Xbar-S chartAn Xbar-S chart is a combination of control charts used to monitor the process variability (as the standard deviation) and average (as the mean) when measuring subgroups at regular intervals from a process.

Statistical Reference Guide v6.24.0

• Distribution

  • Continuous distributions

    • Univariate descriptive statistics
    • Calculating univariate descriptive statistics
    • Univariate plot

      • Dot plot
      • Box plot
      • Mean plot
    • Creating a univariate plot
    • Frequency distribution

      • Cumulative distribution function plot
      • Creating a CDF plot
      • Histogram
      • Creating a histogram
    • Normality

      • Normal distribution
      • Normal probability (Q-Q) plot
      • Creating a normal probability plot
      • Normality hypothesis test
      • Tests for normality
      • Testing the normality of a distribution
      • Central limit theorem and the normality assumption
    • Inferences about distribution parameters

      • Point and interval estimation
      • Parameter estimate
      • Estimators for the central location parameter of a distribution
      • Estimators for the dispersion parameter of a distribution
      • Estimating the parameters of a distribution
      • Hypothesis testing
      • Parameter hypothesis test
      • Parameter equivalence hypothesis test
      • Tests for the central location parameter of a distribution
      • Tests for the dispersion parameter of a distribution
      • Testing distribution parameters
      • Testing equivalence of distribution parameters
  • Discrete distributions

    • Frequency distribution

      • Frequency table
      • Frequency plot
      • Whole-to-part plot
      • Creating a frequency plot
      • Creating a whole-to-part plot
    • Inferences about Binomial distribution parameters

      • Binomial distribution parameter estimate
      • Estimators for the parameter of a Binomial distribution
      • Binomial distribution parameter hypothesis test
      • Tests for the parameter of a Binomial distribution
      • Testing Binomial distribution parameters
    • Inferences about Multinomial distribution parameters

      • Multinomial distribution parameters hypothesis test
      • Tests for the parameters of a Multinomial distribution
      • Testing Multinomial distribution parameters
  • Study design
• Compare groups

  • Calculating univariate descriptive statistics, by group
  • Side-by-side univariate plots
  • Creating side-by-side univariate plots
  • Equality of means/medians hypothesis test
  • Equivalence of means hypothesis test
  • Tests for means/medians
  • Testing equality of means/medians
  • Testing equivalence of means
  • Difference between means/medians effect size
  • Estimators for the difference in means/medians
  • Estimating the difference between means/medians
  • Multiple comparisons
  • Mean-Mean scatter plot
  • Multiple comparison procedures
  • Comparing multiple means/medians
  • Homogeneity of variance hypothesis test
  • Tests for homogeneity of variance
  • Testing homogeneity of variance
  • Study design
• Compare pairs

  • Difference plot
  • Creating a Tukey mean-difference plot
  • Equality of means/medians hypothesis test
  • Equivalence of means hypothesis test
  • Tests for means/medians
  • Testing equality of means/medians
  • Testing equivalence of means
  • Difference between means/medians effect size
  • Estimators for the difference in means/medians
  • Estimating the difference between means/medians
  • Study design
• Contingency tables

  • Contingency table
  • Creating a contingency table
  • Creating a contingency table (related data)
  • Grouped frequency plot
  • Effect size
  • Estimators
  • Estimating the odds ratio
  • Estimating the odds ratio (related data)
  • Relative risk
  • Inferences about equality of proportions

    • Equality of proportions hypothesis test
    • Exact and asymptotic p-values
    • Wald, Score, Likelihood ratio
    • Tests for equality of proportions (independent samples)
    • Testing equality of proportions (independent samples)
    • Tests for equality of proportions (related samples)
    • Testing equality of proportions (related samples)
  • Inferences about independence

    • Independence hypothesis test
    • Continuity correction
    • Tests for independence
    • Testing independence
  • Mosaic plot
  • Creating a mosaic plot
  • Study design
• Correlation and association

  • Scatter plot
  • Creating a scatter plot or scatter plot matrix
  • Covariance
  • Correlation coefficient
  • Color map
  • Calculating a correlation matrix
  • Calculating a covariance matrix
  • Inferences about association

    • Correlation not Causation
    • Parameter estimate
    • Estimators for correlation and association
    • Estimating the correlation/association
    • Correlation/association hypothesis test
    • Testing correlation/association
  • Study design
• Principal component analysis (PCA)

  • Principal components
  • Scree plot
  • Calculating principal components
  • Biplot
  • Monoplot
  • Creating a biplot
  • Creating a correlation monoplot
• Factor analysis (FA)

  • EFA
  • Factor rotation
  • Matrix rotations
  • Extracting factors
• Item reliability

  • Testing item reliability
• Fit model

  • Linear fit

    • Simple regression models
    • Fitting a simple linear regression
    • Advanced models
    • Fitting a multiple linear regression
    • Performing ANOVA
    • Performing 2-way or higher factorial ANOVA
    • Performing ANCOVA
    • Fitting an advanced linear model
    • Scatter plot
    • Summary of fit
    • Parameter estimates
    • Effect of model hypothesis test
    • ANOVA table
    • Predicted against actual Y plot
    • Lack of Fit
    • Effect of terms hypothesis test
    • Effect leverage plot
    • Effect means
    • Plotting main effects and interactions
    • Multiple comparisons
    • Multiple comparison procedures
    • Comparing effect means
    • Residual plot
    • Residuals - normality
    • Residuals - independence
    • Plotting residuals
    • Outlier and influence plot
    • Identifying outliers and other influential points
    • Prediction
    • Making predictions
    • Making inverse predictions
    • Saving variables
  • Logistic / Probit fit

