# Statistical Tests Reviewed

### Chi-square (χ²) Test of Independence

May 22, 2017

BRIEF DESCRIPTION Whereas the One-sample Chi-square (χ²) goodness-of-fit test compares our sample distribution (observed frequencies) of a single variable with a known pre-defined distribution (expected frequencies) such as the population distribution, normal distribution, or poisson distribution, to test for the significance of deviation, the Chi-square (χ²) Test of Independence compares two categorical variables in a cross-tabulation fashion to determine group differences or degree of association (or non-association i.e. independence).  Chi-square (χ²) is a [READ MORE]

### One-Sample Chi-square (χ²) goodness-of-fit test

January 9, 2016

BRIEF DESCRIPTION The Chi-square (χ²) goodness-of-fit test is a univariate measure for categorical scaled data, such as dichotomous, nominal, or ordinal data.  It tests whether the variable’s observed frequencies differ significantly from a set of expected frequencies. For example, is our observed sample’s age distribution of 20%, 40%, 40% significantly different from what we expect (e.g. the population age distribution) of 30%, 30%, 40%. Chi-square (χ²) is a non-parametric procedure.   SIMILAR STATISTICAL PROCEDURES: Binomial goodness-of-fit (for binary data) [READ MORE]

### Analysis of Covariance (ANCOVA)

May 13, 2015

BRIEF DESCRIPTION The Analysis of Covariance (ANCOVA) follows the same procedures as the ANOVA except for the addition of an exogenous variable (referred to as a covariate) as an independent variable. The ANCOVA procedure is quite straightforward: It uses regression to determine if the covariate can predict the dependent variable and then does a test of differences (ANOVA) of the residuals among the groups. If there remains a significant difference among the groups, it signifies a significant difference between the dependent variable and the predictors after the effect of the [READ MORE]

### One-Sample Kolmogorov-Smirnov goodness-of-fit test

February 8, 2015

BRIEF DESCRIPTION The Kolmogorov-Smirnov (K-S) test is a goodness-of-fit measure for continuous scaled data. It tests whether the observations could reasonably have come from the specified distribution, such as the normal distribution (or poisson, uniform, or exponential distribution, etc.), so it most frequently is used to test for the assumption of univariate normality. The categorical data counterpart is the Chi-Square (χ²) goodness-of-fit test. The K-S test is a non-parametric procedure.     SIMILAR STATISTICAL PROCEDURES: Adjusted Kolmogorov-Smirnov Lilliefors test (null [READ MORE]

### One-way (Independent) ANOVA

July 13, 2012

BRIEF DESCRIPTION The One-way ANOVA is an extension of the Two-independent sample t-test as it compares the observed mean on the dependent variable among more than two groups as defined by the independent variable.  For example, is the mean customer satisfaction score (on the dependent variable) significantly different among three customer groups: adult men, adult women, and children (on the independent variable).  In addition to expressing group differences on the dependent variable, we can also express the findings in terms of relationship or association, e.g. “Age [READ MORE]

### Two-independent sample t-test

July 11, 2012

BRIEF DESCRIPTION The Two-independent sample t-test is for continuous scaled data and it compares the observed mean on the dependent variable between two groups as defined by the independent variable.  For example, is the mean customer satisfaction score (on the dependent variable) significantly different between men and women (on the independent variable). The t-test is a parametric procedure.    SIMILAR STATISTICAL PROCEDURES Non-parametric counterparts of the Two-independent t-test include the (Wilcoxon) Mann-Whitney U-test (non-parametric), Wald-Wolfowitz Runs [READ MORE]

### One-sample t-test

July 10, 2012

BRIEF DESCRIPTION The One-Sample t-test is for continuous scaled data and it compares an observed sample mean with a predetermined value. For example, is our customer satisfaction sample mean significantly different from a pre-set figure such as an industry benchmark or an action standard. It also helps us to answer a question such as “Are we 95% confident that the mean score is between 7.5 and 8.5”. The t-test is a parametric procedure.    SIMILAR STATISTICAL PROCEDURES One-sample z-test Non-parametric counterparts of the one-sample t-test include the Wilcoxon [READ MORE]