# Descriptive Statistics & Statistical Analyses

# Descriptive Statistics

## 📊 Mean/Median/Mode 📺

This

**video**defines the the**mean**,**median**, and**mode**. The**mean (average)**of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The**median**is the middle value when a data set is ordered from least to greatest. The**mode**is the**number that occurs most frequently in a data set**.

This

**video**illustrates how to find the**mean**,**median**, and**mode**of a sample data set.

This

**video**provides an example of how to calculate**standard deviation**and**bias**. The**standard deviation**is a measure of the amount of**variation**or**dispersion**of a set of values.

This

**video**defines and provides examples to find the**mean**,**median**,**mode**,**range**, and**standard deviation**of a data set.

This

**video**defines the**margin of error**as**how far from the estimate the true value might be**,**in either direction**. The**confidence interval**is the**estimate****±**the**margin of error.**It also applies these terms to a practical**QR example: a runoff in an election.**

This

**video**explains how to use the**p-value**to solve problems with**hypothesis testing**. When the**p-value is less than alpha**, the**null hypothesis is rejected**and**vice versa**. A simple way to remember this is: '"**If****the p is low, the null must go**!" It also discusses when to use a**one tailed test**compared to a**two tailed test**.

This

**video**provides a**numerical example**using a**sample mean and standard deviation**and a**90% confidence interval**.

This

**video**explains significance testing, using a**p value = 0.05**. It explicates the following:**p > 0.05**is the probability that the**null hypothesis**is**true**.**(1 - p value)**is**alternative hypothesis**is**true**.A

**statistically significant**test result (**p ≤ 0.05**) means that the**test hypothesis is false**or should be**rejected**.**A p value**greater than**0.05**means that**no effect was observed**.

This link provides various

**study guides**and**video tutorials**for a wide range of topics in**Statistics**.

# Statistical Analyses

This

**video**highlights the difference between**correlation**and**causation**, and explains why**correlation does not imply causality**.

This

**video**explains how to calculate the**correlation coefficient, r,**which measures the**strength**and**direction**of a**linear relationship**between**two variables**on a**scatterplot**.

This

**video**provides a comprehensive explanation to the**chi-square distribution**, which is used to examine the**differences between categorical variables in the same population**.

This

**video**defines the**chi-square statistic**as the**square of the difference between the observed (o) and expected (e) values divided by the expected value.**It also provides a**numerical example**applying the**chi-square statistic**to**hypothesis testing**.

**This video**defines**linear regression**as a**linear**approach to**modeling**the relationship between a**dependent variable**(a**scalar response**) and one or more**independent variables**(**explanatory variables**). It also defines:**outliers**,**F-statistic**,**total sums of squares**,**sums of squares for regression**, and**sums of squares for error**.

This

**video**applies**linear regression**to a**numerical example**.

This link is a

**video**tutorial which distinguishes between the**nominal**,**ordinal**,**interval**, and**ratio**scales of measurement.**Nominal**data is**named**data which can be**separated into discrete categories which do not overlap**(i.e. eye color).**Ordinal**data is data which is**placed into some kind of order or scale**(i.e. rating customer satisfaction on a scale from 1-10).**Interval**data is data which comes in the form of**a numerical value where the difference between points is standardized and meaningful**(i.e. temperature).**Ratio**data is much like interval data – it must be**numerical values where the difference between points is standardized and meaningful**, but it also must have a**true zero/no negative values**(i.e. height).

This

**video**defines and provides**examples**of the**nominal**,**ordinal**,**interval**, and**ratio**scales of measurement.

This

**video**explicates how to create a**bar graph,**which presents**categorical data with rectangular bars**, using**data**from a**survey**.

## 📊 Histograms 📺

This

**video**illustrates how and when to use**histograms**to visualize the**frequency distribution**of a data set.

## 📊 Line Graphs 📺

This

**video**explains how and when to use a**line graph**to visually represent data, particularly**data that changes over time**.

## 📊 Pie Charts 📺

This

**video**illustrates how and when to use**pie charts**to visualize data.**Pie charts**are**circular****charts**divided up into**segments**(or "**slices**") which**each represent a value**.

## 📊 Scatter Plots 📺

This

**video**shows how to construct and read**scatter plots**, which are used to**observe relationships between variables**.

This

**video**explains how to read and construct**box and whisker plots**(a**five-number summary**of a set of data), which are used to graphically depict groups of numerical data through their**quartiles**.

This

**video**explains how to organize data into**frequency tables**and**dot (line) plots**.

This

**video**explains the**difference**between a**linear scale**and a**logarithmic scale**. On a**linear scale**, the**value between any two points will never change.**A**logarithmic scale**is one in which the units on the**axis are powers**, or**logarithms**, of a base number.**Exponential growth curves**are displayed on a**logarithmic scale**.