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The **Psychology and Statistics Calculator** contains useful tools for Psychology Students. Click on the buttons to execute the calculator functions. The psychology and statistic functions include the following:

**Observational Statistics (aka Simple Stats)**: Enter a set of comma separated values (e.g., 2,5,2.2,9,7) and see the 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**: Enter a set of comma separated values (e.g., 2,5,2.2,9,7) and a min and max range with a number of bins, and see the distribution of the observations in uniformly sized bins.**Least-squares Trend Line (aka Linear Regression)**: Enter two sets of comma separated values (e.g., 2,5,2.2,9,7) 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:**Enter a set of comma separated values (e.g., 2,5,2.2,9,7) with an 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**: Enter two sets of comma separated values (e.g., 2,5,2.2,9,7) 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.**Analysis of Variance (one way)**: Enter the numeric observations of three groups and see 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.**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.**Wilcoxon Signed Rank Test**: Enter two sets of comma separated values, 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 for 3x2**: 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.

Special Thanks |

Many of these psychology and statistics functions were programmed into vCalc through a Maryland Industrial Partnership (MIPS) grant with St Mary's College of Maryland's Department of Psychology. |

SMCM Psychology and Statistics Collection contains a group of equations created by Caroline Robertson (Caroline4) and reviewed by Richard Platt (rplatt). Caroline Robertson is a student at St. Mary's College of Maryland and created this set of equations as a part of a summer research program designed to develop calculators for vCalc. The purpose of this program was to develop equations that could be used in educational settings. Richard Platt is an Associate Professor of Psychology at St. Mary's College of Maryland. He reviewed the equations for accuracy and usefulness as educational aids. There are a variety of equations here that include most of the ones most commonly encountered in a Psychological Statistics course. In addition to the equations, there is a collection of decision trees that can help with deciding what statistical test is appropriate. There are also a number of other equations that come from a variety of other areas of psychology including psychophysics, learning, and decision-making.