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

# interpreting results

## 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

## 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

## 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

## Test Statistic

## 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

## Odds Ratio

An odds ratio (OR) quantifies the relationship between a variable and the likelihood of an event occurring. A common use for odds ratios is identifying risk factors by assessing the relationship between exposure to a risk factor and a medical outcome. For example, is there an association between exposure to a chemical and a disease? [Read more…] about Odds Ratio

## Case Control Study: Definition, Benefits & Examples

## What is a Case Control Study?

A case control study is a retrospective, observational study that compares two existing groups. Researchers form these groups based on the existence of a condition in the case group and the lack of that condition in the control group. They evaluate the differences in the histories between these two groups looking for factors that might cause a disease. [Read more…] about Case Control Study: Definition, Benefits & Examples

## Five-Number Summary

The five-number summary is an exploratory data analysis tool that provides insight into the distribution of values for one variable. Collectively, this set of statistics describes where data values occur, their central tendency, variability, and the general shape of their distribution. [Read more…] about Five-Number Summary

## Variance

Variance is a measure of variability in statistics. It assesses the average squared difference between data values and the mean. Unlike some other statistical measures of variability, it incorporates all data points in its calculations by contrasting each value to the mean. [Read more…] about Variance

## Mean Squared Error (MSE)

Mean squared error (MSE) measures the amount of error in statistical models. It assesses the average squared difference between the observed and predicted values. When a model has no error, the MSE equals zero. As model error increases, its value increases. The mean squared error is also known as the mean squared deviation (MSD). [Read more…] about Mean Squared Error (MSE)

## Paired T Test

Use a paired t-test when each subject has a pair of measurements, such as a before and after score. A paired t-test determines whether the mean change for these pairs is significantly different from zero. This test is an inferential statistics procedure because it uses samples to draw conclusions about populations.

Paired t tests are also known as dependent samples t tests. The two samples are dependent because they contain the same subjects. Conversely, an independent samples t test contains different subjects in the two samples. [Read more…] about Paired T Test

## Independent Samples T Test

Use an independent samples t test when you want to compare the means of precisely two groups—no more and no less! Typically, you perform this test to determine whether two population means are different. This procedure is an inferential statistical hypothesis test, meaning it uses samples to draw conclusions about populations. The independent samples t test is also known as the two sample t test. [Read more…] about Independent Samples T Test

## Stem and Leaf Plot

## What is a Stem and Leaf Plot?

Stem and leaf plots display the shape and spread of a continuous data distribution. These graphs are similar to histograms, but instead of using bars, they show digits. It’s a particularly valuable tool during exploratory data analysis. They can help you identify the central tendency, variability, skewness of your distribution, and outliers. Stem and leaf plots are also known as stemplots. [Read more…] about Stem and Leaf Plot

## Pareto Charts

A Pareto chart is a specialized bar chart that displays categories in descending order and a line chart representing the cumulative amount. The chart effectively communicates the categories that contribute the most to the total. Frequently, quality analysts use Pareto charts to identify the most common types of defects or other problems.

Learn how to use and interpret these charts and understand the Pareto principle and the 80/20 rule that are behind it. I’ll also show you how to create them using Excel. [Read more…] about Pareto Charts

## Range of a Data Set

The range of a data set is the difference between the maximum and the minimum values. It measures variability using the same units as the data. Larger values represent greater variability.

The range is the easiest measure of dispersion to calculate and interpret in statistics, but it has some limitations. In this post, I’ll show you how to find the range mathematically and graphically, interpret it, explain its limitations, and clarify when to use it. [Read more…] about Range of a Data Set

## Scatterplots: Using, Examples, and Interpreting

Use scatterplots to show relationships between pairs of continuous variables. These graphs display symbols at the X, Y coordinates of the data points for the paired variables. Scatterplots are also known as scattergrams and scatter charts. [Read more…] about Scatterplots: Using, Examples, and Interpreting

## Pie Charts: Using, Examples, and Interpreting

Use pie charts to compare the sizes of categories to the entire dataset. To create a pie chart, you must have a categorical variable that divides your data into groups. These graphs consist of a circle (i.e., the pie) with slices representing subgroups. The size of each slice is proportional to the relative size of each category out of the whole. [Read more…] about Pie Charts: Using, Examples, and Interpreting

## Bar Charts: Using, Examples, and Interpreting

Use bar charts to compare categories when you have at least one categorical or discrete variable. Each bar represents a summary value for one discrete level, where longer bars indicate higher values. Types of summary values include counts, sums, means, and standard deviations. Bar charts are also known as bar graphs. [Read more…] about Bar Charts: Using, Examples, and Interpreting

## Line Charts: Using, Examples, and Interpreting

Use line charts to display a series of data points that are connected by lines. Analysts use line charts to emphasize changes in a metric on the vertical Y-axis by another variable on the horizontal X-axis. Often, the X-axis reflects time, but not always. Line charts are also known as line plots. [Read more…] about Line Charts: Using, Examples, and Interpreting

## Dot Plots: Using, Examples, and Interpreting

Use dot plots to display the distribution of your sample data when you have continuous variables. These graphs stack dots along the horizontal X-axis to represent the frequencies of different values. More dots indicate greater frequency. Each dot represents a set number of observations. [Read more…] about Dot Plots: Using, Examples, and Interpreting