MASH : Maths and Stats Help

Cronbach's Alpha (α)

Introduction

Cronbach's Alpha is a measure of internal consistency/reliability. It is commonly used to determine the reliability of a scale comprised of multiple Likert questions in a survey/questionnaire. Many different thresholds are used to determine an appropriate reliability value, in the Table below you can see a selection of values from Cohen et al., (2018).

Values from Page 744; Cohen, L., Manion, M., & Morrison, M. (2018) Research Methods in Education (8th ed.). Routledge.

Test Procedure

To compute Cronbach’s alpha, you will need to install and load the “psych” package.

Data:

Cronbach’s alpha is a statistic calculated for a set of variables. If you have an object that contains all of your variables of interest, you can use the alpha() function directly by using alpha(cronbachs_data). However, it is very likely that your data will contain more columns than just the variables you want to calculate the reliabilitiy coefficient for, meaning that you will need to select just the required variables and exclude every other variable. A simple way to achieve that is to store each variable in a new data frame.

This can be achieved using the data.frame() function with each argument being one of the variables of interest from the original object.

clean_data <- data.frame(cronbachs_data$Eval_1, cronbachs_data$Eval_2, cronbachs_data$Eval_3, cronbachs_data$Eval_4)

Obtaining the Cronbach’s alpha can be achieved with the alpha() function using the new object created above. The na.rm argument tells the function to automatically remove observations with missing data.

alpha(clean_data, na.rm = TRUE)

## 
## Reliability analysis   
## Call: alpha(x = clean_data, na.rm = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N    ase mean  sd median_r
##       0.83      0.83     0.8      0.56 5.1 0.0063    3 1.1     0.54
## 
##     95% confidence boundaries 
##          lower alpha upper
## Feldt     0.82  0.83  0.85
## Duhachek  0.82  0.83  0.85
## 
##  Reliability if an item is dropped:
##                       raw_alpha std.alpha G6(smc) average_r S/N alpha se
## cronbachs_data.Eval_1      0.77      0.77    0.70      0.53 3.4   0.0091
## cronbachs_data.Eval_2      0.76      0.76    0.68      0.52 3.2   0.0095
## cronbachs_data.Eval_3      0.82      0.82    0.76      0.60 4.6   0.0075
## cronbachs_data.Eval_4      0.81      0.81    0.75      0.58 4.1   0.0079
##                         var.r med.r
## cronbachs_data.Eval_1 0.00059  0.53
## cronbachs_data.Eval_2 0.00062  0.51
## cronbachs_data.Eval_3 0.00864  0.56
## cronbachs_data.Eval_4 0.01328  0.53
## 
##  Item statistics 
##                          n raw.r std.r r.cor r.drop mean  sd
## cronbachs_data.Eval_1 1541  0.84  0.84  0.78   0.70  2.9 1.3
## cronbachs_data.Eval_2 1535  0.85  0.86  0.81   0.73  3.1 1.3
## cronbachs_data.Eval_3 1540  0.77  0.78  0.65   0.60  3.5 1.3
## cronbachs_data.Eval_4 1534  0.81  0.80  0.69   0.63  2.6 1.4
## 
## Non missing response frequency for each item
##                          1    2    3    4    5 miss
## cronbachs_data.Eval_1 0.16 0.27 0.26 0.18 0.13 0.17
## cronbachs_data.Eval_2 0.11 0.26 0.23 0.22 0.18 0.17
## cronbachs_data.Eval_3 0.07 0.16 0.24 0.24 0.29 0.17
## cronbachs_data.Eval_4 0.29 0.25 0.17 0.15 0.14 0.17

Reliability Statistics 

The Cronbach’s alpha coefficient can be found in the “raw_alpha” column of the first table in the output.