Factor Analysis Report
farai
2025-11-30
Combined R Markdown Code
Load Data
Data <- read_csv("C://Users//farai//Downloads//FaDataset.csv")
attach(Data)
names(Data)## [1] "Obs" "Form of letter of application"
## [3] "Appearance" "Academic ability"
## [5] "Likeability" "Self-confidence"
## [7] "Lucidity" "Honesty"
## [9] "Salesmanship" "Experience"
## [11] "Drive" "Ambition"
## [13] "Grasp" "Potential"
## [15] "Keeness to join" "Suitability"options(scipen = 999)Overall Raw Score
Data$OverallRaw <-
Data$`Form of letter of application` +
Data$Appearance +
Data$`Academic ability` +
Data$Likeability +
Data$`Self-confidence` +
Data$Lucidity +
Data$Honesty +
Data$Salesmanship +
Data$Experience +
Data$Drive +
Data$Ambition +
Data$Grasp +
Data$Potential +
Data$`Keeness to join` +
Data$SuitabilityCreate Analysis DataFrame
DataFrame <- Data[, c(
"Form of letter of application",
"Appearance",
"Academic ability",
"Likeability",
"Self-confidence",
"Lucidity",
"Honesty",
"Salesmanship",
"Experience",
"Drive",
"Ambition",
"Grasp",
"Potential",
"Keeness to join",
"Suitability"
)]Scree Plot & Eigenvalues
scree(DataFrame, factors = TRUE, main = "Scree Plot")
ev <- eigen(cor(DataFrame))
ev$values## [1] 7.51379418 2.05630117 1.45581948 1.19789771 0.73915262 0.49457907
## [7] 0.35126183 0.30990202 0.25696154 0.18491037 0.15268036 0.09756308
## [13] 0.08881880 0.06463323 0.03572455cumsum(ev$values)/15## [1] 0.5009196 0.6380064 0.7350610 0.8149208 0.8641977 0.8971696 0.9205871
## [8] 0.9412472 0.9583780 0.9707053 0.9808840 0.9873882 0.9933095 0.9976184
## [15] 1.0000000Orthogonal Factor Analysis
ORTHOFA <- factanal(DataFrame, factors = 3, rotation="varimax", fm="pa")
print(ORTHOFA, digits=3, cutoff=.1, sort=TRUE)##
## Call:
## factanal(x = DataFrame, factors = 3, rotation = "varimax", fm = "pa")
##
## Uniquenesses:
## Form of letter of application Appearance
## 0.536 0.699
## Academic ability Likeability
## 0.944 0.005
## Self-confidence Lucidity
## 0.117 0.198
## Honesty Salesmanship
## 0.442 0.145
## Experience Drive
## 0.356 0.239
## Ambition Grasp
## 0.155 0.198
## Potential Keeness to join
## 0.178 0.419
## Suitability
## 0.191
##
## Loadings:
## Factor1 Factor2 Factor3
## Self-confidence 0.925 0.135
## Lucidity 0.833 0.120 0.307
## Salesmanship 0.872 0.270 0.149
## Drive 0.763 0.381 0.187
## Ambition 0.891 0.174 0.144
## Grasp 0.790 0.286 0.311
## Potential 0.720 0.358 0.420
## Form of letter of application 0.120 0.644 0.189
## Experience 0.799
## Suitability 0.333 0.824 0.137
## Likeability 0.202 0.155 0.964
## Honesty 0.274 -0.242 0.651
## Keeness to join 0.440 0.221 0.582
## Appearance 0.441 0.182 0.272
## Academic ability 0.224
##
## Factor1 Factor2 Factor3
## SS loadings 5.464 2.428 2.286
## Proportion Var 0.364 0.162 0.152
## Cumulative Var 0.364 0.526 0.679
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 128.86 on 63 degrees of freedom.
