How do you know if your data is the result of random chance

How do you know if your data is the result of random chance or environmental factors? Why? Biologists and scientists use relationships they have discovered in the lab to predict events that might happen under more real-life ci some point those predictions are or not real data. It would be nice if the two sets of data matched exactly, but more often than not they don\'t. This could be attributed to random Auctuations in the variables, due a factor that the scientists overlooked. How does the scientist know? There are many statistical calculations that help answer this question. One that is commonly used by biologists is Chi-square. Model 1 Calculating Chi-square Hypothesis: There is an equal chance of flipping heads or tails on a coin. Coin A Observed e): data (o) Expected (e) (o e) (o Heads Tails 200 200 Coin B Observed Expected (e) (o-e) Co- 2 (o-el: Heads Total 1. What is the hypothesis that has been tested in Model 1? 2. Describe in one or two complete sentences the experiment being performed in Model 1 3. How many flips of the coin will be conducted in each trial for the experiment in Model 1? Chi-Square

Solution

6. Coin B:

Observed data (o)

Expected (e)

(o-e)

(o-e)²

(o-e)²/e

(o-e)²/e

Heads

108

100

-8

64

64/100

0.64

Tails

92

100

8

64

64/100

0.64

Total

200

200

1.28

Observed data (o)

Expected (e)

(o-e)

(o-e)²/e

(o-e)²/e

Heads

120

100

-20

400

400/100

4

Tails

80

100

20

400

400/100

4

Total

200

200

8

If thep value for the calculated ² is p > 0.05 (table value greater than calculated value), accept your hypothesis. Degree of freedom is 2-1 =1. The table value is 3.84.

For coin A the calculated value is 1.28 which is less than 3.84. Hence the hypothesis is accepted and the deviation is due to chance alone.

For coin B, the calculated value is 8 which is greater than 3.84 the table value. Here there is great variation and the deviation is not due to chance alone and there are other forces acting on it.

7. Coin A would be a trick coin because the values for observed number of heads and tails are nearer to the expected. There is not much variation to the expected results. The chi square value is also significant. Hence the first coin is rigged.

	Observed data (o)	Expected (e)	(o-e)	(o-e)2	(o-e)2/e	(o-e)2/e
Heads	108	100	-8	64	64/100	0.64
Tails	92	100	8	64	64/100	0.64
Total	200	200				1.28