This document discusses a one sample runs test, which is used to determine if a sample is randomly drawn from a population. It defines a run as a series of like items. The document provides an example of coin flips and illustrates how different outcomes would indicate random or non-random patterns. It presents the formula for the runs test and applies it to an example of testing if diseased trees are randomly or non-randomly grouped. The requirements, advantages, and other applications of the runs test are outlined.
1. ONE SAMPLE RUNS TEST
Milind Gokhale
Nilesh Kataria
Kiran Itagi
Pratik Sharma
Rohit Murari
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2. AGENDA
Purpose of test and terminology
Understanding Basic
Formulae
Problem
Problem Analysis
Requirements for One sample runs test
Advantages
Other applications
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3. PURPOSE OF THE TEST AND TERMINOLOGY
Quite often in research we may be interested in
finding out whether the sample is drawn at random,
so that we can generalise the sample results to the
population
we can apply the technique called ‘Runs test’,
which is exclusively used for the purpose of
ensuring the randomness of parameters of interest
“Run” is defined as a ‘series of like items‘.
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4. UNDERSTANDING
For example, flipping a coin 10 times might have resulted in obtaining either head (H) or tail
(T) in each throw as follows
If the number of samples is very small or Very large then this would indicate a non-random
pattern. For example, consider again a throw of a coin for 10 times.
This shows that there is a perceivable pattern in the sample. (Due to non random-Influence)
HH TT HHHH T H
1 2 3 4 5
Total Runs = 5
HHHH TTTT
1 2
Total Runs = 2
H T H T H T H T H T
1 2 3 4 5 6 7 8 9 10
Total Runs = 10
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5. FORMULAE
mr = (2n1n2 / n1+n2) +1
PROBLEM
H= Healthy Tree D= Diseased Tree
H0 = The trees are planted/placed randomly
Ha = Diseased trees come in non-random grouping
HH DD HHHH DDD HHHH DDDDD HHHHHHHHH
1 2 3 4 5 6 7
Total Runs = 7
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6. PROBLEM ANALYSIS
mr = 14.33
sr = 2.38
1% significance
Z value for 0.495
= 2.58
Upper limit =
mr + (2.58 * 2.38)
= 20.47
Lower limit =
mr – (2.58 * 2.38)
= 8.19
R=7 in CR. So Reject Ho; Accept Ha.
There is strong indication that diseased trees come in non-random grouping.
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7. REQUIREMENTS
This checks for randomness of the sample
selected.
It is highly useful in checking the randomness of
residuals in regression or time series and
forecasting models.
ADVANTAGES
This test checks for randomness of the sample
selected.
It is highly useful in checking the randomness of
residuals in regression or time series and
forecasting models. 7
8. OTHER APPLICATIONS
Thus a runs test is used to test the randomness
dichotomous observations like head/tail, yes/no,
men/women, married/single, high/low,
increasing/decreasing
Possibly in stock market technical analyses or
Forecasting and Analyses.
In time series analyses finding out whether the errors
(residuals) of the models are randomly distributed
finding out the randomness of defective items in the
quality control process 8