statistics stratified sampling

A measure of the accuracy of a test or measuring instrument obtained by measuring the same individuals twice and computing the correlation of the two sets of measures.

Reliability Coefficient is defined and given by the following function:


${Reliability\ Coefficient,\ RC = (\frac{N}{(N-1)}) \times (\frac{(Total\ Variance\ – Sum\ of\ Variance)}{Total Variance})}$

Where −

  • ${N}$ = Number of Tasks


Problem Statement:

An undertaking was experienced with three Persons (P) and they are assigned with three distinct Tasks (T). Discover the Reliability Coefficient?

P0-T0 = 10 
P1-T0 = 20 
P0-T1 = 30 
P1-T1 = 40 
P0-T2 = 50 
P1-T2 = 60 


Given, Number of Students (P) = 3 Number of Tasks (N) = 3. To Find, Reliability Coefficient, follow the steps as following:

Step 1

Give us a chance to first figure the average score of the persons and their tasks

The average score of Task (T0) = 10 + 20/2 = 15 
The average score of Task (T1) = 30 + 40/2 = 35 
The average score of Task (T2) = 50 + 60/2 = 55 

Step 2

Next, figure the variance for:

Variance of P0-T0 and P1-T0: 
Variance = square (10-15) + square (20-15)/2 = 25
Variance of P0-T1 and P1-T1: 
Variance = square (30-35) + square (40-35)/2 = 25
Variance of P0-T2 and P1-T2: 
Variance = square (50-55) + square (50-55)/2 = 25 

Step 3

Presently, figure the individual variance of P0-T0 and P1-T0, P0-T1 and P1-T1, P0-T2 and P1-T2. To ascertain the individual variance value, we ought to include all the above computed change values.

Total of Individual Variance = 25+25+25=75

Step 4

Compute the Total change

Variance= square ((P0-T0) 
 - normal score of Person 0) 
 = square (10-15) = 25
Variance= square ((P1-T0) 
 - normal score of Person 0) 
 = square (20-15) = 25 
Variance= square ((P0-T1) 
 - normal score of Person 1) 
 = square (30-35) = 25 
Variance= square ((P1-T1) 
 - normal score of Person 1) 
 = square (40-35) = 25
Variance= square ((P0-T2) 
 - normal score of Person 2) 
 = square (50-55) = 25 
Variance= square ((P1-T2) 
- normal score of Person 2) 
 = square (60-55) = 25 

Now, include every one of the qualities and figure the aggregate change

Total Variance= 25+25+25+25+25+25 = 150

Step 5

At last, substitute the qualities in the underneath offered equation to discover

${Reliability\ Coefficient,\ RC = (\frac{N}{(N-1)}) \times (\frac{(Total\ Variance\ – Sum\ of\ Variance)}{Total Variance}) \\[7pt]
= \frac{3}{(3-1)} \times \frac{(150-75)}{150} \\[7pt]
= 0.75 }$

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2.statistics analysis of variance

3.statistics arithmetic mean

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5.statistics arithmetic mode

6.statistics arithmetic range

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23.statistics continuous uniform distribution

24.statistics cumulative frequency

25.statistics coefficient of variation

26.statistics correlation coefficient

27.statistics cumulative plots

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29.statistics data collection

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31.statistics data collection observation

32.statistics data collection case study method

33.statistics data patterns

34.statistics deciles statistics

35.statistics dot plot

36.statistics exponential distribution

37.statistics f distribution

38.statistics f test table

39.statistics factorial

40.statistics frequency distribution

41.statistics gamma distribution

42.statistics geometric mean

43.statistics geometric probability distribution

44.statistics goodness of fit

45.statistics grand mean

46.statistics gumbel distribution

47.statistics harmonic mean

48.statistics harmonic number

49.statistics harmonic resonance frequency

50.statistics histograms

51.statistics hypergeometric distribution

52.statistics hypothesis testing

53.statistics interval estimation

54.statistics inverse gamma distribution

55.statistics kolmogorov smirnov test

56.statistics kurtosis

57.statistics laplace distribution

58.statistics linear regression

59.statistics log gamma distribution

60.statistics logistic regression

61.statistics mcnemar test

62.statistics mean deviation

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64.statistics multinomial distribution

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66.statistics normal distribution

67.statistics odd and even permutation

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72.statistics pie chart

73.statistics poisson distribution

74.statistics pooled variance r

75.statistics power calculator

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82.statistics process sigma

83.statistics quadratic regression equation

84.statistics qualitative data vs quantitative data

85.statistics quartile deviation

86.statistics range rule of thumb

87.statistics rayleigh distribution

88.statistics regression intercept confidence interval

89.statistics relative standard deviation

90.statistics reliability coefficient

91.statistics required sample size

92.statistics residual analysis

93.statistics residual sum of squares

94.statistics root mean square

95.statistics sample planning

96.statistics sampling methods

97.statistics scatterplots

98.statistics shannon wiener diversity index

99.statistics signal to noise ratio

100.statistics simple random sampling

101.statistics skewness

102.statistics standard deviation

103.statistics standard error se

104.statistics standard normal table

105.statistics statistical significance

106.statistics formulas

107.statistics notations

108.statistics stem and leaf plot

109.statistics stratified sampling

110.statistics student t test

111.statistics sum of square

112.statistics tdistribution table

113.statistics ti 83 exponential regression

114.statistics transformations

115.statistics trimmed mean

116.statistics type i amp ii errors

117.statistics variance

118.statistics venn diagram

119.statistics weak law of large numbers

120.statistics z table

121.discuss statistics

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