Input data: Numeric data arranged in column to test normality ;

Significance level area: Choose the significance level which is defined as the probability of rejecting a null hypothesis by the test;

Main comands area: Select "OK" to return the results of normality test, "Clear contents" to exclude data entered and results obtained, and "Return" to return to selection screen of the statistical module;

Preliminary results: Area intended to show all results of each calculation step;

Results area: Area that synthesizes and shows all important test results (Dn value, pvalue and conclusion)

Input data 1 and 2: Numeric data arranged in column to test variance ;

Type of test:

• One variance (Chi-Square test): Compares sample variance from Input data set 1 with null hypotheses variance.
• Two variances (F-test): Compare variance between the two input data sets.

Significance level area: Choose the significance level which is defined as the probability of rejecting a null hypothesis by the test;

Null hypothesis (Ho):

• One variance (Chi-Square test): You must enter the null hypothesis value ;
• Two variances (F-test): Automatically entered null hypothesis (population variance = 1.0)

Alternative hypothesis (Ha):

• Two-tailed
  • For Chi-Square test (Ha: σ ≠ σ₀ and Ho:σ = σ₀)
  • For F-test (Ha: σ1 ≠ σ2 and Ho: σ1 = σ2)
• Lower-tailed
  • For Chi-Square test (Ha: σ < σ₀ and Ho:σ ≥ σ₀)
  • For F-test (Ha: σ1 < σ2 and Ho: σ1 ≥ σ2)
• Upper-tailed
  • For Chi-Square test (Ha: σ > σ₀ and Ho:σ ≤ σ₀)
  • For F-test (Ha: σ1 > σ2 and Ho: σ1 ≤ σ2)

where σ is sampled variance, σ₀ is variance under null hypothesis, σ1 and σ2 variances of two sampled groups.

Other commands: Select "Calculate" to return the results of variance test, "Clear contents" to exclude data entered, and "Return" to return to selection screen of the statistical module;

Input data 1 and 2: Numeric data arranged in column to mean test ;

Type of test:

• One-sample: Compares sampled mean from Input data set 1 with null hypotheses mean (µ₀).
• Independent samples (Equal variances): Compare mean between the two input data sets (µ1 and µ2).
• Independent samples (Different variances): Compares mean between the two input data sets (µ1 and µ2)
• Paired: Compares if the mean difference between input data set 1 and input data set 2 is equal to 0 (µ_D).

Significance level area: Choose the significance level which is defined as the probability of rejecting a null hypothesis by the test;

Null hypothesis (Ho):

• One-sample: You must enter the null hypothesis value µ₀
• Independent samples (Equal variances): Automatically entered null hypothesis (µ1 - µ2 ≤ or ≥ or = 0.0).
• Independent samples (Different variances): Automatically entered null hypothesis (µ1 - µ2 ≤ or ≥ or = 0.0).
• Paired: Automatically entered null hypothesis (µ_D ≤ or ≥ or = 0.0).

Alternative hypothesis (Ha):

• Two-tailed
  • For one-sample (Ha: µ ≠ µ₀ and Ho: µ = µ₀)
  • For Independent samples (Ha: µ1- µ2 ≠0 and Ho: µ1- µ2 =0)
  • For paired (Ha: µ_D ≠ 0 and Ho: µ_D = 0)
• Lower-tailed
  • For one-sample (Ha: µ < µ₀ and Ho: µ ≥ µ₀)
  • For Independent samples (Ha: µ1- µ2 <0 and Ho: µ1- µ2 ≥0)
  • For paired (Ha: µ_D < 0 and Ho: µ_D ≥ 0)
• Upper-tailed
  • For one-sample (Ha: µ > µ₀ and Ho: µ ≤ µ₀)
  • For Independent samples (Ha: µ1- µ2 >0 and Ho: µ1- µ2 ≤0)
  • For paired (Ha: µ_D > 0 and Ho: µ_D ≤0)

where µ is sampled mean, µ₀ is mean under null hypothesis, µ1 and µ2 means of two sampled groups.

Other commands: Select "Calculate" to return the results of mean test, "Clear contents" to exclude data entered, and "Return" to return to selection screen of the statistical module;

Input data 1 and 2: Numeric data arranged in column to mean test ;

Type of test:

• One-sample: Compares sampled median from Input data set 1 with null hypotheses mean (θ₀).
• Independent samples: Compares medians between the two input data sets (θ1 and θ2).
• Paired: Compares if the median difference between input data set 1 and input data set 2 is equal to 0 (θ_D).

Significance level area: Choose the significance level which is defined as the probability of rejecting a null hypothesis by the test;

Null hypothesis (Ho):

• One-sample: You must enter the null hypothesis value θ₀
• Independent samples (Different variances): Automatically entered null hypothesis (θ1 - θ2 ≤ or ≥ or = 0.0).
• Paired: Automatically entered null hypothesis (θ_D ≤ or ≥ or = 0.0).

Alternative hypothesis (Ha):

• Two-tailed
  • For one-sample (Ha: θ ≠ θ₀ and Ho: θ = θ₀)
  • For Independent samples (Ha: θ1- θ2 ≠0 and Ho: θ1- θ2 =0)
  • For paired (Ha: θ_D ≠ 0 and Ho: θ_D = 0)
• Lower-tailed
  • For one-sample (Ha: θ < θ₀ and Ho: θ ≥ θ₀)
  • For Independent samples (Ha: θ1- θ2 <0 and Ho: θ1- θ2 ≥0)
  • For paired (Ha: θ_D < 0 and Ho: θ_D ≥ 0)
• Upper-tailed
  • For one-sample (Ha: θ > θ₀ and Ho: θ ≤ θ₀)
  • For Independent samples (Ha: θ1- θ2 >0 and Ho: θ1- θ2 ≤0)
  • For paired (Ha: θ_D > 0 and Ho: θ_D ≤0)

where θ is sampled median, θ₀ is median under null hypothesis, θ1 and θ2 medians of two sampled groups.

Other commands: Select "Calculate" to return the results of median test, "Clear contents" to exclude data entered, and "Return" to return to selection screen of the statistical module;

Objective: Compare observed and estimated data;

Observed data: Numeric data arranged in column;

Estimated data (compared): Numeric data arranged in column;

Calculate: Returns the values of Adjustment coefficient (AC), Efficiency (EF), Coefficient of Residual Mass (CRM), Root Mean Square Error (RMSE), Maximum Error (ME) and Mean Difference (MD)

Other commands: Select "Clear contents" to exclude data entered, and "Return" to return to selection screen of the statistical module;