# Module: Statsample::SRS

Defined in:
lib/statsample/srs.rb

## Class Method Summary collapse

• Sample size estimation for proportions, finite poblation.

• Sample size estimation for proportions, infinite poblation.

• Finite population correction (over standard deviation).

• Finite population correction (over variance) Source: Cochran(1972).

• Confidente interval using X.

• Confidence Interval using T-Student Use with n < 60.

• Confidente Interval using Z Use with n > 60.

• Proportion confidence interval with x value Uses estimated proportion, sample without replacement.

• Proportion confidence interval with t values Uses estimated proportion, sample without replacement.

• Proportion confidence interval with z values Uses estimated proportion, sample without replacement.

• Standard deviation for sample distribution of a proportion.

• Standard deviation for sample distribution of a proportion Estimated proportion, sample with replacement Based on stattrek.com/Lesson6/SRS.aspx.

• Standard deviation for sample distribution of a proportion Know proportion, sample without replacement.

• Standard deviation for sample distribution of a proportion Know proportion, sample with replacement.

• Total estimation sd based on sample.

• Total estimation sd based on sample.

• Non sample fraction.

• .standard_error_esd_wor(s, sam, pop) ⇒ Object (also: standard_error, se)

Standard error of the mean.

• Standard error of the mean.

• .standard_error_ksd_wr(s, sam, pop) ⇒ Object (also: standard_error_esd_wr)

Standard error.

• Standard error of total estimation.

## Class Method Details

### .estimation_n(d, prop, n_pobl, margin = 0.95) ⇒ Object

Sample size estimation for proportions, finite poblation.

 ``` 41 42 43 44``` ```# File 'lib/statsample/srs.rb', line 41 def estimation_n(d,prop,n_pobl,margin=0.95) n0=estimation_n0(d,prop,margin) n0.quo( 1 + ((n0 - 1).quo(n_pobl))) end```

### .estimation_n0(d, prop, margin = 0.95) ⇒ Object

Sample size estimation for proportions, infinite poblation

 ``` 35 36 37 38 39``` ```# File 'lib/statsample/srs.rb', line 35 def estimation_n0(d,prop,margin=0.95) t=Distribution::Normal.p_value(1-(1-margin).quo(2)) var=prop*(1-prop) t**2*var.quo(d**2) end```

### .fpc(sam, pop) ⇒ Object

Finite population correction (over standard deviation)

 ``` 24 25 26``` ```# File 'lib/statsample/srs.rb', line 24 def fpc(sam,pop) Math::sqrt((pop-sam).quo(pop-1)) end```

### .fpc_var(sam, pop) ⇒ Object

Finite population correction (over variance) Source: Cochran(1972)

 ``` 20 21 22``` ```# File 'lib/statsample/srs.rb', line 20 def fpc_var(sam,pop) (pop - sam).quo(pop - 1) end```

### .mean_confidence_interval(mean, s, n_sample, n_population, x) ⇒ Object

Confidente interval using X.

Better use mean_confidence_interval_z or mean_confidence_interval_t

 ``` 163 164 165 166``` ```# File 'lib/statsample/srs.rb', line 163 def mean_confidence_interval(mean,s,n_sample,n_population,x) range=x*se(s,n_sample,n_population) [mean-range,mean+range] end```

### .mean_confidence_interval_t(mean, s, n_sample, n_population, margin = 0.95) ⇒ Object

Confidence Interval using T-Student Use with n < 60

 ``` 150 151 152 153``` ```# File 'lib/statsample/srs.rb', line 150 def mean_confidence_interval_t(mean,s,n_sample,n_population,margin=0.95) t=Distribution::T.p_value(1-((1-margin) / 2),n_sample-1) mean_confidence_interval(mean,s,n_sample,n_population,t) end```

### .mean_confidence_interval_z(mean, s, n_sample, n_population, margin = 0.95) ⇒ Object

Confidente Interval using Z Use with n > 60

 ``` 156 157 158 159``` ```# File 'lib/statsample/srs.rb', line 156 def mean_confidence_interval_z(mean,s,n_sample,n_population,margin=0.95) z=Distribution::Normal.p_value(1-((1-margin) / 2)) mean_confidence_interval(mean,s,n_sample,n_population, z) end```

### .proportion_confidence_interval(p, sam, pop, x) ⇒ Object

Proportion confidence interval with x value Uses estimated proportion, sample without replacement

 ``` 64 65 66 67 68``` ```# File 'lib/statsample/srs.rb', line 64 def proportion_confidence_interval(p, sam,pop , x) #f=sam.quo(pop) one_range=x * Math::sqrt((qf(sam, pop) * p * (1-p)).quo(sam-1)) + (1.quo(sam * 2.0)) [p-one_range, p+one_range] end```

### .proportion_confidence_interval_t(prop, n_sample, n_population, margin = 0.95) ⇒ Object

Proportion confidence interval with t values Uses estimated proportion, sample without replacement.

 ``` 50 51 52 53``` ```# File 'lib/statsample/srs.rb', line 50 def proportion_confidence_interval_t(prop, n_sample, n_population, margin=0.95) t = Distribution::T.p_value(1-((1-margin).quo(2)) , n_sample-1) proportion_confidence_interval(prop,n_sample,n_population, t) end```

### .proportion_confidence_interval_z(p, n_sample, n_population, margin = 0.95) ⇒ Object

Proportion confidence interval with z values Uses estimated proportion, sample without replacement.

