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Stats Study Guide

# Stats Study Guide - Stats Study Guide Bivariate statistics...

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Stats Study Guide Bivariate statistics: Means -For a real-valued random variable X , the mean is the expectation of X . Note that not every probability distribution has a defined mean (or variance); For a data set, the mean is the sum of the observations divided by the number of observations. The mean is often quoted along with the standard deviation : the mean describes the central location of the data, and the standard deviation describes the spread. T-test A t -test is any statistical hypothesis test in which the test statistic has a Student's t distribution if the null hypothesis is true. It is applied when sample sizes are small enough that using an assumption of normality and the associated z-test leads to incorrect inference . A test of the null hypothesis that the means of two normally distributed populations are equal. Given two data sets, each characterized by its mean , standard deviation and number of data points, we can use some kind of t test to determine whether the means are distinct, provided that the underlying distributions can be assumed to be normal ANOVA- In statistics , analysis of variance ( ANOVA ) is a collection of statistical models , and their associated procedures, in which the observed variance is partitioned into components due to different explanatory variables . , Correlation (bivariate, partial, distances), Nonparametric tests A cross tabulation (often abbreviated as cross tab ) displays the joint distribution of two or more variables . They are usually presented as a contingency table in a matrix format. Whereas a frequency distribution provides the distribution of one variable, a contingency table describes the distribution of two or more variables simultaneously. Each cell shows the number of respondents that gave a specific combination of responses, that is, each cell contains a single cross tabulation. The following is a fictitious example of a 3 × 2 contingency table. The variable “Wikipedia usage” has three categories: heavy user, light user, and non user. These categories are all inclusive so the columns sum to 100%. The other variable "underpants" has two categories: boxers, and briefs. These categories are not all inclusive so the rows need not sum to 100%. Each cell gives the percentage of subjects that share that combination of traits.

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boxers briefs heavy Wiki user 70% 5% light Wiki user 25% 35% non Wiki user 5% 60% Cross tabs are frequently used because: 1. They are easy to understand. They appeal to people that do not want to use more sophisticated measures. 2. They can be used with any level of data: nominal, ordinal, interval, or ratio - cross tabs treat all data as if it is nominal 3. A table can provide greater insight than single statistics 4. It solves the problem of empty or sparse cells 5. they are simple to conduct the chi-square distribution (also chi-squared or χ 2 distribution ) is one of the most widely used theoretical probability distributions in inferential statistics , i.e. in
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Stats Study Guide - Stats Study Guide Bivariate statistics...

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