Jorge Huanca Martinez https://jorgehmartinez.github.io/blog/ Medición, evaluación y datos para la educación y el desarrollo social. quarto-1.11.9 Sun, 12 Mar 2023 00:00:00 GMT Working Memory, Mathematical Anxiety Jorge Huanca Martinez https://jorgehmartinez.github.io/blog/posts/2023-03-12-working-memory-math-anxiety/

Step 1: Install and load the packages

pacman::p_load("broom","ggpubr","tidyverse","readr")

Step 2: Load the data into R

# Load the database
data_math <- read.csv("data/WMAth data.csv")

Step 3: Explore outcome variable (must be numeric)

We checked if the independient variables (VI) are numeric

glimpse(data_math)
Rows: 116
Columns: 8
$ age         <int> 42, 23, 23, 21, 23, 22, 31, 24, 27, 23, 27, 24, 25, 26, 24…
$ Opposites   <int> 19, 31, 29, 29, 31, 31, 37, 44, 66, 56, 40, 30, 19, 28, 46…
$ Nspan       <int> 27, 48, 40, 46, 46, 42, 41, 46, 47, 38, 41, 32, 38, 46, 42…
$ Colors      <int> 5, 9, 6, 9, 9, 7, 6, 5, 11, 10, 3, 7, 11, 7, 14, 8, 12, 7,…
$ PSWQ        <int> 49, 53, 77, 74, 51, 49, 64, 28, 69, 43, 52, 53, 41, 54, 38…
$ MARS        <int> 89, 53, 95, 109, 80, 92, 121, 47, 102, 67, 81, 108, 116, 6…
$ Fluency     <int> 101, 151, 120, 119, 115, 112, 83, 154, 155, 104, 148, 90, …
$ Calculation <int> 18, 33, 36, 29, 33, 23, 16, 40, 27, 32, 31, 20, 29, 35, 28…
#Independent variables
#Opposites: Verbal Working Memory
#Nspan: Verbal Working Memory
#Colors: Visuospatial Working Memory
#PSWQ:The Penn State Worry Questionnaire, 16-item, 1-5 Likert  
#MARS:The mathematical anxiety rating scale, 30-item, 0-4 Likert 
#Dependent variables
#Fluency:Math Performance Assessment.
#Calculation:Math Performance Assessment.

Step 4: Make sure data assumptions

A. Linearity

# Influence of Working Memory
plot(Calculation ~ Opposites + Nspan + Colors, data = data_math)

# Influence of Math Anxiety
plot(Fluency + Calculation ~ MARS + PSWQ, data = data_math)

B. Independence of observations

Teoricamente se entiende que las variables son independientes

library(car)
Loading required package: carData

Attaching package: 'car'
The following object is masked from 'package:dplyr':

    recode
The following object is masked from 'package:purrr':

    some
#correlation
cor(data_math$Calculation, data_math$MARS)
[1] -0.4866136
cor(data_math$Calculation, data_math$Opposites)
[1] 0.3959613
cor(data_math$Calculation, data_math$Nspan)
[1] 0.3183924
#variance inflation factor
vif(m_rendimiento_lm)
     MARS Opposites     Nspan 
 1.110124  1.105262  1.169471

C. Normality

#Independent variables
#Verbal Working Memory
hist(data_math$Opposites) 

hist(data_math$Nspan)

#Math Anxiety
hist(data_math$MARS)

#Independent variables
hist(data_math$Fluency)

hist(data_math$Calculation)

# Se puede evaluar la normalidad por  QQplot, Kurtosis

Step 5: Perform the linear regression analysis

m_rendimiento_lm <- lm(Calculation ~ MARS + Opposites + Nspan, data = data_math)
summary(m_rendimiento_lm)

Call:
lm(formula = Calculation ~ MARS + Opposites + Nspan, data = data_math)

Residuals:
     Min       1Q   Median       3Q      Max 
-14.6986  -4.7717  -0.6258   4.5865  19.0717 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 26.80750    4.04794   6.622 1.28e-09 ***
MARS        -0.11188    0.02265  -4.940 2.75e-06 ***
Opposites    0.19403    0.05426   3.576 0.000516 ***
Nspan        0.10409    0.07362   1.414 0.160182    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.982 on 112 degrees of freedom
Multiple R-squared:  0.3448,    Adjusted R-squared:  0.3273 
F-statistic: 19.65 on 3 and 112 DF,  p-value: 2.642e-10

Step 6: Check the homocedasticity

par(mfrow=c(2,2))
plot(m_rendimiento_lm)

par(mfrow=c(1,1))

Step 7: Perform a graph to visualize the results

print(m_rendimiento_lm)

Call:
lm(formula = Calculation ~ MARS + Opposites + Nspan, data = data_math)

Coefficients:
(Intercept)         MARS    Opposites        Nspan  
    26.8075      -0.1119       0.1940       0.1041  
# Get the Intercept and coefficients as vector elements.
cat("# # # # The Coefficient Values # # # ","\n")
# # # # The Coefficient Values # # #  
a <- coef(m_rendimiento_lm)[1]
print(a)
(Intercept) 
    26.8075 
Xedad <- coef(m_rendimiento_lm)[2]
Xprom <- coef(m_rendimiento_lm)[3]
print(Xedad)
      MARS 
-0.1118795 
print(Xprom)
Opposites 
0.1940296
]]> R regression psychometrics https://jorgehmartinez.github.io/blog/posts/2023-03-12-working-memory-math-anxiety/ Sun, 12 Mar 2023 00:00:00 GMT