ONE SAMPLE RUNS TESTMilind Gokhale

Nilesh Kataria

Kiran Itagi

Pratik Sharma

Rohit Murari

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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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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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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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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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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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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.

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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

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