 ``` 57 58 59 60``` ```# File 'lib/statsample/srs.rb', line 57 def proportion_confidence_interval_z(p, n_sample, n_population, margin=0.95) z=Distribution::Normal.p_value(1-((1-margin).quo(2))) proportion_confidence_interval(p,n_sample,n_population, z) end```

### .proportion_sd_ep_wor(p, sam, pop) ⇒ Object

Standard deviation for sample distribution of a proportion. Estimated proportion, sample without replacement. Reference:

• Cochran, 1972, Técnicas de muestreo

 ``` 93 94 95 96``` ```# File 'lib/statsample/srs.rb', line 93 def proportion_sd_ep_wor(p, sam,pop) fsc=(pop-sam).quo((sam-1)*pop) Math::sqrt(fsc*p*(1-p)) end```

### .proportion_sd_ep_wr(p, n_sample) ⇒ Object

Standard deviation for sample distribution of a proportion Estimated proportion, sample with replacement Based on stattrek.com/Lesson6/SRS.aspx.

 ``` 86 87 88``` ```# File 'lib/statsample/srs.rb', line 86 def proportion_sd_ep_wr(p, n_sample) Math::sqrt(p*(1-p).quo(n_sample-1)) end```

### .proportion_sd_kp_wor(p, sam, pop) ⇒ Object

Standard deviation for sample distribution of a proportion Know proportion, sample without replacement.

Sources:

• Cochran(1972)

 ``` 80 81 82``` ```# File 'lib/statsample/srs.rb', line 80 def proportion_sd_kp_wor(p, sam, pop) fpc(sam,pop)*Math::sqrt(p*(1-p).quo(sam)) end```

### .proportion_sd_kp_wr(p, n_sample) ⇒ Object

Standard deviation for sample distribution of a proportion Know proportion, sample with replacement. Based on stattrek.com/Lesson6/SRS.aspx

 ``` 72 73 74``` ```# File 'lib/statsample/srs.rb', line 72 def proportion_sd_kp_wr(p, n_sample) Math::sqrt(p*(1-p).quo(n_sample)) end```

### .proportion_total_sd_ep_wor(prop, sam, pop) ⇒ Object

Total estimation sd based on sample. Estimated proportion, sample without replacement Source: Cochran(1972)

 ``` 108 109 110 111``` ```# File 'lib/statsample/srs.rb', line 108 def proportion_total_sd_ep_wor(prop, sam, pop) fsc=((pop - sam).to_f / ( sam - 1)) Math::sqrt(fsc*pop*prop*(1-prop)) end```

### .proportion_total_sd_kp_wor(prop, sam, pop) ⇒ Object

Total estimation sd based on sample. Known proportion, sample without replacement Reference:

• Cochran(1972)

 ``` 102 103 104``` ```# File 'lib/statsample/srs.rb', line 102 def proportion_total_sd_kp_wor(prop, sam, pop) pob * proportion_sd_kp_wor(p, sam, pop) end```

### .qf(sam, pop) ⇒ Object

Non sample fraction.

1 - sample fraction

 ``` 31 32 33``` ```# File 'lib/statsample/srs.rb', line 31 def qf(sam , pop) 1-(sam.quo(pop)) end```

### .standard_error_esd_wor(s, sam, pop) ⇒ ObjectAlso known as: standard_error, se

Standard error of the mean. Estimated variance, without replacement Cochran (1972) p.47

 ``` 135 136 137``` ```# File 'lib/statsample/srs.rb', line 135 def standard_error_esd_wor(s,sam,pop) s.quo(Math::sqrt(sam)) * Math::sqrt(qf(sam,pop)) end```

### .standard_error_ksd_wor(s, sam, pop) ⇒ Object

Standard error of the mean. Known variance, sample w/o replacement

 ``` 126 127 128``` ```# File 'lib/statsample/srs.rb', line 126 def standard_error_ksd_wor(s,sam,pop) s.quo(Math::sqrt(sam)) * Math::sqrt(qf(sam,pop)) end```

### .standard_error_ksd_wr(s, sam, pop) ⇒ ObjectAlso known as: standard_error_esd_wr

Standard error. Known variance, sample with replacement.

 ``` 121 122 123``` ```# File 'lib/statsample/srs.rb', line 121 def standard_error_ksd_wr(s, sam, pop) s.quo(Math::sqrt(sam)) * Math::sqrt((pop-1).quo(pop)) end```

### .standard_error_total(s, sam, pop) ⇒ Object

Standard error of total estimation

 ``` 144 145 146``` ```# File 'lib/statsample/srs.rb', line 144 def standard_error_total(s,sam,pop) pop*se(s,sam,pop) end```