The One-Way Analysis of Variance (ANOVA) calculator computes the ANOVA F score and degrees of freedom for a number of groups.
INSTRUCTIONS: Enter the following in comma separated lists:
- (OB) Observation Table of Groups
- (OC) Output Choice (F-Score or Details)
ANOVA F-Score: The calculator returns the F-score and degrees of freedom for the null hypothesis. Note: there has to be an equal number of observations in the three groups. The calculator also returns the following support statistics:
- F Score
- Numerator: degrees of freedom Between:
- Denominator: degrees of freedom Within:
- Details
- Mean of Groups
- Grand Mean of All Groups Combined
- Sum of Squares (total)
- Sum of Squares (Within)
- Sum of Squares (Between)
- Variance Between
- Variance Within
Example
A school administrator want to know if the time / day of taking tests significantly affect test scores. Let's consider four groups of students taking pop quizzes. Group 1 only gets tested on Mondays first period. Group 2 only gets tested Wednesday after lunch. Group 3 only gets tested in the last period on Fridays, and Group 4 on random days and times. The quiz has 12 questions with a range of potential scores from 0 to 12.
| Group 1 | Group2 | Group3 | Group 4 |
|---|---|---|---|
| 11 | 7 | 6 | 5 |
| 9 | 9 | 5 | 3 |
| 10 | 8 | 7 | 4 |
The above data would be entered into this calculator as follows:
11,7,6,5
9,9,5,3
10,8,7,4
How many degrees of freedom(DF) do you see?
What is the F-Score?
Based on that, compare it to the chosen alpha level (see below) and determine if you accept or reject the hypothesis.
The Math / Science
In ANALYSIS of VARIANCE (ANOVA), the formula for the sample variance is:
`s^2 = (sum y^2 - (sumy)^2/n)/(n-1)`
DF Among = a - 1
DF Within = a(n-1)
Total DF = an-1
F - Tables
Alpha = 0.1
Alpha = 0.05
Statistics Calculators
- Observational Stats: This function accepts a table of numbers separated by commas and calculates observational statistics for any of the columns. This includes count, min, max, sum, sum of squares (Σx²), square of the sum (Σx)², mean, median, mode, range, mid point, rand, sort up, sort down, rand, population variance, population standard deviation, the sample/experimental variance, sample/experimental standard deviation.
- Frequency Distribution: This function lets you enter a string of numbers separated by commas, a low and high range and a number of bins. It then computes how many of the observations are in each of the bins between the high and low values designated.
- Paired Sample t-test: This computes the various parameters associated with the Paired Sample t-test.
- ANOVA (one way): The is one way analysis of variance
- (χ2) Chi-Square Test: This computes the Chi-Square value for an nxm array of data and provides the degrees of freedom.
- Linear Regression: This computes the regression line (least-squares) through a set of X and Y observations. It also computes the regression coefficient (r).
- y = a + bx: This is linear equation used with Linear Regression to predict values of Y.
- Wilcoxon Signed Rank Test: This provides the Wilcoxon statistics and critical value for two groups of numeric observations based on an alpha value and whether it's a one or two tailed test.
- Slope-Intercept form of a Line based on two points.
- Slope between two points
- Range value based on the slope-intercept formula of a line and a value of the domain.
- Compute the Probability between z SCORES
- College Level Statistics Calculator (Stat Calc).
- Count of Observations in a Set - this is the number (n) of values in a set.
- Minimum Value in a Set - this is the minimum observed value
- Maximum Value in a Set- this is the maximum value in the set.
- Numeric Sort (up and down) - this returns a comma separated list of the observations in ascending or descending order.
- Create a random subset of the a list of numeric values
- Random number from a range you specify
- Frequency distribution of data.
- Σx - this is the sum of the values in a set.
- Σx² - this is the sum of the squared values
- (Σx)² - this is the square of the summed values.
- Mean - the is the mean (average) of the observed values
- Median - the middle ordered value
- Mode - the most recurring observation
- Mid Point in a Set - this is the mid point of the observation range.
- Range in a Set - this is the difference between the max and the min.
- Population Variance of the values
- Population standard deviation of the values
- Sample Variance of the values
- Sample Standard Deviation of the values
- Compute the z SCORE based on the mean and standard deviation
- Compute the z SCORE in a set of observations
- Compute the percentile of a single observation (y) in a set (X)
- SDOM - standard deviation of mean
- Percent Relative Standard Deviation
References
- One Way ANOVA video: https://youtu.be/q48uKU_KWas