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# Inferential Statistics

Inferential statistics is one of the major branches of the field. It involves using data from a sample to infer details about a population.

An Example of a Hypothesis Test
It is one thing to read about the method hypothesis testing, it is another to see an example worked out. Read an entired worked out example.

What Is a Degree of Freedom?
The number of degrees of freedom is a measure of how many values can vary in a statistical calculation.

How to Calculate the Margin of Error
Typically poll results are accompanied by a margin of error. How does is this margin of error calculated? It's really just a statement of the sample size and level of confidence being used.

An Example of Chi-Square Test for a Multinomial Experiment
See two examples of how a chi-square test is used in dealing with a multinomial experiment.

When Do You Use a Multinomial Experiment?
See out what conditions are necessary in order to use a multinomial experiment.

The Difference Between the Null Hypothesis and Alternative Hypothesis
Hypothesis testing involves construction of two statements, the null hypothesis and the alternative hypothesis. Find out the relationship between these hypotheses and how to distinguish between them.

Differences in Descriptive and Inferential Statistics
Statistics has two main areas, known as descriptive statistics and inferential statistics. Although these areas use the same procedures, there are a number of differences between them.

Different Methods for Inference About the Mean
There are a number of methods for statistical inference about the mean. Find out which method is appropriate for which situations.

What Is ANOVA?
Analysis of Variance or ANOVA is a statistical technique used to compare several populations. Rather than compare parameters two at a time, ANOVA allows us to consider all of the parameters at once.

Why Say Fail to Reject?
One misconception that arises in statistical testing is that some are not careful with their language. Rather than saying that they "fail to reject the null hypothesis" they say that they "accept the null hypothesis." Find out why is is incorrect to say that we accept the null hypothesis.

What Level of Alpha Determines Statistical Significance?
Tests of significance involve a level of significance. This number, denoted by alpha, is a probability. One question many students have is, "What level of significance should be used?"

Is a Type I Error or a Type II Error More Serious?
Statistical tests have two kinds of errors: type I and type II. We may wonder which of these two errors is more serious to make.

One area of statistical inference involves hypothesis tests. There are many subtle mistakes that are made in this process. Find out what they are, and what the correct way is to avoid these pitfalls.

What Is a Sampling Distribution
An important topic in statistics is that of a sampling distribution. By considering a simple random sample as being derived from a distribution of samples of equal size, we can use results from probability and mathematical statistics to reduce variability.

How to Calculate a Confidence Interval for a Mean
Read through step by step instructions on how to calculate a two-sided confidence interval for a mean, when the population standard deviation is known.

How to Calculate a Confidence Interval for a Mean
Read through step by step instructions on how to calculate a two-sided confidence interval for a mean, when the population standard deviation is unknown.

Parametric and Nonparametric Methods in Statistics
One type of division in statistics is between parametric and nonparametric methods. Find out what the differences are between these.

What Is the Conservative Approximation?
For inference with two independent populations the number of degrees of freedom can be determined with Welch's formula. A conservative approximation involves much less calculation.

Degrees of Freedom for Independence of Variables in Two-Way Table
One type of hypothesis test concerns the independence of two categorical variables. See how to calculate the number of degrees of freedom for this type of test of significance.

What Is the Runs Test?

How to Find Degrees of Freedom
Many statistics problems require the determination of the number of degrees of freedom. See how many degrees of freedom you should use for different situations.

Proportions in Statistics
One area of inferential statistics concerns proportions. Sample proportions can be used to estimate population proportions.

Example of an ANOVA Calculation
One factor analysis of variance (ANOVA) is a useful statistical tool. See the worked out details of a sample ANOVA calculation.