Quantitative Variable Analysis

Data Entry

? ✖ Enter data separated by comma, semicolon, space, tab or newlines
Repeated values: 4x3 becomes 3 3 3 3

Number of Independent Samples:
Variable Name: , units:

Data Set A:

Data Set B:

Summary Statistics

Statistic	Group A	Group B
Measures of Center
Mean (x̄) =	0	0
Median (x͂) =	0	0
Mode =	0	0
Midrange =	0	0
Measures of Spread
Range =	0	0
Inter-Quartile Range (IQR) =	0	0
Sample Variance (s²) =	NaN	NaN
Sample Standard Deviation (s) =	NaN	NaN
Standard Error of the Mean (s_x̄) =	NaN	NaN
Pop. Standard Deviation (σ) =	0	0
Other Statistics
Sample Size (n) =	1	1
Minimum =	0	0
First Quartile (Q1) =	0	0
Third Quartile (Q3) =	0	0
Maximum =	0	0
Percentile =	0	0
Skew =	NaN	NaN
Kurtosis =	NaN	NaN

Normality

QQ Plot:
95% Bands Worm Plot | GOF Bins:

Confidence Intervals

Confidence Level

Mean Estimation

? ✖ Enter the confidence level above (a decimal smaller than 1.0) and a confidence interval calculated using the t distribution will be constructed.
The confidence interval should be interpreted 'We are X% confident that the interval accurately captures the population mean.'.

x̄_{Group A}-x̄_{Group B} = 0.0000

95% confidence interval for μ_{Group A}-μ_{Group B} :
Pooled Variances: (NaN, NaN)

Unpooled Variances: (NaN, NaN)

Variance Estimation

? ✖ Enter the confidence level above (a decimal smaller than 1.0) and a confidence interval calculated using the chi squared distribution will be constructed.
The confidence interval should be interpreted 'We are X% confident that the interval accurately captures the population variance.'.

95% CI for σ²_{Group A}/σ²_{Group B} : (NaN, NaN)

Proportion Estimation

? ✖ Enter the confidence level above (a decimal smaller than 1.0)

The approximate (Wald) confidence interval uses the normal distribution to approximate the sampling distribution of p̂. This should not be used if the sample size is small enough that there are fewer than 10 successes or failures.
The Exact (Clopper-Pearson) interval uses a binomial distribution for the sampling distribution of p̂. It may be wider than it needs to be though.
The Wilson Score Interval is an improvement over the Wald approximation and performs well even for small sample sizes and extreme proportions.
The Agresti-Coull interval is cute approximation too the binomial interval; For a 95% confidence interval it uses the "add 2 success and 2 failures" rule of thumb.

Consider a success: X

Group A
Successes (x_{Group A}) = 0
Sample size (n_{Group A}) = 1
Sample Proportion (p̂_{Group A}) = 0
Group B
Successes (x_{Group B}) = 0
Sample size (n_{Group B}) = 1
Sample Proportion (p̂_{Group B}) = 0

95% confidence interval for p_{Group A}-p_{Group B}
Approximate (normal): (0.0000, 0)

Hypothesis Testing

Significance Level (α)

T Test for Difference of Means

? ✖ The t test uses the t distribution to model the sampling distribution of the sample mean. \(t=\dfrac{\overline{x}-\mu_0}{s/\sqrt{n}}\).

H₀: μ μ_A-μ_B	=
H₁: μ μ_A-μ_B		0

x̄_{Group A}-x̄_{Group B} = 0.0000

H₀: μ_{Group A}-μ_{Group B} = 0
H₁: μ_{Group A}-μ_{Group B} ≠ 0
Pooled Variances:
T stat: NaN
degrees of freedom: 0
Rejection region: |T|>NaN
p-value: NaN
Unpooled Variances (Welch's):
T stat: NaN
degrees of freedom: NaN
Rejection region: |T|>NaN
p-value: NaN

Test for Difference of Proportions

? ✖ Two tests are done- one using the Wald approximation (normal approximation) to the sampling distribution of the sample proportion.
The Exact test uses the binomial distribution to calculate the p-value.

Consider a success: X

H₀: π_A-π_B	=
H₁: π_A-π_B		0

H₀: p_{Group A}-p_{Group B} = 0
H₁: p_{Group A}-p_{Group B} ≠ 0
Z stat: NaN
Rejection region: |Z|>1.96
Approximate (normal) p-value: NaN

Test for Variance

? ✖ (notes to come)

H₀: σ_{Group A} = σ_{Group B}
H₁: σ_{Group A} ≠ σ_{Group B}
F test:
Test stat F: NaN
Rejection region: F<NaN or F>NaN
p-value: NaN
Levene's Test
Mean: W = NaN (p-value=NaN)
Median: W = NaN (p-value=NaN)
Conover Test
Z = NaN
p-value = NaN

Test for Median

? ✖ (notes to come)

H₀: Population medians are the same

H₁: Population medians differ

Mann-Whitney Test
Median A = 0.0000
Median B = 0.0000
n_A=1
n_B=1
U = 0.5
Sample sizes too small to test significance
Mood's Median Test
χ² = NaN
d.f. = 1
p-value = NaN

Kolmogorov-Smirnov Test

H₀: Population distributions are the same

H₁: Population distributions differ

D = 0
Not significant
Approximate p-value: 0

	Mean	Standard Deviation	Size
Group A
Group B
Group C
Group D
Group E
Group F
Group G
Group H
Group I
Group J
Group K
Group L

	Number of successes (x)	Sample Size (n)
Group A
Group B
Group C
Group D
Group E
Group F
Group G
Group H
Group I
Group J
Group K
Group L

	Group A	Group B
Sample Mean (x̄)
Sample Standard Deviation (s)
Sample Size (n)

Samples	Sample

H₀: σ²	=
H₁: σ²		1