Sample a set of observations drawn from a
  larger set, the population, about which
  information is desired
• Example Avg. height of male and female students
  at MSU
• Measure height of males and females in BIO 122
• Make inferences about the general population
  based on student population

4
Sample Size

• Degree of variation successive observations
  made within a sample from the same population are
  likely to vary from one another we will measure
  this to determine how much variation is in our
  sample.
• Degree of error How well does the sample
  represent the actual population? Degree of error
  will decrease with an increase in sample size.

5
Types of Variables

• Variables the properties being examined, an
  item that can take on different values
• Qualitative discrete, example dead or alive
• Quantitative continuous, example height
• Is the measurement Qualitative or Quantitative?
• - Coin toss Heads or tails
• - Body weight numerical value

6

• Two characteristics to be estimated
• 1. Mean average value
• 2. Variance amount of variation in the sample
  data

7
Formula for the Mean
Where Xi each observation n sample size
8
Formula for Variance
9
(No Transcript)
10
T-test

• A test for differences between means of
  independent samples (difference between mean
  heights of males and females)

11
Hypotheses

• Null Hypothesis (HO)
• Alternate Hypothesis (HA)

12
Example

• Does a particular drug reduce resting heart rate
  in patients?
• Null hypothesis Resting heart rate of patients
  treated with drug is the same as the control
  group
• Alternate hypothesis Resting heart rate of
  patients treated with drug is different than the
  control group

13

• Null Hypothesis hypothesis that mean heights of
  males and females are the same.
• Alternate Hypothesis the mean heights of males
  and females are different

14

• If the probability is less than 5 in 100 (plt0.05)
  significant difference between means
• Degrees of freedom It is a measure of how much
  precision an estimate of variability has
• df (n1n2) - 2

15

• 0.05 is column of interest
• Degrees Freedom is row of interest
• Find t-critical value
• CONCLUSION
• If t-stat is gt t-critical, plt 0.05 and Reject Ho
• If t-stat is lt t-critical, pgt0.05 and Fail to
  Reject Ho

16
(No Transcript)
17

• Reject Ho there is a difference between the
  means of the two samples
• Fail to reject Ho there is no difference
  between the means of the two samples

18
Effect of Variance
19
Practice

• T-test by hand using height data
• How to do on excel

20
Structure of the leaf
21
Stomata and Guard Cells
22
Opening and Closing Stomata

• Transport of K across the plasma membrane causes
  the turgor changes of guard cells
• Stomata open when guard cells accumulate
  potassium (take up water)
• When potassium leaves the guard cells, water
  follows and the stoma closes

23
Hydrocotyle or Water Wort
24
Stomatal density

• Would you expect greater stomatal density on the
  top or the bottom of the leaf?

25
Making a stomatal cast

• Pick a leaf
• Paint a thin layer of fingernail polish on each
  side of the leaf
• Allow the polish to dry
• Peel the polish off (carefully) and make a cast

26
Comparing of stomata on plant leaves

• Quantify the number of stomata per area on leaves
  of Hydrocotyle
• Use one leaf obtained from a shady area, and
  another from a sunny area.

27
Sun leaves vs. Shade leaves

• Shade leaves-
• Thinner (fewer layers of mesophyll)
• More efficient at lower light levels

• Sun leaves
• Thicker and smaller
• Higher photosynthetic saturation point
• Adapted to xeric conditions

28
Rate of Photosynthesis- Sun Vs. Shade Leaves

• Shade leaves curve B
• Sun leaves curve A

29
Experimental Procedure

• Determine the area of the field of view under
  high power (pr2) using a stage micrometer
• Choose one sun leaf and one shade leaf
• Make casts on the side that had greater density
• Make one cast/leaf

30
Procedure continued

• Choose two fields of view and record data
• Compile class data on excel sheet on front
  computer

31
Graphing (pgs. 73-80)
32
Components of a Good Graph

• Descriptive Legend
• Labeled x- and y-axes
• Independent and dependent variables
• Units
• Error bars

33
Homework

• T-test on Stomata density of Sun and Shade leaves
  (data from web page)
• Answer questions page 70
• Complete answers to Graphs on pages 77-80
• Read rat dissection lab