Statistics By Jim

Making statistics intuitive

conceptual

What is a Variable?

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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

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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

Confidence Intervals: Interpreting, Finding & Formulas

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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

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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. 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

Test Statistic

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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

Reliability vs Validity: Differences & Examples

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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

Nominal, Ordinal, Interval, and Ratio Scales

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The nominal, ordinal, interval, and ratio scales are levels of measurement in statistics. These scales are broad classifications describing the type of information recorded within the values of your variables. Variables take on different values in your data set. For example, you can measure height, gender, and class ranking. Each of these variables uses a distinct level of measurement. [Read more…] about Nominal, Ordinal, Interval, and Ratio Scales

Case Control Study: Definition, Benefits & Examples

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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

Simple Random Sampling: Definition & Examples

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What is Simple Random Sampling?

Simple random sampling (SRS) is a probability sampling method where researchers randomly choose participants from a population. All population members have an equal probability of being selected. This method tends to produce representative, unbiased samples. [Read more…] about Simple Random Sampling: Definition & Examples

Convenience Sampling: Definition & Examples

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What is Convenience Sampling?

Convenience sampling is a non-probability sampling method where researchers use subjects who are easy to contact and obtain their participation. Researchers find participants in the most accessible places, and they impose no inclusion requirements. Convenience sampling is also known as opportunity or availability sampling. [Read more…] about Convenience Sampling: Definition & Examples

Systematic Sampling: Definition, Advantages & Examples

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What is Systematic Sampling?

Systematic sampling is a probability sampling method for obtaining a representative sample from a population. To use this method, researchers start at a random point and then select subjects at regular intervals of every nth member of the population. Like other probability sampling methods, the researchers must identify their population of interest before sampling from it. [Read more…] about Systematic Sampling: Definition, Advantages & Examples

Mean Squared Error (MSE)

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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)

Validity in Research and Psychology: Types & Examples

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What is Validity in Psychology, Research, and Statistics?

Validity in research, statistics, psychology, and testing evaluates how well test scores reflect what they’re supposed to measure. Does the instrument measure what it claims to measure? Do the measurements reflect the underlying reality? Or do they quantify something else? [Read more…] about Validity in Research and Psychology: Types & Examples