## The p-value is 0.00000198Create Ortho Factor Averages
Data$OrthoFA1 <- (
Data$`Self-confidence` +
Data$Lucidity +
Data$Salesmanship +
Data$Drive +
Data$Ambition +
Data$Grasp +
Data$Potential
) / 7
Data$OrthoFA2 <- (
Data$`Form of letter of application` +
Data$Experience +
Data$Suitability
) / 3
Data$OrthoFA3 <- (
Data$Likeability +
Data$Honesty +
Data$`Keeness to join`
) / 3Ortho Reliability
Ortho1_DataFrame <- Data[, c("Self-confidence","Salesmanship","Grasp","Drive","Ambition","Lucidity","Potential")]
Ortho2_DataFrame <- Data[, c("Form of letter of application","Experience","Suitability")]
Ortho3_DataFrame <- Data[, c("Likeability","Honesty","Keeness to join")]
alpha(Ortho1_DataFrame)##
## Reliability analysis
## Call: alpha(x = Ortho1_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.96 0.96 0.97 0.78 25 0.0086 5.9 2.7 0.78
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.94 0.96 0.98
## Duhachek 0.94 0.96 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Self-confidence 0.96 0.96 0.96 0.79 23 0.0096 0.0028 0.78
## Salesmanship 0.95 0.95 0.96 0.77 20 0.0107 0.0040 0.78
## Grasp 0.95 0.95 0.96 0.78 21 0.0104 0.0028 0.78
## Drive 0.96 0.96 0.97 0.79 23 0.0095 0.0033 0.78
## Ambition 0.95 0.95 0.96 0.77 21 0.0104 0.0040 0.78
## Lucidity 0.95 0.95 0.96 0.78 21 0.0102 0.0034 0.78
## Potential 0.95 0.96 0.96 0.78 22 0.0099 0.0032 0.78
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Self-confidence 48 0.87 0.88 0.86 0.83 6.9 2.4
## Salesmanship 48 0.93 0.92 0.91 0.89 4.9 3.4
## Grasp 48 0.92 0.91 0.91 0.88 6.2 3.0
## Drive 48 0.87 0.87 0.84 0.83 5.3 2.9
## Ambition 48 0.92 0.92 0.91 0.88 6.0 2.9
## Lucidity 48 0.91 0.91 0.90 0.87 6.3 3.2
## Potential 48 0.90 0.89 0.88 0.86 5.7 3.2alpha(Ortho2_DataFrame)##
## Reliability analysis
## Call: alpha(x = Ortho2_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.82 0.76 0.61 4.7 0.043 5.4 2.7 0.59
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.71 0.82 0.89
## Duhachek 0.74 0.82 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N
## Form of letter of application 0.82 0.82 0.69 0.69 4.5
## Experience 0.73 0.74 0.59 0.59 2.8
## Suitability 0.70 0.71 0.55 0.55 2.4
## alpha se var.r med.r
## Form of letter of application 0.052 NA 0.69
## Experience 0.076 NA 0.59
## Suitability 0.084 NA 0.55
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Form of letter of application 48 0.80 0.83 0.67 0.62 6.0 2.7
## Experience 48 0.88 0.87 0.78 0.70 4.2 3.3
## Suitability 48 0.89 0.88 0.81 0.73 6.0 3.3alpha(Ortho3_DataFrame)##
## Reliability analysis
## Call: alpha(x = Ortho3_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.81 0.77 0.59 4.4 0.046 6.6 2.3 0.65
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.70 0.82 0.89
## Duhachek 0.72 0.82 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Likeability 0.62 0.62 0.45 0.45 1.6 0.110 NA 0.45
## Honesty 0.81 0.81 0.69 0.69 4.4 0.054 NA 0.69
## Keeness to join 0.78 0.78 0.65 0.65 3.6 0.062 NA 0.65
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Likeability 48 0.92 0.91 0.86 0.78 6.1 2.8
