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### How to Test a Hypothesis for One Population Mean

You can use a hypothesis test to examine or challenge a statistical claim about a population mean if the variable is numerical (for example, age, income, time, and so on) and only one population or group [more…]

### How to Use the *t*-Test to Handle Small Samples and Unknown Standard Deviations

When using a test statistic for one population mean, there are two cases where you must use the *t*-distribution instead of the *Z*-distribution. The first case is where the sample size is small [more…]

### How to Test a Null Hypothesis Based on One Population Proportion

You can use a hypothesis test to test a statistical claim about a population proportion when the variable is categorical (for example, gender or support/oppose) and only one population or group is being [more…]

### How to Compare Two Independent Population Averages

You can compare numerical data for two statistical populations or groups (such as cholesterol levels in men versus women, or income levels for high school versus college grads) to test a claim about the [more…]

### How to Test for an Average Difference Using the Paired *t*-Test

You can test for an average difference using the paired *t*-test when the variable is numerical (for example, income, cholesterol level, or miles per gallon) and the individuals in the statistical sample [more…]

### How to Calculate a Correlation

Can one statistic measure both the strength and direction of a linear relationship between two variables? Sure! Statisticians use the *correlation coefficient* [more…]

### How to Interpret a Correlation Coefficient *r*

In statistics, the correlation coefficient *r* measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of [more…]

### Using Linear Regression to Predict an Outcome

Statistical researchers often use a linear relationship to predict the (average) numerical value of *Y* for a given value of *X* using a straight line (called the [more…]

### How to Calculate a Regression Line

In statistics, you can calculate a regression line for two variables if their scatterplot shows a linear pattern and the correlation between the variables is very strong [more…]

### How to Interpret a Regression Line

In statistics, once you have calculated the slope and *y-*intercept to form the best-fitting regression line in a scatterplot, you can then interpret their values. [more…]

### How to Compare Two Population Proportions

For statistical purposes, you can compare two populations or groups when the variable is categorical (for example, smoker/nonsmoker, Democrat/Republican, support/oppose an opinion, and so on) and you’re [more…]

### Working with Statistical Two-Way Tables

To explore the links between two categorical variables, you first need to organize the data that’s been collected, and a table is a great way to do that. A [more…]

### What the Distribution Tells You about a Statistical Data Set

The *distribution* of a statistical data set (or a population) is a listing or function showing all the possible values (or intervals) of the data and how often they occur. When a distribution of categorical [more…]

### Identifying Bad Statistical Samples

After a statistical study has been designed, be it a survey or an experiment, you need to select a sample of individuals who represent a cross-section of the entire population. This is critical to producing [more…]

### Identifying Statistical Bias in Your Data Sample

*Statistical b**ias* is the systematic favoritism of certain individuals or certain responses in a study. Bias is the nemesis of statisticians, and they do everything they can to avoid it. Want an example [more…]

### Describing Your Statistical Data with Numbers

After collecting good statistical data, you can summarize it with *d**escriptive statistics**.* These are numbers that describe a data set in terms of its important features: [more…]

### How to Spot Mathematical Errors in Statistical Data

After examining the design of the study and how data was collected, the next thing to do when you come upon a statistic or the result of a statistical study is to look for mathematical errors in the data [more…]

### Types of Statistical Data: Numerical, Categorical, and Ordinal

When working with statistics, it’s important to recognize the different types of data: numerical (discrete and continuous), categorical, and ordinal. *Data* [more…]

### What a *p*-Value Tells You about Statistical Data

When you perform a hypothesis test in statistics, a *p*-value helps you determine the significance of your results. Hypothesis tests are used to test the validity of a claim that is made about a population [more…]

### How Correlation, Regression, and Two-Way Tables Clarify Statistical Data

One of the most common goals of statistical research is to find links between variables. Using correlation, regression, and two-way tables, you can use data to answer questions like these: [more…]

### How to Interpret a Scatterplot

Scatterplots are useful for interpreting trends in statistical data. Each observation (or point) in a scatterplot has two coordinates; the first corresponds to the first piece of data in the pair [more…]