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library(psych)##
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## %+%, alphalibrary(CTT)##
## Attaching package: 'CTT'
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## The following objects are masked from 'package:psych':
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## polyserial, reliabilityThis dataset represents responses from 100 students who completed a 20 item multiple-choice test designed to measure their understanding of basic statistics concepts.
Each item is scored dichotomously, meaning:
The purpose of this dataset is to help students practice Classical Test Theory (CTT) analysis.
data <- import("CTt_week10_assignment_dataset.xlsx")Please use head() function and then check the data quality
head(data)## StudentID Item1 Item2 Item3 Item4 Item5 Item6 Item7 Item8 Item9 Item10 Item11
## 1 S001 0 0 0 0 0 0 1 0 1 0 0
## 2 S002 1 1 0 1 1 1 1 1 1 0 0
## 3 S003 1 1 1 1 1 1 1 1 0 0 0
## 4 S004 0 0 1 0 1 1 0 0 0 0 0
## 5 S005 1 0 0 1 1 1 0 1 0 0 0
## 6 S006 0 1 1 1 1 1 1 1 1 1 1
## Item12 Item13 Item14 Item15 Item16 Item17 Item18 Item19 Item20
## 1 1 1 0 0 0 0 0 0 0
## 2 0 0 0 1 1 0 0 1 1
## 3 1 0 0 1 1 0 0 0 1
## 4 0 0 0 0 0 0 0 0 0
## 5 1 0 0 1 0 0 0 0 1
## 6 1 0 1 1 1 1 1 0 0please use describe() function and then calculate descriptive statistics
describe(data)## vars n mean sd median trimmed mad min max range skew
## StudentID* 1 100 50.50 29.01 50.5 50.50 37.06 1 100 99 0.00
## Item1 2 100 0.67 0.47 1.0 0.71 0.00 0 1 1 -0.71
## Item2 3 100 0.65 0.48 1.0 0.69 0.00 0 1 1 -0.62
## Item3 4 100 0.61 0.49 1.0 0.64 0.00 0 1 1 -0.44
## Item4 5 100 0.68 0.47 1.0 0.72 0.00 0 1 1 -0.76
## Item5 6 100 0.63 0.49 1.0 0.66 0.00 0 1 1 -0.53
## Item6 7 100 0.65 0.48 1.0 0.69 0.00 0 1 1 -0.62
## Item7 8 100 0.54 0.50 1.0 0.55 0.00 0 1 1 -0.16
## Item8 9 100 0.47 0.50 0.0 0.46 0.00 0 1 1 0.12
## Item9 10 100 0.56 0.50 1.0 0.58 0.00 0 1 1 -0.24
## Item10 11 100 0.51 0.50 1.0 0.51 0.00 0 1 1 -0.04
## Item11 12 100 0.56 0.50 1.0 0.58 0.00 0 1 1 -0.24
## Item12 13 100 0.39 0.49 0.0 0.36 0.00 0 1 1 0.44
## Item13 14 100 0.42 0.50 0.0 0.40 0.00 0 1 1 0.32
## Item14 15 100 0.43 0.50 0.0 0.41 0.00 0 1 1 0.28
## Item15 16 100 0.40 0.49 0.0 0.38 0.00 0 1 1 0.40
## Item16 17 100 0.40 0.49 0.0 0.38 0.00 0 1 1 0.40
## Item17 18 100 0.36 0.48 0.0 0.32 0.00 0 1 1 0.57
## Item18 19 100 0.34 0.48 0.0 0.30 0.00 0 1 1 0.67
## Item19 20 100 0.30 0.46 0.0 0.25 0.00 0 1 1 0.86
## Item20 21 100 0.34 0.48 0.0 0.30 0.00 0 1 1 0.67
## kurtosis se
## StudentID* -1.24 2.90
## Item1 -1.51 0.05
## Item2 -1.63 0.05
## Item3 -1.82 0.05
## Item4 -1.44 0.05
## Item5 -1.74 0.05
## Item6 -1.63 0.05
## Item7 -1.99 0.05
## Item8 -2.01 0.05
## Item9 -1.96 0.05
## Item10 -2.02 0.05
## Item11 -1.96 0.05
## Item12 -1.82 0.05
## Item13 -1.92 0.05
## Item14 -1.94 0.05
## Item15 -1.86 0.05
## Item16 -1.86 0.05
## Item17 -1.69 0.05
## Item18 -1.57 0.05
## Item19 -1.27 0.05
## Item20 -1.57 0.05Interpretation:
The dataset contains responses from 100 students across 20 items. The
head() output confirms the dataset loaded correctly, and
describe() shows item means ranging approximately from 0.30
to 0.68, indicating variation in item difficulty. The dataset appears
clean and appropriate for CTT analysis.
response_data <- data %>%
select(Item1:Item20)itemanalysis_ctt <- itemAnalysis(response_data)itemanalysis_ctt##
## Number of Items
## 20
##
## Number of Examinees
## 100
##
## Coefficient Alpha
## 0.812(Task 1-1)
Three items with highest item difficulty:
Item4 (0.68), Item1 (0.67), Item2 (0.65)
Three items with lowest difficulty:
Item19 (0.30), Item18 (0.34), Item20 (0.34)
(Task 1-2)
Item difficulty looks good overall, most items fall within the acceptable range of 0.30 to 0.80, with a healthy mix of easier and harder questions to measure a range of student abilities.
(Task 2-1)
Three items with strongest item discrimination:
Item9 (0.60), Item8 (0.51), Item15 (0.49)
Three items with weakest item discrimination:
Item13 (0.21), Item7 (0.25), Item6 (0.25)
(Task 2-2)
Discrimination looks strong overall — most items scored above 0.30, and none fell below the 0.20 threshold. A few items on the lower end could use a closer look, but the test holds up well across the board.
Overall, the test holds up well — difficulty values are nicely spread out, and most items do a good job separating higher and lower performers. A few items could be tweaked, but the test is solid overall.