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`r^2 = ( "t" ^2) /( "t" ^2 + "df" )`

Enter a value for all fields

The **r-squared effect size measure** calculator computes the measure (r²) based on the t-score and the degrees of freedom.

**INSTRUCTIONS:** Enter the following:

- (
**t**) t-score - (
**df**) Degrees of Freedom

**r-squared (r²):** The calculator returns the effect value as a real number. Note: Small: 0.01-0.09, Medium: 0.09-0.25 and Large: 0.25 and higher.

The **r-squared effect size measure, `r^2 = t^2 /(t^2 + df),` **is important for determining the size of the difference between the means. It describes what percentage of the data can be explained by the results, or how much of the variability in the data is explained by the independent variable (Gravetter and Wallnau, 2013).

The formula for the **r-squared effect size measure** is:

r² = t² /(t² + df)

where:

- r² = r-squared effect size measure
- t = t-score
- df = degrees of freedom

Small: 0.01-0.09

Medium: 0.09-0.25

Large: 0.25 and higher

The t-test calculator (CLICK HERE) lets you enter pairs of observation, either via upload of a csv or manually (e.g.,):

- one-tailed
- alpha = 0.05
- Table of Paired Data
- 2.0,3.0
- 4.0,2.0
- 4.2,55.0
- 78.0,87.0
- -4.0,55.0

It also lets you specify an alpha level and whether the test is one or two tailed, then it calculates the following results:

- t Score: 1.81
- Critical t value: 2.1319
- Number of Pairs: 5
- Group X Mean: 16.84
- Group X SD: 34.35
- Group Y Mean: 40.4
- Group Y SD: 36.98
- Degrees of Freedom: 4
- Standard Error: 12.99

The **Psychology and Statistics Calculator** contains useful tools for Psychology Students. The psychology statistics functions include the following:

**Wilcoxon Signed Rank Test**: Enter two sets, whether it's a one or two tail test and an alpha value to see the Wilcoxon statistic and the critical value.**Bayes' Theorem for Disease Testing**: Enter a base rate probability, probability of false positives and the probability of correct positives to see a ratio of people with the disease, approximate number of false and true positives and the theorem's percent likelihood of a having the disease if tested positive.**chi-square Test**: Enter a 3x2 matrix to see the expected values matrix with row and column totals, degrees of freedom and the chi-square value.**Rescorla-Wagner Formula (alpha and beta version)**: Enter salience for conditional stimuli, rate of unconditional stimuli, maximum conditioning for unconditioned stimuli and the total associative strength of all stimuli present to see the change in strength between conditional and unconditional stimuli.**Rescorla-Wagner Formula (k version)**: Enter Maximum conditioning possible for the unconditioned stimuli, total associative strength of all stimuli present, combined salience of the conditioned and unconditioned stimuli, and number of trials to see the change in strength associated with the trials.**Ricco's Law**: Enter the area of visually unresolved target and constant of background luminance when eyes are adapted to see Ricco's Law factor.**Ricco's Law (K variable)**: Enter the scotopic vision constant, background luminance and photopic vision constant.**Stevens' Power Law**: Enter proportionality constant, magnitude of stimulation, type of stimulation exponent to see magnitude of sensation.**Weber Fraction**: Enter just-noticeable difference for intensity and stimulus intensity to see the weber fraction.**Weber-Fechner's Law**: Enter just-noticeable difference for intensity, instantaneous stimulus, stimulus intensity and the threshold to see the factor.**Random Integer:**This provides a random number (integer) between a lower and upper bound.**Observational Statistics (aka Simple Stats)**: Observational statistics on a set including: count, min, max, mean, median, mode, mid-point, range, population and sample variance and standard deviation, mean absolute deviation, standard deviation of mean, sum of values, sum of squared values, square of the sum, and the sorted set.**Frequency Distribution**: Frequency distribution of a set of observations in uniformly sized bins between a minimum and maximum.**Least-squares Trend Line (aka Linear Regression)**: Linear regression line on a set of paired numbers and see (r) the correlation coefficient,(n) number of observations, (μX) mean of the X values, (μY) mean of Y values, (ΣX) sum of the X values, (ΣY) sum of the Y values, (Σ(X⋅Y) ) sum of the X*Y product values, (ΣX^{2}) sum of X^{2}values, (ΣY^{2}) sum of Y^{2}values, (a) y intercept of regression line, and (b) slope of regression line.**Single-Sample t-test:**t-Test parameters including alpha level, population mean and whether it's one or two tailed and see the degrees of freedom, critical t-value, t score and the standard error.**Paired Sample t-test**: Test of two sets of values with an alpha level and whether it's one or two tailed and see the number of observations, mean and standard deviation for both sets, the degrees of freedom, critical t-value, t-score and the Standard Error value.**Effect Size (r-squared)**: Enter a t-test result and the degrees of freedom to see r^{2}.**Effect Size (Cohen's d):**Enter the mean from two groups and the estimated standard deviation to see the effective size.**Analysis of Variance (one way)**: ANOVA for numeric observations of three groups. Computes the F Score, Numerator: degrees of freedom Between, Denominator: degrees of freedom Within, mean of each group, grand mean, total sum of squares, sum of square within and between, and variance within and between.

Gravetter, F. J., & Wallnau, L. B. (2013). *Statistics for the Behavioral Sciences. *Wadsworth, CA: Cengage Learning.