Quantitative Methods and Experimental Design

1
Quantitative Methods and Experimental Design

• Hypothesis testing
• Replicate sampling
• Errors and distributions
• Probabilities
• Statistical tests (Students t test)
• Plotting experimental data

2
Testable Hypothesis

• General questions
• How are assembly/disassembly regulated?
• Do microtubules represent a simple dynamic
  equilibrium?
• Narrow to a single testable hypothesis
• Protein synthesis is central to gene expression
• Statement synthesis of new protein is necessary
  for flagellar growth in Chlamydomonas

3
Hypothesis Testing

• Null hypothesis
• no change
• no effect
• should be only one null hypothesis
• Alternative hypothesis(es)
• positive change
• negative change
• multiple choices possible

4
Replicate Sampling
fix and stain sample
low power field of view
high power field of view
5
Types of Error
amputation
start
20 min
40 min
6
Sampling Error
Fix and stain 3 samples, same time
mean 3.1 µm
mean 3.3 µm
mean 2.8 µm
7
Sampling and Data Distribution
average cells

• time 0 10 20 30
  40 50 60 70 80 min

30 min sample
0 1 2 3 4
length (µm)
0 1 2 3 4
length (µm)
8
Effect of Sample Size
n 5
n 20
dependent variable
independent variable
n 50
n 200
n 8
9
Representing Error
normal distribution
frequency
34.1
34.1
2.1
2.1
13.6
13.6
-3 -2 -1 µ
1 2 3
standard deviations
Write mean standard deviation e.g., 13 3 µm
mean µ
standard deviation
10
Representing Error on a Graph
In text or table write mean standard
deviation E.g., 13 3 µm
On a Graph
Use an error bar
Use standard deviation of the mean
typical sample standard deviation
cap bar mean

sample mean plus std error

sample mean minus std error
typical standard deviation of the mean
11
Plot Continuous Variables
12
Sample Graph

• Typical graph features
• Labeled axes
• Independent variable on x axis
• Error bars
• Trend line
• Proportion
• Figure caption w/number

Figure 1. Time course of growth of tentacles of
mysterious alien creature.
13
Badly Proportioned Graphs
OOPS
14
Comparing Data Sets
large difference in means
small difference in means
small error
small error
1 µm
3 µm
10
10
large difference in means
small difference in means
large error
large error
1 µm
3 µm
10
10
15
Comparing Small Samples
Blue group 1 Red group 2
small sample
1 2 3 4 5 6 7 8
Eventual outcomes
group 1 ? group 2
group 1 group 2
16
Non-Normal Distributions
skewed distribution
unknown distribution
frequency
frequency
length
length
bimodal distribution
frequency
length
17
Probability and Hypothesis Testing

• Zero p lt 1
• Zero and one represent certainty
• Null hypothesis group 1 group 2
• p probability favoring null hypothesis
• If p lt 0.05, then reject the null hypothesis
• If p gt 0.05, then accept null or gather more data

18
Students t Test

• Two sample test for small samples
• Assumes normal distribution if large enough
  sample taken
• Returns t statistic
• t, sample sizes, probability table yield p value
• If p lt 0.05, reject null hypothesis

19
T Test Rationale

• t µ1 - µ2 (A B)1/2
• t is greater with larger difference in means µ1
  - µ2
• (A B)1/2 is expression of random error
• t is smaller with larger error (A B)1/2
• Larger value of t means smaller value of p
• Smaller p means greater confidence in result

20
Paired or Unpaired?

• Paired one to one correspondence between each
  data point in set one and a unique data point in
  set two
• Example same subject before/after
• Unpaired random sampling of population
• Example cells fixed and stained at start of
  experiment, different set of cells from same
  culture fixed/stained at 2 hrs