Biometry (BIOL4090) Quiz #10.
Student name: _________KEY______________________
This 30-minute quiz is worth 5 points. Show all your work to get partial (full) credit. You may use a
calculator, but not a smart phone. You may also leave calculations as ratios if necessary. I have extra
paper, if you need some. Write your name on every page and staple them together with this cover page.
1) You have data on the number of cats that danced / didn’t dance, depending on the reward they
were given (food vs affection).
1a) Write down the null hypothesis (Ho) and alternate hypothesis (Ha) for this test (+0.125 each):
Ho: column and row values are independent from each other
Ha: column and row values are not independent are not independent from each other
1b) Write down the equation of the Chi Square statistic (+0.125) and explain each term (+0.125):
2 

Observed
Observed: observed values
ij - Modelij

2
Modelij
Model: expected values (i and j denote columns and rows)
1c) Write down the equation for the expected values (+0.125) and explain each term (+0.125):
Model ij  Eij 
Row Total i  Column Total j
n
Model: expected values n: grand total (number of all observations) (i and j denote columns and rows)
1
1d) List the two Chi-square assumptions regarding the model predictions (+0.125 each). Explain what
approach can be used when each of the assumptions is violated (+0.125 each):
-
Assumption 1: At least 80% of the expected cells have values larger than 5. When this
assumption is violated, you can use the Yates’ continuity correction
-
Assumption 2: Every one (100%) of the expected cells have values larger than 0. When this
assumption is violated, you can use the Fisher Exact Test, or you can combine the cells into
fewer categories
1e) Enter the expected values (model predictions) in the contingency table below (+0.125 for each
cell). Show your calculations for full credit (value: +0.05, calculation: +0.075).
RTYes  CTFood 76  38

 14.44
n
200
RTNo  CTFood 124  38


 23.56
n
200
RTYes  CTAffection 76  162


 61.56
n
200
RTNo  CTAffection 124  162


 100.44
n
200
Model Food, Yes 
Model Food, No
Model Affection, Yes
Model Affection,No
1f) Did we meet the two assumptions concerning the expected values of the Chi-Square test?
(Explain why / why not it was met in this example) (+0.125):
-
At least 80% of expected values > 5: YES
100% of expected values > 1: YES
1g) Calculate the Chi-Square for this test (+0.125):
2
To get the Chi-square, sum these four terms = 25.356
1h) Finally, answer these questions about the Chi-square (+0.125 for each):
-
What is the minimum possible value: _____0______
-
What is the maximum possible value: _____infinite______
1i) Interpret the Outcome – Standardized Residuals: Using the results below, explain which
combinations of conditions are significant, as revealed by the value of the standardized residuals:
-
For each case, Explain: Is the standardized residual significant? why / why not?
Dance / Food (+0.10): Std Residual (3.6) is larger than 1.96 – significant excess
Dance / Affection (+0.10): Std Residual (-1.7) is not smaller than -1.96 – nonsignificant deficit
No-dance / Food (+0.10): Std Residual (-2.8) is smaller than -1.96 – significant deficit
No-dance / Affection (+0.10): Std Residual (1.4) is smaller than 1.96 – nonsignificant excess
2a) For the analyses described below, list the non-parametric test that you would use (+0.125 each):
-
Compares two independent groups of scores: Mann-Whitney Test
-
Compares two dependent groups of scores: Wilcoxon signed rank Test
-
Compares > 2 independent groups of scores: Kruskal-Wallis Test
3
- Compares > 2 dependent groups of scores: Friedman’s Test
2b) You have two groups and you want to compare the data using a non-parametric test.
Rank the data – from the lowest to the largest number (Hint: a value of 1 has a rank of 1):
Data
1
2
3
2
2
3
5
10
100
Group
1
1
1
1
2
2
2
2
2
Rank
1
3
5.5
3
3
5.5
7
8
9
What is the grand median (for all the data combined)? ____3____ (+0.25)
For each group, how many values are above / below / equal to the grand median (+0.125 for each):
Group1 Group2
Above
0
3
Equal
1
1
Below
3
1
For each group, report the following (+0.125 each):
-
Group 1:
Sum of ranks:
12.5
Mean rank:
3.125
Median value:
-
2
Group 2:
Sum of ranks:
32.5
Mean rank:
6.5
Median value:
5
4