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# Chapter 8 Distributions

## Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are…

## Degrees of Freedom

The degree of freedom for a particular statistical calculation is the number of values that are free to vary. Thus, the minimum number of independent…

## Student t Distribution

The population standard deviation is rarely known in many day-to-day examples of statistics. When the sample sizes are large, it is easy to estimate…

## Choosing Between z and t Distribution

The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution…

## Chi-square Distribution

How does one determine if bingo numbers are evenly distributed or if some numbers occurred with a greater frequency? Or if the types of movies people…

## Finding Critical Values for Chi-Square

Consider a curve representing sample data drawn randomly from a normally distributed population. One must construct confidence intervals to estimate…

## Estimating Population Standard Deviation

When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate…

## Goodness-of-Fit Test

The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one…

## Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the…

## Contingency Table

A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency…

## Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their…

## Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis…

## Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies…

## Test for Homogeneity

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether…

## F Distribution

The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of…

## A Direct and Simple Method to Assess Drosophila melanogaster's Viability from Embryo to Adult

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In Drosophila melanogaster, viability assays are used to determine the fitness of certain genetic backgrounds. Allelic variations can result in…

## Preparation and Characterization of Individual and Multi-drug Loaded Physically Entrapped Polymeric Micelles

Amphiphilic block copolymers like polyethyleneglycol-block-polylactic acid (PEG-b-PLA) can self-assemble into micelles above their critical micellar…

## A Protocol for Using Gene Set Enrichment Analysis to Identify the Appropriate Animal Model for Translational Research

Recent studies that compared transcriptomic datasets of human diseases with datasets from mouse models using traditional gene-to-gene comparison…

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