## Honesty 48 0.81 0.82 0.67 0.60 8.0 2.5
## Keeness to join 48 0.84 0.83 0.71 0.63 5.6 2.7Ortho Overall Score
Data$Ortho_Overall <-
Data$OrthoFA1 +
Data$OrthoFA2 +
Data$OrthoFA3 +
Data$`Academic ability`
head(Data[order(-Data$Ortho_Overall), ], 3)## # A tibble: 3 × 21
## Obs Form of letter of applicatio…¹ Appearance `Academic ability` Likeability
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 40 10 6 9 10
## 2 39 10 6 9 10
## 3 8 9 9 9 8
## # ℹ abbreviated name: ¹`Form of letter of application`
## # ℹ 16 more variables: `Self-confidence` <dbl>, Lucidity <dbl>, Honesty <dbl>,
## # Salesmanship <dbl>, Experience <dbl>, Drive <dbl>, Ambition <dbl>,
## # Grasp <dbl>, Potential <dbl>, `Keeness to join` <dbl>, Suitability <dbl>,
## # OverallRaw <dbl>, OrthoFA1 <dbl>, OrthoFA2 <dbl>, OrthoFA3 <dbl>,
## # Ortho_Overall <dbl>Oblique Factor Analysis
OBLIQFA <- factanal(DataFrame, factors=3, rotation="oblimin", fm="pa")
print(OBLIQFA, digits=3, cutoff=.1, sort=TRUE)##
## Call:
## factanal(x = DataFrame, factors = 3, rotation = "oblimin", fm = "pa")
##
## Uniquenesses:
## Form of letter of application Appearance
## 0.536 0.699
## Academic ability Likeability
## 0.944 0.005
## Self-confidence Lucidity
## 0.117 0.198
## Honesty Salesmanship
## 0.442 0.145
## Experience Drive
## 0.356 0.239
## Ambition Grasp
## 0.155 0.198
## Potential Keeness to join
## 0.178 0.419
## Suitability
## 0.191
##
## Loadings:
## Factor1 Factor2 Factor3
## Self-confidence 1.013 -0.251
## Lucidity 0.831 0.140
## Salesmanship 0.896 0.135
## Drive 0.746 0.265
## Ambition 0.932
## Grasp 0.758 0.153 0.147
## Potential 0.639 0.232 0.279
## Form of letter of application 0.639 0.149
## Experience 0.822
## Suitability 0.213 0.798
## Likeability 1.008
## Honesty 0.168 -0.341 0.665
## Keeness to join 0.303 0.120 0.528
## Appearance 0.393 0.102 0.189
## Academic ability 0.228
##
## Factor1 Factor2 Factor3
## SS loadings 5.254 2.15 1.933
##
## Factor Correlations:
## Factor1 Factor2 Factor3
## Factor1 1.000 0.316 0.454
## Factor2 0.316 1.000 0.209
## Factor3 0.454 0.209 1.000
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 128.86 on 63 degrees of freedom.
## The p-value is 0.00000198Oblique Factor Averages
Data$ObliqFA1 <- (
Data$`Self-confidence` +
Data$Salesmanship +
Data$Grasp +
Data$Drive +
Data$Ambition +
Data$Lucidity +
Data$Potential
) / 7
Data$ObliqFA2 <- (
Data$`Form of letter of application` +
Data$Experience +
Data$Suitability
) / 3
Data$ObliqFA3 <- (
Data$Likeability +
Data$Honesty +
Data$`Keeness to join`
) / 3Oblique Reliability
Obliq1_DataFrame <- Data[, c("Self-confidence","Salesmanship","Grasp","Drive","Ambition","Lucidity","Potential")]
Obliq2_DataFrame <- Data[, c("Form of letter of application","Experience","Suitability")]
Obliq3_DataFrame <- Data[, c("Likeability","Honesty","Keeness to join")]
alpha(Obliq1_DataFrame)##
## Reliability analysis
## Call: alpha(x = Obliq1_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.96 0.96 0.97 0.78 25 0.0086 5.9 2.7 0.78
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.94 0.96 0.98
