# 1. A brief description

This post will summarize the advancement of using R to analyze data obtained in behavioral and relevant areas.

# 2. Recent Applications

1. Use null model to do the statistics (Benitez & Saffran, 2018)
str(Cnd_Prdct)
## 'data.frame':    30 obs. of  1 variable:
##  $Prop: num 0.396 0.701 0.61 0.558 0.425 ... Prop <- Cnd_Prdct$Prop
ptp <- car::powerTransform(Prop)
summary(ptp)
## bcPower Transformation to Normality
##      Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
## Prop    1.4004           1       0.2077        2.593
##
## Likelihood ratio test that transformation parameter is equal to 0
##  (log transformation)
##                            LRT df      pval
## LR test, lambda = (0) 6.760718  1 0.0093186
##
## Likelihood ratio test that no transformation is needed
##                             LRT df    pval
## LR test, lambda = (1) 0.4629567  1 0.49625
Prop  <- Cnd_Prdct$Prop n <- length(Prop) Y_Bar <- 0.5 Y_Hat <- ave(Prop) SST <- sum((Prop - Y_Bar) ^ 2) SSR <- sum((Y_Bar - Y_Hat) ^ 2) SSE <- sum((Prop - Y_Hat) ^ 2) MSR <- SSR / 1 MSE <- SSE / (n - 1) F_val <- MSR / MSE p_val <- pf(F_val, 1, n - 1, lower.tail = FALSE) data.frame( Soource = c("Regression", "Residual", "Total"), Sum_of_Squares = c(SSR, SSE, SST), df = c(1, n - 1, n), Mean_Square = c(MSR, MSE, NA), F_Value = c(F_val, NA, NA), p_Value = c(p_val, NA, NA) ) ## Soource Sum_of_Squares df Mean_Square F_Value p_Value ## 1 Regression 0.1809633 1 0.18096330 8.131123 0.007936818 ## 2 Residual 0.6454134 29 0.02225563 NA NA ## 3 Total 0.8263767 30 NA NA NA Cnd_Prdct$ Prop1  <- Cnd_Prdct $Prop - 0.5 Cnd_Prdct$ Priori  <- 0.5
fm1 <- lm(Prop1 ~ 1, data = Cnd_Prdct)
car::Anova(fm1, type = 3)
## Anova Table (Type III tests)
##
## Response: Prop1
##              Sum Sq Df F value   Pr(>F)
## (Intercept) 0.18096  1  8.1311 0.007937 **
## Residuals   0.64541 29
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
fm2 <- lm(Prop - 0.5 ~ 1, data = Cnd_Prdct)
car::Anova(fm2, type = 3)
## Anova Table (Type III tests)
##
## Response: Prop - 0.5
##              Sum Sq Df F value   Pr(>F)
## (Intercept) 0.18096  1  8.1311 0.007937 **
## Residuals   0.64541 29
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
fm3 <- lm(Prop ~ 1, offset = Priori, data = Cnd_Prdct)
summary(fm3)
##
## Call:
## lm(formula = Prop ~ 1, data = Cnd_Prdct, offset = Priori)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -0.3731 -0.1142  0.0065  0.1207  0.2393
##
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.07767    0.02724   2.852  0.00794 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1492 on 29 degrees of freedom
car::Anova(fm3, type = 3)
## Anova Table (Type III tests)
##
## Response: Prop
##              Sum Sq Df F value   Pr(>F)
## (Intercept) 0.18096  1  8.1311 0.007937 **
## Residuals   0.64541 29
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Appendix

Cnd_Prdct <- structure(list(Prop = c(0.39585635359116, 0.70073664825046,
0.610405156537753, 0.557918968692449, 0.425111812680873, 0.460589318600368,
0.533519553072626, 0.816942909760589, 0.675046040515654, 0.691252302025783,
0.378453038674033, 0.620461720599842, 0.472296764009471, 0.204590897132334,
0.786266771902131, 0.610497237569061, 0.752617732175743, 0.547697974217311,
0.433149171270718, 0.707044198895028, 0.713351749539595, 0.72744014732965,
0.529281767955801, 0.66798210997106, 0.387845303867403, 0.532136279926335,
0.804307116104869, 0.652394106813996, 0.489134438305709, 0.445672191528545
)), row.names = c(4L, 6L, 10L, 12L, 16L, 18L, 20L, 22L, 24L,
26L, 28L, 30L, 34L, 36L, 38L, 40L, 42L, 44L, 46L, 48L, 50L, 52L,
54L, 56L, 58L, 60L, 62L, 66L, 70L, 72L), class = "data.frame")

# 3. References

Benitez, V. L., & Saffran, J. R. (2018). Predictable events enhance word learning in toddlers. Current Biology. Journal Article. doi:10.1016/j.cub.2018.06.017