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A-priori Sample Size Calculator for Student t-Tests
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A-priori Sample Size Calculator for Student t-Tests
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This calculator will tell you the minimum required total sample size and per-group sample size for a one-tailed or two-tailed t-test study, given the probability level, the anticipated effect size, and the desired statistical power level.
Please supply the necessary parameter values, and then click 'Calculate'.
Anticipated effect size (Cohen's
d
):
By convention, Cohen's d effect sizes of 0.2, 0.5, and 0.8 are considered small, medium, and large, respectively.
Desired statistical power level:
By convention, this value should be greater than or equal to 0.80.
Probability level:
Also known as the p-value, alpha level, or type I error rate. By convention, this value should be less than or equal to 0.05 to claim statistical significance.
Formulas
The following formulas are involved in the calculation of a-priori sample size values for a t-test:
Beta function:
Cohen's d effect size for a t-test:
where
x
_{1}
and
x
_{2}
are the means of group 1 and group 2, and
σ
_{1}
^{2}
and
σ
_{2}
^{2}
are the variances of group 1 and group 2.
Gamma function:
Lower incomplete beta function:
Noncentral t-distribution cumulative distribution function:
where
μ
is the noncentrality parameter,
v
is the degrees of freedom,
Γ
is the gamma function and
I
is the regularized lower incomplete beta function.
Noncentral t-distribution noncentrality parameter:
where
d
is the Cohen's d effect size, and
n
_{1}
and
n
_{2}
are the sample sizes for group 1 and group 2.
Regularized lower incomplete beta function:
where the numerator is the lower incomplete beta function, and the denominator is the beta function.
References
The following references can be used to cite this a-priori sample size calculator for student t-tests:
Soper, D.S. (2014). A-priori Sample Size Calculator for Student t-Tests [Software]. Available from http://www.danielsoper.com/statcalc
Abramowitz, M. and Stegun, I.A., eds. (1965). Handbook of Mathematical Functions. New York, NY: Dover.
Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd Edition). Hillsdale, NJ: Lawrence Earlbaum Associates.
Related Calculators
The following statistics calculators are related to this a-priori sample size calculator for student t-tests, and may be useful for your research:
Sample Size Calculators
A-priori Sample Size Calculator for Hierarchical Multiple Regression
A-priori Sample Size Calculator for Multiple Regression
A-priori Sample Size Calculator for Structural Equation Models
t-Distribution Calculators
Beta (Type II Error Rate) Calculator for a Student t-Test
Confidence Interval Calculator for the Population Mean
Cumulative Distribution Function (CDF) Calculator for the Noncentral t-Distribution
Cumulative Distribution Function (CDF) Calculator for the t-Distribution
Effect Size (Cohen's d) Calculator for a Student t-Test
One-Sample t-Test Calculator
p-Value Calculator for a Student t-Test
Post-hoc Statistical Power Calculator for a Student t-Test
Probability Density Function (PDF) Calculator for the Noncentral t-Distribution
Probability Density Function (PDF) Calculator for the t-Distribution
Student t-Value Calculator
t-Statistic and Degrees of Freedom Calculator
t-Value Calculator for Correlation Coefficients
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