Question

7. There is various flickering light in our environment; for instance, light from computer screens and fluorescent bulbs. If the frequency of the flicker is below a certain threshold, the flicker can be detected by the eye. Different people have slightly different flicker "threshold" frequencies (known as the critical flicker frequency, or CFF). Knowing the critical threshold frequency below which flicker is detected can be important for product manufacturing as well as tests for ocular disease. Do people with different eye color have different threshold flicker sensitivity? A 1973 study ("The Effect of Iris Color on Critical Flicker Frequency," Journal of General Psychology [1973], 91-95) obtained the data from a random sample of 19 subjects. This data is in the spreadsheet CFF. Do these data suggest that people with different eye color have different threshold sensitivity to flickering light? In other words, do the data suggest that threshold sensitivity to flickering light is related to eye color?

Answer 1

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AS FOR GIVEN DATA..

In oredr to determine the box plot of this dta we find out the different parameter of box plot as:

1st quartile	25.35
2nd quartile (median)	26.8
Third quartile,	28.15
	2.8
	21.15
	32.35

Therefore the box plot is drawn as follows: (boxplot show all data within the upper and lower boundary, so we dont have any outlier)

Mean of all 19 observation is :

As mean =meadian, so the data is symmetric in nature and approximately normally distributed.

In order to test whether the people with different eye color have different threshold flicker sensitivity, we carry one way ANOVA test as follows:

The assumption of one way ANOVA analysis is as follows:

1. The samples are independently drawn from the population. Here all sample are drawn from the population randomly and independent to each other.
2. All the populations from which the samples have been drawn are normally distributed.
3. All variance of all the population are equal.

We define the test hypothesis as:

The null hypothesis is defimed as:

against the alternative hypothesis as:

Now we carry out the ANOVA analysis on the basis of this assumption and test hypothesis as follows:

Eye color	Brown		Green		Blue
	26.8	718.24	26.4	696.96	25.7	660.49
	27.9	778.41	24.2	585.64	27.2	739.84
	23.7	561.69	28	784	29.9	894.01
	25	625	26.9	723.61	28.5	812.25
	26.3	691.69	29.1	846.81	29.4	864.36
	24.8	615.04			28.3	800.89
	25.7	660.49
	24.5	600.25
Total	204.7	5250.81	105.5	2790.21	169	4771.84

Therefore sum of all the value in the three samples is:

Therefore the correction factor is:

Therefore the sum of square between the samples :

with degree of freedom ,

Now the total sum of square is determined as:

  

with degree of freedom ,

Therefore the sum of square with in the sample is :

with degree of freedom

Therefore , mean square between the sample is

Now the ANOVA table is written as:

Sources of Variance	SS	Degree of freedom	Mean square	F –statistics	P-Value
SSB
SSW
SST

As the P -value is is more than the (95% ) level of significance and

,

Therefore we failed to reject the null hypothesis ( that is accept the null hypothesis and reject the alternative hypothesis)

and we have sufficient evidence to conclude that the people with different eye color do not have different threshold flicker sensitivity, ( all are have same average threshold flicker sensitivity).

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