    • Generalized linear models
    • Fitting a simple logistic regression
    • Fitting an advanced logistic model
    • Fitting a simple probit regression
    • Parameter estimates
    • Odds ratio estimates
    • Estimating odds ratios
    • Effect of model hypothesis test
    • Effect of term hypothesis test
  • Study design
• Method comparison / Agreement

  • Correlation coefficient
  • Scatter plot
  • Fit Y on X

    • Ordinary linear regression
    • Deming regression
    • Passing-Bablok regression
  • Fitting ordinary linear regression
  • Fitting Deming regression
  • Fitting Passing-Bablok regression
  • Linearity
  • Residual plot
  • Checking the assumptions of the fit
  • Average bias
  • Estimating the bias between methods at a decision level
  • Testing commutability of other materials
  • Difference plot (Bland-Altman plot)
  • Fit differences
  • Plotting a difference plot and estimating the average bias
  • Limits of agreement (LoA)
  • Plotting the Bland-Altman limits of agreement
  • Mountain plot (folded CDF plot)
  • Plotting a mountain plot
  • Partitioning and reducing the measuring interval
  • Agreement measures for binary and semi-quantitative data
  • Chance corrected agreement measures for binary and semi-quantitative data
  • Agreement plot
  • Estimating agreement between two binary or semi-quantitative methods
  • Study design
  • Study design for qualitative methods
• Measurement systems analysis (MSA)

  • Precision

    • Conditions of measurement

      • Reproducibility
      • Intermediate precision
      • Repeatability
    • Variance components
    • Estimating the precision of a measurement system
    • Testing precision against a performance claim
    • Precision profile plot
    • Plotting a precision profile
    • Variance function
    • Fitting a variance function
  • Trueness

    • Bias
    • Estimating the bias of a measurement system
    • Testing against an assigned value
    • Testing bias against allowable bias
    • Linearity
    • Estimating the linearity of a measurement procedure (EP06-A)
    • Estimating the linearity of a measurement procedure (EP06-Ed2)
    • Interferences
  • Detection capability

    • Limit of blank (LoB)
    • Limit of detection (LoD)
    • Estimating the detection limit of a measurement system
    • Estimating the detection limit using a precision profile
    • Estimating the detection limit using a probit fit
    • Verifying a detection capability claim
    • Limit of quantitation (LoQ)
  • Study design
• Reference interval

  • Reference limits

    • Normal theory quantile
    • Quantile
    • Bootstrap quantile
    • Harrell-Davis quantile
    • Robust bi-weight quantile
  • Estimating a reference limit or interval
  • Histogram
  • Box plot
  • Normal probability (Q-Q) plot
  • Testing the normality of a reference distribution
  • Transforming the reference distribution
  • Transferring reference limits
  • Study design
• Diagnostic performance

  • Measures of diagnostic accuracy

    • Sensitivity / Specificity
    • Likelihood ratios
    • Predictive values
    • Youden J
  • Estimating sensitivity and specificity of a diagnostic test
  • Comparing the sensitivity and specificity two diagnostic tests
  • ROC plot
  • Plotting a single ROC curve
  • Comparing two or more ROC curves
  • Area under the curve (AUC)
  • Testing the area under the curve
  • Difference between the areas under two curves
  • Testing the difference between the areas under two curves
  • Decision thresholds
  • Decision plot
  • Finding the optimal decision threshold
  • Predicting the decision threshold
  • Study design
• Survival/Reliability

  • Kaplan-Meier survival function
  • Plotting a Kaplan-Meier survival curve
  • Equality of survival functions test
  • Tests for the equality of survival functions
  • Comparing two or more survival functions
  • Proportional hazards fit

    • Fitting a proportional hazard model
    • Hazard ratio estimates
    • Estimating hazard ratios
    • Baseline survival function
    • Effect of model hypothesis test
    • Effect of term hypothesis test
• Control charts

  • Shewhart control charts

    • Shewhart variables control charts

      • Xbar-R chart
      • Xbar-S chart
      • Xbar chart
      • R chart
      • S chart
      • I-MR chart
      • I chart
      • MR chart
      • Creating a Xbar-R / S control chart
      • Creating an I-MR control chart
    • Shewhart attributes control charts

      • NP chart
      • P chart
      • C chart
      • U chart
      • Creating an NP / P control chart
      • Creating a C / U control chart
    • Shewhart control chart rules
    • Applying rules to a Shewhart control chart
    • Formatting a control chart
    • Labeling control chart points
    • Displaying stratification in a control chart
    • Applying phases/stages for each change in a process
  • Time-weighted control charts

    • Uniformly Weighted Moving Average (UWMA) chart
    • Exponentially Weighted Moving Average (EWMA) chart
    • Creating a UWMA control chart
    • Creating an EWMA control chart
    • CUmulative SUM (CUSUM) chart
    • Creating a CUSUM control chart
  • Study design
• Process capability

  • Capability ratios (Cp/Pp indices)
  • Z benchmark
  • Nonconforming units
  • Estimating process capability
• Pareto analysis

  • Pareto chart
  • Creating a Pareto chart
  • Creating comparative Pareto charts
  • Merging Pareto chart categories
  • Varying Pareto chart bar colors
  • Reordering Pareto chart bars
  • Sorting bars on comparative Pareto charts
  • Study design
• Study Designs
• Bibliography