A chi-square (Χ2) distribution is a continuous probability distribution that is used in many hypothesis tests.
The shape of a chi-square distribution is determined by the parameter k. The graph below shows examples of chi-square distributions with different values of k.
Continue reading: Chi-Square (Χ²) Distributions | Definition & Examples
Quartiles are three values that split sorted data into four parts, each with an equal number of observations. Quartiles are a type of quantile.
Quartiles can also split probability distributions into four parts, each with an equal probability.
Continue reading: Quartiles & Quantiles | Calculation, Definition & Interpretation
The Pearson correlation coefficient (r) is the most common way of measuring a linear correlation. It is a number between –1 and 1 that measures the strength and direction of the relationship between two variables.
| Pearson correlation coefficient (r) | Correlation type | Interpretation | Example |
|---|---|---|---|
| Between 0 and 1 | Positive correlation | When one variable changes, the other variable changes in the same direction. | Baby length & weight:
The longer the baby, the heavier their weight. |
| 0 | No correlation | There is no relationship between the variables. | Car price & width of windshield wipers:
The price of a car is not related to the width of its windshield wipers. |
| Between 0 and –1 |
Negative correlation | When one variable changes, the other variable changes in the opposite direction. | Elevation & air pressure:
The higher the elevation, the lower the air pressure. |
Continue reading: Pearson Correlation Coefficient (r) | Guide & Examples
A Poisson distribution is a discrete probability distribution. It gives the probability of an event happening a certain number of times (k) within a given interval of time or space.
The Poisson distribution has only one parameter, λ (lambda), which is the mean number of events. The graph below shows examples of Poisson distributions with different values of λ.
Continue reading: Poisson Distributions | Definition, Formula & Examples
Skewness is a measure of the asymmetry of a distribution. A distribution is asymmetrical when its left and right side are not mirror images.
A distribution can have right (or positive), left (or negative), or zero skewness. A right-skewed distribution is longer on the right side of its peak, and a left-skewed distribution is longer on the left side of its peak:
You might want to calculate the skewness of a distribution to:
Continue reading: Skewness | Definition, Examples & Formula
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test:
The effect is usually the effect of the independent variable on the dependent variable.
Continue reading: Null and Alternative Hypotheses | Definitions & Examples
Student’s t table is a reference table that lists critical values of t. Student’s t table is also known as the t table, t-distribution table, t-score table, t-value table, or t-test table.
A critical value of t defines the threshold for significance for certain statistical tests and the upper and lower bounds of confidence intervals for certain estimates. It is most commonly used when:
The critical values of t are calculated from Student’s t distribution. Student’s t distribution is the distribution of the test statistic t. The critical values of t are difficult to calculate by hand, which is why most people use a t table or computer software instead.
Continue reading: Student’s t Table (Free Download) | Guide & Examples
The coefficient of determination is a number between 0 and 1 that measures how well a statistical model predicts an outcome.
| Coefficient of determination (R2) | Interpretation |
|---|---|
| 0 | The model does not predict the outcome. |
| Between 0 and 1 | The model partially predicts the outcome. |
| 1 | The model perfectly predicts the outcome. |
The coefficient of determination is often written as R2, which is pronounced as “r squared.” For simple linear regressions, a lowercase r is usually used instead (r2).
Continue reading: Coefficient of Determination (R²) | Calculation & Interpretation