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### Why You Need to Identify a Population for Statistical Research

For virtually any statistical study of a population, you have to center your attention on a particular group of individuals (for example, a group of people, cities, animals, rock specimens, exam scores [more…]

### Avoid Bias with Random Statistical Samples

How do you select a statistical sample in a way that avoids bias? The key word is *random.* A *random sample* is a sample selected by equal opportunity; that is, every possible sample of the same size as yours [more…]

### How to Identify Statistical Bias

*Bias* is a word you hear all the time in statistics, and you probably know that it means something bad. But what really constitutes bias? *Bias* is systematic favoritism that is present in the data collection [more…]

### Why Mean and Median Are Both Important in Statistical Data

In statistics, the average and the median are two different representations of the center of a data set and can often give two very different stories about the data, especially when the data set contains [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…]

### Comparing Statistical Surveys and Statistical Experiments

There are two major types of statistical studies: surveys and experiments. After a question has been formed, researchers must design an effective study to collect data that will help answer that question [more…]

### How Hypothesis Tests Are Used in Statistics

One main staple of research studies is called hypothesis testing. A *hypothesis test* is a technique for using data to validate or invalidate a claim about a population. For example, a politician may claim [more…]

### Avoid Drawing the Wrong Conclusions from Statistical Data

Statistical formulas don’t know whether they are being used properly, and they don’t warn you when your results are incorrect. In order to draw the appropriate conclusions, it’s up to you to avoid overstating [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 Statistical Correlation and Causation Are Different

Of all of the misunderstood statistical issues, the one that’s perhaps the most problematic is the misuse of the concepts of correlation and causation. [more…]

### How to Break Down Categorical Statistics Using Two-Way Tables

You can break categorical data down using two-way tables (also known as contingency tables, cross-tabulations or crosstabs) to summarize statistical information about different groups. [more…]

### Why Standard Deviation Is an Important Statistic

The standard deviation is a commonly used statistic, but it doesn’t often get the attention it deserves. Although the mean and median are out there in common sight in the everyday media, you rarely see [more…]

### What Percentile Tells You about a Statistical Value

Percentiles report the relative standing of a particular value within a statistical data set. If that’s what you’re most interested in, the actual mean and standard deviation of the data set are not important [more…]

### How the Central Limit Theorem Is Used in Statistics

The normal distribution is used to help measure the accuracy of many statistics, including the sample mean, using an important result called the *Central Limit Theorem.* [more…]

### How Treatment Groups, Control Groups, Placebos, and Blind Experiments Are Used in Statistics

Statistical studies often involve several kinds of experiments: treatment groups, control groups, placebos, and blind and double-blind tests. An *experiment* [more…]

### How to Interpret the Margin of Error in Statistics

You’ve probably heard or seen results like this: “This statistical survey had a margin of error of plus or minus 3 percentage points.” What does this mean? Most surveys are based on information collected [more…]

### How to Define a Random Statistical Variable

In statistics, a *random variable* is a characteristic, measurement, or count that changes randomly according to a certain set or pattern. Random variables are usually denoted with capital letters such as [more…]

### Statistical Distributions: Binomial, Normal, and *t*-Distribution

A statistical distribution is a listing of the possible values of a variable (or intervals of values), and how often (or at what density) they occur. It can take several forms, including binomial, normal [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 *z*-Values Are Used in Statistics

If a statistical data set has a normal distribution, it is customary to standardize all the data to obtain standard scores known as *z*-values or *z*-scores. The distribution of [more…]

### Finding Standard Deviation in a Statistical Sample

Standard deviation tells you how the values are spread out in a statistical sample. For example, have you heard anyone report that a certain result was found to be “two standard deviations above the mean” [more…]