Epidemiology module of practical skills for mbbs student

Practical exercise

Random error and sample size

When a coin is flipped, the result, ie. heads or tails, is a random event (provided it is a fair coin, and the person flipping it is not a trickster).

Question: If you were to conduct an experiment to test if a coin is fair, what proportion of the time would you expect the coin to land with ‘heads up’? (ie. what is the hypothesized result of the experiment?)
Exercise: Let each person in the group conduct his or her own experiment to test a coin.

Each person flips a coin 5 times and records the number of times the coin lands heads up, then compute the percentage ‘heads’. If there are 25 people in the group, this exercise is similar to doing the same study (with n=5 ‘tosses’), 25 separate times.

Put the results in the following table:

Percent ‘heads’	Indicate with a mark for each person
0%
20%
40%
60%
80%
100%

Repeat this series of experiments, this time with each person flipping their coin 25 times. Again each persons calculates the percentage ‘heads’ from his or her own ‘study’.

Percent ‘heads’	Indicate with a mark for each person
0-10%
11-20%
21-30%
31-40%
41-50%
51-60%
61-70%
71-80%
81-90%
91-100%

Record the results from the two series of experiments as frequency histograms on the following graphs.

R
esults from first series of ‘studies’ with n=5

R
esults from second series of ‘studies’ with n=25

Questions:

1. 
   What can you conclude about the most likely percentage of ‘heads’ one would obtain from a single study? Does this ‘most likely’ value change when the sample size of the study is larger or smaller?
   

2. 
   What can you conclude about the expected ‘variation’ in results due to chance when the sample size is smaller v. larger.
   

3. 
   If a colleague were to tell you that she tested a coins by flipping it several times and she found it came up ‘heads’ 20% of the time, could she conclude that the coin is rigged?
   

4. 
   Two colleagues came to you with results of their studies on 2 different coins. They each tested different coins by flipping them several times and they found one came up ‘heads’ 20% of the time (ie. a ‘head rate’ of 20%) and the other came up ‘heads’ 65% of the time (a ‘head rate’ of 65%).
   

What is the difference in ‘head rates’ between the two studies? What is the rate ratio?

Are you confident that these differences are real? What additional information would you need to know in order to decide in the coins are similar?