 A dot plot is a graphical display of data.
 A boxandwhisker plot is a graphical way to display the median, quartiles, and extremes of a data set to show the distribution of the data.
 Stemandleaf plot is a method of organizing numerical data in order of place value.
 A frequency table show the number of times each score appears.
 In statistics, a histogram is a graphical representation of the distribution of data. It is an estimate of the probability distribution of a continuous data.
 The standard score, zvalue, zscore, or normal score, is a measurement of a score's relationship to the mean. A zvalue of 0 means the score is the same as the mean. A zscore can also be positive or negative, indicating whether it is above or below the mean and by how many standard deviations., where μ is the mean and σ is the standard deviation of the population.
 Covariance measures the degree to which two variables change together. The covariance of two variables is positive if they vary together in the same direction.
 A covariance matrix is a matrix whose element in the i, j position is the covariance between the i^{th} and j^{th} elements of a random vector.
 Scatter plot is a graph of plotted points that show the relationship between two sets of data.
 A parametric test makes assumptions about the parameters of the population distribution from which data are drawn.
 Normality tests are tests of the null hypothesis that a sample has been drawn from a normal distribution. Tests of normality include the quantilequantile plot (QQ plot), the probabilityprobability plot (PP plot), skewness, kurtosis, the JarqueBera test, the ShapiroWilk W test, the KolmogorovSmirnov normality test, W/S normality test, D'Agostino's D normality test, D'Agostino Ksquared test.
 A confidence interval for the mean gives an estimated range of values which is likely to include an unknown population mean, the estimated range being calculated from a given set of sample data.
 The one sample ttest is used when we want to know whether our sample comes from a particular population. The onesample ttest is used only for tests of the sample mean.
 The two sample ttest is used for the significance of the difference between the means of two independent samples.
 The paired ttest determines whether two paired sets of data differ from each other in a significant way under the assumptions that the paired differences are independent and normally distributed.
 The oneway analysis of variance (oneway ANOVA) is used to compare means of two or more samples (using the Fdistribution). The ANOVA tests the null hypothesis that samples in two or more groups are drawn from population with the same mean values.
 The twoway analysis of variance is an extension to the oneway analysis of variance. There are two independent variables. The twoway ANOVA examines the influence of different independent variables on one dependent variable.
 The sample standard deviation is just a value calculated from a sample of data. Sometimes we compute the confidence interval for a standard deviation.
 A chisquare test can be used to test if the variance of a population is equal to a certain value.
 For the equality of the variances of two populations, an Ftest can be used.
 Bartlett's test is used to test if three or more samples are from populations with equal variances.
 Pearson correlation coefficient is a measure of the linear correlation between two variables. It requires both variables to be measured on an interval or ratio scale.
 Simple regression analysis is a statistical process for estimating the relationships between one independent variable and one dependent variable. According to the functional model, simple regression analysis include linear, quadratic, exponential, logarithmic, sigmoid, etc
 When there are two or more independent variables and one dependent variable, multiple regression analysis can be used. This test is used also when there is an interaction between two independent variables.
 A nonparametric test makes no assumptions about the parameters of the population distribution from which data are drawn.
 Randomness tests are used to analyze the distribution pattern of a set of data. Randomness test for a sequence tests the null hypothesis that the observations in the sample are randomly generated. Randomness test for two samples tests the null hypothesis that data are randomly allocated into two samples.
 One sample sign test is a nonparametric equivalent of the one sample ttest in parametric test.
 MannWhitney U test is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but the assumption of normal distribution of data is not necessary for use of this test. The MannWhitney U test is nonparametric equivalent of the parametric two sample ttest.
 When there are two samples of data, KolmogorovSmirnov test is used to test whether or not these two samples may come from the same distribution. This test does not require the assumption that the population is normally distributed.
 FlignerPolicello test is a nonparametric test that compare two location parameters (medians) from distributions.
 Two sample sign test can be used to test the hypothesis that the difference median is zero between the distributions of two random variables.
 Wilcoxon signedrank test is designed to test a hypothesis about the median of a population distribution. It often involves the use of matched pairs, for example, before and after data.
 KruskalWallis H test is used to test whether multiple samples have come from the same distribution. This test does not assume that the data are normally distributed. It is the nonparametric analogue of the parametric oneway analysis of variance.
