The chi-square goodness of fit test evaluates whether proportions of categorical or discrete outcomes in a sample follow a population distribution with hypothesized proportions. In other words, when you draw a random sample, do the observed proportions follow the values that theory suggests. [Read more…] about Chi-Square Goodness of Fit Test: Uses & Examples

# conceptual

## Sampling Error: Definition, Sources & Minimizing

## What is Sampling Error?

Sampling error is the difference between a sample statistic and the population parameter it estimates. It is a crucial consideration in inferential statistics where you use a sample to estimate the properties of an entire population. [Read more…] about Sampling Error: Definition, Sources & Minimizing

## Cohort Study: Definition, Benefits & Examples

## What is a Cohort Study?

A cohort study is a longitudinal experimental design that follows a group of participants who share a defining characteristic. For example, a cohort study can select subjects who have exposure to a risk factor, are in the same profession, population or generation, or experience a particular event, such as a medical procedure. This design determines whether exposure to a risk factor affects an outcome. [Read more…] about Cohort Study: Definition, Benefits & Examples

## Inter-Rater Reliability: Definition, Examples & Assessing

## What is Inter-Rater Reliability?

Inter-rater reliability measures the agreement between subjective ratings by multiple raters, inspectors, judges, or appraisers. It answers the question, is the rating system consistent? High inter-rater reliability indicates that multiple raters’ ratings for the same item are consistent. Conversely, low reliability means they are inconsistent. [Read more…] about Inter-Rater Reliability: Definition, Examples & Assessing

## How to Find the Mode

There are several ways to find the mode depending upon the data type and sample size. In statistics, the mode is the most frequently occurring value in a data set. It is a measure of central tendency. To learn more about the mode, read my post, Measures of Central Tendency. [Read more…] about How to Find the Mode

## Bimodal Distribution: Definition, Examples & Analysis

A bimodal distribution has two peaks. In the context of a continuous probability distribution, modes are peaks in the distribution. The graph below shows a bimodal distribution. [Read more…] about Bimodal Distribution: Definition, Examples & Analysis

## Margin of Error: Formula and Interpreting

## What is the Margin of Error?

The margin of error (MOE) for a survey tells you how near you can expect the survey results to be to the correct population value. For example, a survey indicates that 72% of respondents favor Brand A over Brand B with a 3% margin of error. In this case, the actual population percentage that prefers Brand A likely falls within the range of 72% ± 3%, or 69 – 75%. [Read more…] about Margin of Error: Formula and Interpreting

## Quartile: Definition, Finding, and Using

## What are Quartiles?

Quartiles are three values that split your dataset into quarters. [Read more…] about Quartile: Definition, Finding, and Using

## Construct Validity: Definition and Assessment

## What is Construct Validity?

Construct validity relates to the soundness of inferences that you draw from test scores and other measurements. Specifically, it addresses whether a test measures the intended construct. For example, does a test that evaluates self-esteem truly measure that construct or something else? [Read more…] about Construct Validity: Definition and Assessment

## Qualitative Research: Goals, Methods & Benefits

Qualitative research aims to understand ideas, experiences, and opinions using non-numeric data, such as text, audio, and visual recordings. The focus is on language, behaviors, and social structures. Qualitative researchers want to present personal experiences and produce narrative stories that use natural language to provide meaningful answers to their research questions. [Read more…] about Qualitative Research: Goals, Methods & Benefits

## What is a Variable?

The definition of a variable changes depending on the context. Typically, a letter represents them, and it stands in for a numerical value. In algebra, a variable represents an unknown value that you need to find. For mathematical functions and equations, you input their values to calculate the output. In an equation, a coefficient is a fixed value by which you multiply the variable.

In statistics, a variable is a characteristic of interest that you measure, record, and analyze. Statisticians understand them by defining the type of information they record and their role in an experiment or study. [Read more…] about What is a Variable?

## Linear Regression

## What is Linear Regression?

Linear regression models the relationships between at least one explanatory variable and an outcome variable. These variables are known as the independent and dependent variables, respectively. When there is one independent variable (IV), the procedure is known as simple linear regression. When there are more IVs, statisticians refer to it as multiple regression. [Read more…] about Linear Regression

## Null Hypothesis: Definition, Rejecting & Examples

## What is a Null Hypothesis?

The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test. [Read more…] about Null Hypothesis: Definition, Rejecting & Examples

## Confidence Intervals: Interpreting, Finding & Formulas

## What is a Confidence Interval?

A confidence interval (CI) is a range of values that is likely to contain the value of an unknown population parameter. These intervals represent a plausible domain for the parameter given the characteristics of your sample data. Confidence intervals are derived from sample statistics and are calculated using a specified confidence level. [Read more…] about Confidence Intervals: Interpreting, Finding & Formulas

## Kurtosis: Definition, Leptokurtic & Platykurtic

## What is Kurtosis?

Kurtosis is a statistic that measures the extent to which a distribution contains outliers. It assesses the propensity of a distribution to have extreme values within its tails. There are three kinds of kurtosis: leptokurtic, platykurtic, and mesokurtic. Statisticians define these types relative to the normal distribution. Higher kurtosis values indicate that the distribution has more outliers falling relatively far from the mean. Distributions with smaller values have a lower tendency for producing extreme values. When you’re assessing a sample, outliers have the greatest impact on this statistic. [Read more…] about Kurtosis: Definition, Leptokurtic & Platykurtic

## F-table

These F-tables provide the critical values for right-tail F-tests. Your F-test results are statistically significant when its test statistic is greater than this value. [Read more…] about F-table

## Sampling Distribution: Definition, Formula & Examples

## What is a Sampling Distribution?

A sampling distribution of a statistic is a type of probability distribution created by drawing many random samples of a given size from the same population. These distributions help you understand how a sample statistic varies from sample to sample. [Read more…] about Sampling Distribution: Definition, Formula & Examples

## Critical Value: Definition, Finding & Calculator

## What is a Critical Value?

A critical value defines regions in the sampling distribution of a test statistic. These values play a role in both hypothesis tests and confidence intervals. In hypothesis tests, critical values determine whether the results are statistically significant. For confidence intervals, they help calculate the upper and lower limits. [Read more…] about Critical Value: Definition, Finding & Calculator

## Test Statistic: Definition, Types & Formulas

## What is a Test Statistic?

A test statistic assesses how consistent your sample data are with the null hypothesis in a hypothesis test. Test statistic calculations take your sample data and boil them down to a single number that quantifies how much your sample diverges from the null hypothesis. As a test statistic value becomes more extreme, it indicates larger differences between your sample data and the null hypothesis. [Read more…] about Test Statistic: Definition, Types & Formulas

## Reliability vs Validity: Differences & Examples

Reliability and validity are criteria by which researchers assess measurement quality. Measuring a person or item involves assigning scores to represent an attribute. This process creates the data that we analyze. However, to provide meaningful research results, that data must be good. And not all data are good! [Read more…] about Reliability vs Validity: Differences & Examples