One sample runs test

One Sample runs test presentation to study and explain one sample runs test in key ideas in management and statistics.

1. One Sample Runs Test Milind Gokhale Nilesh Kataria Kiran Itagi Pratik Sharma Rohit Murari 1

2. Agenda Purpose of test and terminology Understanding Basic Formulae Problem Problem Analysis Requirements for One sample runs test Advantages Other applications 2

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‘. 3

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 4

5. Formulae m r = (2n 1 n 2 / n 1 +n 2 ) +1 Problem H= Healthy Tree D= Diseased Tree H = The trees are planted/placed randomly H a = Diseased trees come in non-random grouping HH DD HHHH DDD HHHH DDDDD HHHHHHHHH 1 2 3 4 5 6 7 Total Runs = 7 5

6. Problem Analysis m r = 14.33 s r = 2.38 1% significance Z value for 0.495 = 2.58 Upper limit = m r + (2.58 * 2.38) = 20.47 Lower limit = m r – (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. 6

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