## Duhachek 0.94 0.96 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Self-confidence 0.96 0.96 0.96 0.79 23 0.0096 0.0028 0.78
## Salesmanship 0.95 0.95 0.96 0.77 20 0.0107 0.0040 0.78
## Grasp 0.95 0.95 0.96 0.78 21 0.0104 0.0028 0.78
## Drive 0.96 0.96 0.97 0.79 23 0.0095 0.0033 0.78
## Ambition 0.95 0.95 0.96 0.77 21 0.0104 0.0040 0.78
## Lucidity 0.95 0.95 0.96 0.78 21 0.0102 0.0034 0.78
## Potential 0.95 0.96 0.96 0.78 22 0.0099 0.0032 0.78
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Self-confidence 48 0.87 0.88 0.86 0.83 6.9 2.4
## Salesmanship 48 0.93 0.92 0.91 0.89 4.9 3.4
## Grasp 48 0.92 0.91 0.91 0.88 6.2 3.0
## Drive 48 0.87 0.87 0.84 0.83 5.3 2.9
## Ambition 48 0.92 0.92 0.91 0.88 6.0 2.9
## Lucidity 48 0.91 0.91 0.90 0.87 6.3 3.2
## Potential 48 0.90 0.89 0.88 0.86 5.7 3.2alpha(Obliq2_DataFrame)##
## Reliability analysis
## Call: alpha(x = Obliq2_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.82 0.76 0.61 4.7 0.043 5.4 2.7 0.59
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.71 0.82 0.89
## Duhachek 0.74 0.82 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N
## Form of letter of application 0.82 0.82 0.69 0.69 4.5
## Experience 0.73 0.74 0.59 0.59 2.8
## Suitability 0.70 0.71 0.55 0.55 2.4
## alpha se var.r med.r
## Form of letter of application 0.052 NA 0.69
## Experience 0.076 NA 0.59
## Suitability 0.084 NA 0.55
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Form of letter of application 48 0.80 0.83 0.67 0.62 6.0 2.7
## Experience 48 0.88 0.87 0.78 0.70 4.2 3.3
## Suitability 48 0.89 0.88 0.81 0.73 6.0 3.3alpha(Obliq3_DataFrame)##
## Reliability analysis
## Call: alpha(x = Obliq3_DataFrame)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.81 0.77 0.59 4.4 0.046 6.6 2.3 0.65
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.70 0.82 0.89
## Duhachek 0.72 0.82 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Likeability 0.62 0.62 0.45 0.45 1.6 0.110 NA 0.45
## Honesty 0.81 0.81 0.69 0.69 4.4 0.054 NA 0.69
## Keeness to join 0.78 0.78 0.65 0.65 3.6 0.062 NA 0.65
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Likeability 48 0.92 0.91 0.86 0.78 6.1 2.8
## Honesty 48 0.81 0.82 0.67 0.60 8.0 2.5
## Keeness to join 48 0.84 0.83 0.71 0.63 5.6 2.7Oblique Overall Score
Data$Obliq_Overall_Score <-
Data$ObliqFA1 +
Data$ObliqFA2 +
Data$ObliqFA3 +
Data$`Academic ability`
head(Data[order(-Data$Obliq_Overall_Score), ], 3)## # A tibble: 3 × 25
## Obs Form of letter of applicatio…¹ Appearance `Academic ability` Likeability
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 40 10 6 9 10
## 2 39 10 6 9 10
## 3 8 9 9 9 8
## # ℹ abbreviated name: ¹`Form of letter of application`
## # ℹ 20 more variables: `Self-confidence` <dbl>, Lucidity <dbl>, Honesty <dbl>,
## # Salesmanship <dbl>, Experience <dbl>, Drive <dbl>, Ambition <dbl>,
## # Grasp <dbl>, Potential <dbl>, `Keeness to join` <dbl>, Suitability <dbl>,
## # OverallRaw <dbl>, OrthoFA1 <dbl>, OrthoFA2 <dbl>, OrthoFA3 <dbl>,
## # Ortho_Overall <dbl>, ObliqFA1 <dbl>, ObliqFA2 <dbl>, ObliqFA3 <dbl>,
## # Obliq_Overall_Score <dbl>