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Simulate data with specific characteristics.

## Usage

simulate_correlation(n = 100, r = 0.5, mean = 0, sd = 1, names = NULL, ...)

simulate_ttest(n = 100, d = 0.5, names = NULL, ...)

simulate_difference(n = 100, d = 0.5, names = NULL, ...)

## Arguments

n

The number of observations to be generated.

r

A value or vector corresponding to the desired correlation coefficients.

mean

A value or vector corresponding to the mean of the variables.

sd

A value or vector corresponding to the SD of the variables.

names

A character vector of desired variable names.

...

Arguments passed to or from other methods.

d

A value or vector corresponding to the desired difference between the groups.

## Examples


# Correlation --------------------------------
data <- simulate_correlation(r = 0.5)
plot(data$V1, data$V2)

cor.test(data$V1, data$V2)
#>
#> 	Pearson's product-moment correlation
#>
#> data:  data$V1 and data$V2
#> t = 5.7155, df = 98, p-value = 1.18e-07
#> alternative hypothesis: true correlation is not equal to 0
#> 95 percent confidence interval:
#>  0.3366433 0.6341398
#> sample estimates:
#> cor
#> 0.5
#>
summary(lm(V2 ~ V1, data = data))
#>
#> Call:
#> lm(formula = V2 ~ V1, data = data)
#>
#> Residuals:
#>     Min      1Q  Median      3Q     Max
#> -1.8566 -0.5694 -0.1116  0.5070  2.4567
#>
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -1.548e-17  8.704e-02   0.000        1
#> V1           5.000e-01  8.748e-02   5.715 1.18e-07 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.8704 on 98 degrees of freedom
#> Multiple R-squared:   0.25,	Adjusted R-squared:  0.2423
#> F-statistic: 32.67 on 1 and 98 DF,  p-value: 1.18e-07
#>

# Specify mean and SD
data <- simulate_correlation(r = 0.5, n = 50, mean = c(0, 1), sd = c(0.7, 1.7))
cor.test(data$V1, data$V2)
#>
#> 	Pearson's product-moment correlation
#>
#> data:  data$V1 and data$V2
#> t = 4, df = 48, p-value = 0.000218
#> alternative hypothesis: true correlation is not equal to 0
#> 95 percent confidence interval:
#>  0.2574879 0.6832563
#> sample estimates:
#> cor
#> 0.5
#>
round(c(mean(data$V1), sd(data$V1)), 1)
#> [1] 0.0 0.7
round(c(mean(data$V2), sd(data$V2)), 1)
#> [1] 1.0 1.7
summary(lm(V2 ~ V1, data = data))
#>
#> Call:
#> lm(formula = V2 ~ V1, data = data)
#>
#> Residuals:
#>     Min      1Q  Median      3Q     Max
#> -3.2354 -0.9753 -0.0633  1.2648  3.3477
#>
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   1.0000     0.2104   4.754 1.86e-05 ***
#> V1            1.2143     0.3036   4.000 0.000218 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 1.487 on 48 degrees of freedom
#> Multiple R-squared:   0.25,	Adjusted R-squared:  0.2344
#> F-statistic:    16 on 1 and 48 DF,  p-value: 0.000218
#>

# Generate multiple variables
cor_matrix <- matrix(
c(
1.0, 0.2, 0.4,
0.2, 1.0, 0.3,
0.4, 0.3, 1.0
),
nrow = 3
)

data <- simulate_correlation(r = cor_matrix, names = c("y", "x1", "x2"))
cor(data)
#>      y  x1  x2
#> y  1.0 0.2 0.4
#> x1 0.2 1.0 0.3
#> x2 0.4 0.3 1.0
summary(lm(y ~ x1, data = data))
#>
#> Call:
#> lm(formula = y ~ x1, data = data)
#>
#> Residuals:
#>      Min       1Q   Median       3Q      Max
#> -2.12568 -0.76836 -0.08657  0.61647  2.76996
#>
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -2.455e-17  9.848e-02   0.000    1.000
#> x1           2.000e-01  9.897e-02   2.021    0.046 *
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.9848 on 98 degrees of freedom
#> Multiple R-squared:   0.04,	Adjusted R-squared:  0.0302
#> F-statistic: 4.083 on 1 and 98 DF,  p-value: 0.04604
#>

# t-test --------------------------------
data <- simulate_ttest(n = 30, d = 0.3)
plot(data$V1, data$V0)

round(c(mean(data$V1), sd(data$V1)), 1)
#> [1] 0 1
diff(t.test(data$V1 ~ data$V0)$estimate) #> mean in group 1 #> 0.09185722 summary(lm(V1 ~ V0, data = data)) #> #> Call: #> lm(formula = V1 ~ V0, data = data) #> #> Residuals: #> Min 1Q Median 3Q Max #> -2.0821 -0.6721 0.0000 0.6032 2.0821 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) -0.04593 0.26139 -0.176 0.862 #> V01 0.09186 0.36966 0.248 0.806 #> #> Residual standard error: 1.012 on 28 degrees of freedom #> Multiple R-squared: 0.0022, Adjusted R-squared: -0.03344 #> F-statistic: 0.06175 on 1 and 28 DF, p-value: 0.8056 #> summary(glm(V0 ~ V1, data = data, family = "binomial")) #> #> Call: #> glm(formula = V0 ~ V1, family = "binomial", data = data) #> #> Coefficients: #> Estimate Std. Error z value Pr(>|z|) #> (Intercept) -2.983e-17 3.656e-01 0.000 1.000 #> V1 9.601e-02 3.740e-01 0.257 0.797 #> #> (Dispersion parameter for binomial family taken to be 1) #> #> Null deviance: 41.589 on 29 degrees of freedom #> Residual deviance: 41.523 on 28 degrees of freedom #> AIC: 45.523 #> #> Number of Fisher Scoring iterations: 3 #> # Difference -------------------------------- data <- simulate_difference(n = 30, d = 0.3) plot(data$V1, data$V0) round(c(mean(data$V1), sd(data$V1)), 1) #> [1] 0 1 diff(t.test(data$V1 ~ data$V0)$estimate)
#> mean in group 1
#>             0.3
summary(lm(V1 ~ V0, data = data))
#>
#> Call:
#> lm(formula = V1 ~ V0, data = data)
#>
#> Residuals:
#>    Min     1Q Median     3Q    Max
#> -1.834 -0.677  0.000  0.677  1.834
#>
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)  -0.1500     0.2562  -0.586    0.563
#> V01           0.3000     0.3623   0.828    0.415
#>
#> Residual standard error: 0.9922 on 28 degrees of freedom
#> Multiple R-squared:  0.0239,	Adjusted R-squared:  -0.01096
#> F-statistic: 0.6857 on 1 and 28 DF,  p-value: 0.4146
#>
summary(glm(V0 ~ V1, data = data, family = "binomial"))
#>
#> Call:
#> glm(formula = V0 ~ V1, family = "binomial", data = data)
#>
#> Coefficients:
#>               Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -4.569e-17  3.696e-01   0.000    1.000
#> V1           3.251e-01  3.877e-01   0.839    0.402
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#>     Null deviance: 41.589  on 29  degrees of freedom
#> Residual deviance: 40.865  on 28  degrees of freedom
#> AIC: 44.865
#>
#> Number of Fisher Scoring iterations: 4
#>