# Statistics

The core of MaxStat…learn about the powerful and reliable statistical procedures MaxStat offers. MaxStat provides more than 100 statistical tests commonly used in the analysis of scientific data, including descriptive, hypothesis, linear and nonlinear regression, correlation, multivariate analysis, and time series. MaxStat even helps you to design your experiments by computing sample sizes and power. Below is a list of statistical features supported by MaxStat.

### BASIC STATISTICS

Descriptive:
Both column and row statistics

• Sample size
• Minimum and maximum
• Sum
• Mean
• Standard error of the mean
• Standard deviation
• Confidence range of the mean
• Coefficient of variation
• Geometric mean
• Median
• Percentiles (25, 75, and user-selected)
• Skewness
• Kurtosis

Row means

• Sample size
• Minimum and maximum
• Mean
• Standard error of the mean
• Standard deviation

Normality tests

• Anderson-Darling
• Shapiro-Wilk
• Kolmogorov-Smirnov
• Lilliefors t
• Bera-Jeraque

Variance tests

• Bartlett
• Two sample F test
• chi-square

Outliers

• Grubbs’ test

### DISTRIBUTIONS

Discrete distributions

• Binominal
• Negative binominal
• Geometric
• Poisson
• Uniform, discrete

Continous distributions

• Beta
• Cauchy
• Chi-square
• Erlang
• Exponential
• F distribution
• Gamma
• Gaussian (normal)
• Laplace
• Logistic
• Log-normal
• Maxwell
• Raleigh
• Student
• Triangular
• Uniform
• Weibull

Histogram

• Counts of points, frequencies, and percent frequencies

### HYPOTHESIS TESTING

t-tests and nonparametric

• Paired t-test
• Unpaired t-test
• One sample t-test
• One sample Z-test
• Two sample F-test
• One sample chi-square test
• One sample Wilcoxon signed rank
• Paired Wilcoxon signed rank
• Mann-Whitney
• McNemar
• Cochran

1-way ANOVA

• One-way ANOVA
• Repeated measures one-way ANOVA
• Kruskal-Wallis test

2-way ANOVA

• Two-way ANOVA
• Repeated measures two-way ANOVA
• Friedman test

### CONTINGENCY TABLE

Contingency table

• Contingency table with Yates correction

### REGRESSION ANALYSIS

Linear regression
Multiple linear regression

• Parameters and slopes with confidence interval
• With weighing option
• Forcing through origin
• Residual values

Logistic regression

• With selectable tolerance

Nonlinear regression

• 51 built-in functions
• User-defined functions
• Parameters with confidence interval and standard error
• Automatic initial values
• With weighing option

### CORRELATION

Pearson correlation, parametric
Spearman correlation, nonparametric

• Between two variables, correlation coefficient with confidence interval
• Matrix of multiple variables with correlation coefficient and p values

### MULTIVARIATE ANALYSIS

Principal component analysis

• Based on
• Raw data
• Correlation matrix
• Covariance matrix

Multidimensional Scaling

• Distance calculation by
• Euclidean
• City block
• Chebyshev

### TIME SERIES

Auto correlation

• Optional: Covariance

Exponential forecast

• Single
• Double
• Triple

ARAR forecast

• Optional: Memory shortening filter

Smoothing data

• Exponential (single, double, or triple)
• Single moving average

### EXPERIMENTAL DESIGNER

Sample size

• Confidence intervals
• Hypothesis testing
• Correlation
• ANOVA

Power analysis

• Hypothesis testing
• Correlation
• ANOVA

Factorial design analysis

• Full factorial designs with
• Two levels
• Mixed levels