 Mood's median test is a nonparametric method that tests the null hypothesis that the medians of the populations from which two or more samples are drawn are identical.
 JonckheereTerpstra Test (Jonckheere's Trend Test) is a nonparametric test for an ordered alternative hypothesis within an independent samples design.
 Friedman test is used to detect differences in treatments across multiple test subjects. This test uses chisquare distribution. It is a nonparametric equivalent of the parametric twoway analysis of variance.
 Quade test is used to detect differences in treatments across multiple test subjects. This test uses Fdistribution. It is a nonparametric equivalent of the parametric twoway analysis of variance.
 SkillingsMack test is used to detect differences in the treatments across multiple test subjects. It can be used for the data set with missing values. With no missing values, SkillingMack test provides the same result as the Friedman test.
 Levene's testis used to test whether two or more samples have equal variances. Some statistical tests assume that variances are equal across groups or samples. The Levene's test can be used to verify that assumption. Levene's test is an alternative to the Bartlett's test. The Levene's test is less sensitive than the Bartlett's test to departures from normality. If you are not sure that your data come from a normal distribution, then Lenvene's test can be a better choice.
 Spearman's rank correlation coefficient, like the Pearson r, measure the strength of relationship between two variables. While the Pearson correlation coefficient requires both variables to be measured on an interval or ratio scale, the Spearman's correlation coefficient only requires data that are at least ordinal.
 Kendall coefficient W is a number of measures of correlation. It is an extension of Spearman correlation procedure to more than two groups.
 Categorical data represent types of data which may be divided into groups. Examples of categorical data are sex, T/F, and educational level.
 Counting nominal data is a basic step before any statistical procedures.
 One sample proportion test is used to compare a sample proportion to a specific value, or a population proportion.
 Two sample proportion test compares two sample proportions to see if there is a difference.
 Chisquare goodnessoffit test is used when you have one categorical variable from a population. It can be used to determine whether sample data are consistent with a hypothesized, or expected distribution.
 Chisquare independence testis used when you have two categorical variables from a population. It can be used to determine whether there is a significant association between the two variables.
 Chisquare homogeneity test is used to a single categorical variable from two different populations. It can be used to determine whether frequency counts are distributed identically across different populations.
 Fisher's exact test is a statistical test to determine if there are association between two categorical variables. Fisher's exact test is more accurate than the chisquare test of independence when the expected numbers are small.
 McNemar test is a test on a 2x2 contingency table when you want to test the difference between paired proportions.
 Cochran Q test is a nonparametric test to verify if several treatments have identical effects. Cochran Q test is an extension to the McNemar test for three or more matched sets of frequencies or proportions.
 The degree of association between two variables can be assessed by number of coefficient, such as the phi coefficient, the contingency coefficient, and Cramer's V.
 Binary logistic regression is used to analyze a data set in which there are one or more independent variables that determine an outcome. The outcome is measured with only two possible outcomes.
 A standard normal distribution is a normal distribution with mean=0 and variance=1.
 Suppose we have a random sample of size n drawn from a normal population with mean μ and standard deviation σ Let m denote the sample mean and s, the sample standard deviation. Then the quantity
has a Student's tdistribution with n1 degrees of freedom.
 If Y_{i} have independent standard normal distribution, then has a chisquare distribution with r degrees of freedom.
 If a random variable X has a chisquared distribution with m degrees of freedom and a random variable Y has a chisquared distribution with n degrees of freedom, and X and Y are independent, then is distributed as Fdistribution with m and n degrees of freedom.
 The Central Limit Theorem says that many samples containing n elements from a population, the distribution of the means of those samples is approximately normal when n is large enough. It is very useful because it tells us that if n is large enough, distributions can be treated as normal distributions.
 Binomial distribution is the distribution of a total number of successes in a given number of trials when there are exactly two mutually exclusive outcomes of a trial.
 Poisson distribution is a probability distribution which arises when counting the number of occurrences of a rare event in a long series of trials. A discrete random variable X is said to have a Poisson distribution with the population mean, if for k=0, 1, 2, ..., the probability function of X is given by where e is the base of the natural logarithm, and k! is the factorial of k.
 The inverse matrix of a square matrix A, is a matrix A^{1} such that AA^{1}=I, where I is the identity matrix.
