Statistics

Descriptive Statistics & Statistical Analyses

Descriptive Statistics

Mean/Median/Mode
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  • 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.

Mean/Median/Mode, Example
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  • This video illustrates how to find the mean, median, and mode of a sample data set.

Standard Deviation
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  • 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.

Mean, Median, Mode, Range, and Standard Deviation
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  • This video defines and provides examples to find the mean, median, mode, range, and standard deviation of a data set.

Confidence Intervals and Margin of Error
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  • 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.

p-Values and Hypothesis Testing
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  • 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.

Interpreting Confidence Levels, Example
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  • This video provides a numerical example using a sample mean and standard deviation and a 90% confidence interval.

p-Values and Significance Tests
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  • 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 the probability that the 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.

General Statistics Resources
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  • This link provides various study guides and video tutorials for a wide range of topics in Statistics.
Statistical Analyses

Correlation vs. Causation
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  • This video highlights the difference between correlation and causation, and explains why correlation does not imply causality.

Calculating r, the Correlation Coefficient
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  • 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.

Chi-Square Distribution
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  • 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.

Chi-Square Statistic for Hypothesis Testing
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  • 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.

Linear Regression
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  • 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.

Linear Regression, Example
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  • This video applies linear regression to a numerical example.

Levels of Measurement (Nominal, Ordinal, Interval, Ratio)
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  • 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).

The Difference Between Levels of Measurement (Nominal, Ordinal, Interval, Ratio)
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  • This video defines and provides examples of the nominal, ordinal, interval, and ratio scales of measurement.
Creating, Reading & Interpreting Different Types of Graphs & Tables

Creating a Bar Graph
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  • This video explicates how to create a bar graph, which presents categorical data with rectangular bars, using data from a survey.

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

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

Pie Charts
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  • 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
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  • This video shows how to construct and read scatter plots, which are used to observe relationships between variables.

Box and Whisker Plots
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  • 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.

Frequency Tables & Dot Plots
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  • This video explains how to organize data into frequency tables and dot (line) plots.

The Difference between Linear and Logarithmic Scales
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  • 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.