Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
The course is:
Designed to help familiarize you with the most common methods
used in Animal Science to set-up and analyze experimental data.
Hopefully you will become more “procedurally aware”. This is to
say that you will be able to recognize the conditions necessary to
affect scientifically sound experiments and carry out a valid
analyses of those experimental data.
The course is not:
Intended to be an exhaustive overview of all possible methods and
we will not derive all of the variables in each method with
mathematical proofs. The course will also not delve into the
philosophy of scientific inference and procedure and we’ll not talk
about such things as inductive vs. deductive reasoning etc.
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
You should already be familiar with:
Types of data: nominal, ordinal, interval and ratio
Frequency counts vs. Scores
Continuous vs. Discrete data
Descriptive statistics - means, modes, medians, variance, standard
deviation, standard error, etc.
Independence of variables, repeated and independent measures
Parametric vs. Non-parametric data
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
Differences between Parametric and Non-parametric Data
Parametric
Non-parametric
Typical Data
Ratio or Interval
Ordinal or Nominal
Assumed Distribution
Normal
Any
Assumed Variance
Homogenous
Any
Data Relationships
Independent
Any
Central Measures
Mean
Median
Usefulness
Varied conclusions
Simple; Less affected by
outliers
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
Testing Parametric vs. Non-parametric Data
Parametric
Non-parametric
Independent Measures
(of 2 groups)
t-test
Mann-Whitney test
Independent Measures
(of > 2 groups)
1-way ANOVA
Kruskal-Wallis test
Repeated Measures
(with 2 conditions)
Matched-pair , t-test
Wilcoxon test
Repeated Measures
(>2 conditions)
1-way, repeated measures
ANOVA
Friedman’s test
Correlation
Pearson Correlation
Spearman Rank test
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
Testing Two Means
Student’s t-Test
This parametric test indicates the separation of two sets of measurements. It is a test
to determine if two sets of measures are actually different and an experimental effect
has been demonstrated. Typically this test is set up with a null hypothesis that
indicates two measures (such as population or sample means) are the same.
Ho: μ1 = μ2 or x1̄ = x2̄
“Two groups of dairy cows produce the same amount of milk on two different diets”
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
Student’s t-Test
The test assumes a normal distribution of the data, that the underlying variances are
equal and there is random assignment of the measures.
∞
Actually, the t-distribution is the same as the normal (Z) distribution when n =
With small sample sizes, the t distribution is “leptokurtic” (which is often the case with
biological samples).
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
Student’s t-Test
The value of “t” or the “t statistic” is calculated :
t = experimental effect / variability
or
t = the difference in group means / SE of difference between group means
t = x̄ - μ
S
Looks a lot like
a “Z” score!
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
Student’s t-Test
There are two basic types of t-tests:
Independent measures – unmatched samples
Matched-pair measures – samples are in pairs
Independent Measures: two – sample test
Tan k 1: fish grown without probiotic treatment on a normal diet.
Tan k 2: fish grown with probiotic treatment on a normal diet.
Ho: μ1 = μ2 or x̄1 = x̄2
All we need to generate a tscore and test whether fish in Tank 2 have grown
differently than Tank 1 is an average of their weights (a mean) and the spread
around that average (SD).
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
Homogeneity of Variances
An underlying assumption of the t-test and ANOVAs is that,
σ21 = σ22
This is also an assumption for tests that examine more than two variances. So given
that , we can test for the “Homogeneity of Variances”
Ho: σ21 = σ22 = … = σ2k
(where k is the number of samples)
Ha: σ21 ≠ σ22 ≠ …
When variances are equal they are said to be “Homoscedastic”.
Special Topics 504: Practical Methods in Analyzing Animal Science Experiments
A Simplified Test for Homogeneity of Variances
Divide the largest variance by the smallest variance to obtain an F-ratio.
If the F-ratio is less than the value in the appropriate cell, you can assume the variances
are homogeneous.
Number of groups / treatments
df
very large
2
3
4
5
6
7
8
9
10
11
12
2
39.0
87.5
142
202
266
333
403
475
550
626
704
3
15.4
27.8
39.2
50.7
62.0
72.9
83.5
93.9
104
114
124
4
9.6
15.5
20.6
25.2
29.5
33.6
37.5
41.1
44.6
48.0
51.4
5
7.2
10.8
13.7
16.3
18.7
20.8
22.9
24.7
26.5
28.2
29.9
6
5.82
8.38
10.4
12.1
13.7
15.0
16.3
17.5
18.6
19.7
20.7
7
4.99
6.94
8.44
9.70
10.8
11.8
12.7
13.5
14.3
15.1
15.8
8
4.43
6.00
7.18
8.12
9.03
9.78
10.5
11.1
11.7
12.2
12.7
9
4.03
5.34
6.31
7.11
7.80
8.41
8.95
9.45
99.1
10.3
10.7
10
3.72
4.85
5.67
6.34
6.92
7.42
7.87
8.28
8.66
9.01
9.34
12
3.28
4.16
4.75
5.30
5.72
6.09
6.42
6.72
7.00
7.25
7.43
15
2.86
3.54
4.01
4.37
4.68
4.95
5.19
5.40
5.59
5.77
5.95
20
2.46
2.95
3.29
3.54
3.76
3.94
4.1
4.24
4.37
4.49
4.59
30
2.07
2.40
2.61
2.78
2.91
3.02
3.12
3.21
3.29
3.36
3.39
60
1.67
1.85
1.96
2.04
2.11
2.17
2.22
2.26
2.3
2.33
2.36
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00