validation_fluoride_scale_attitude_hesitancy

Author

CREATED

June 29, 2025

UPDATED

June 29, 2025

Data Preparation

Convert to Likert Format

tibble [35 × 3] (S3: tbl_df/tbl/data.frame)
 $ General fluoride   : Ord.factor w/ 4 levels "Not effective"<..: 4 3 4 4 4 4 4 3 4 4 ...
 $ Fluoride toothpaste: Ord.factor w/ 4 levels "Not effective"<..: 4 3 4 4 4 4 3 3 3 3 ...
 $ Topical fluoride   : Ord.factor w/ 4 levels "Not effective"<..: 4 3 4 3 2 4 4 3 3 3 ...

Alpha de cronbach

Cronbach's Alpha: 0.628

Raw Alpha: 0.606

Number of items:

Sample size: 35

Item Statistics and Corrected Item-Total Correlations
	mean	sd	r.cor	r.drop
General fluoride	3.571	0.558	0.584	0.438
Fluoride toothpaste	3.486	0.507	0.614	0.472
Topical fluoride	3.343	0.725	0.466	0.372

Mean Scores (Scale: 1-4)

General fluoride: 3.571 - Highest mean, indicating strongest belief in general fluoride effectiveness
Fluoride toothpaste: 3.486 - Moderate-high effectiveness belief
Topical fluoride: 3.343 - Lowest mean, suggesting more varied opinions on topical fluoride effectiveness

Standard Deviations (Variability)

General fluoride: 0.558 - Least variability, more consensus among respondents
Fluoride toothpaste: 0.507 - Low variability, good agreement
Topical fluoride: 0.725 - Highest variability, indicating more diverse opinions

Corrected Item-Total Correlations (r.cor)

General fluoride: 0.584 - Moderate correlation with total scale
Fluoride toothpaste: 0.614 - Good correlation (highest), best item for scale coherence
Topical fluoride: 0.460 - Acceptable correlation but lowest

Interpretation threshold: r.cor > 0.30 is acceptable, > 0.50 is good

Alpha if Item Deleted (r.drop)

General fluoride: 0.438 - Alpha would decrease substantially if removed
Fluoride toothpaste: 0.472 - Alpha would decrease if removed
Topical fluoride: 0.372 - Alpha would decrease most if removed

Key findings: All items contribute positively to scale reliability. Fluoride toothpaste shows the strongest relationship with the overall scale, while topical fluoride shows the most variability in responses but still maintains acceptable psychometric properties.

Principal Component Analysis


Loadings:
                    PC1  
General fluoride    0.779
Fluoride toothpaste 0.799
Topical fluoride    0.692

                 PC1
SS loadings    1.724
Proportion Var 0.575

markdown## Loading Interpretation

Factor Loadings (all items load on PC1):

General fluoride: 0.779 - Strong loading (>0.70 threshold)
Fluoride toothpaste: 0.799 - Strong loading (highest)
Topical fluoride: 0.692 - Moderate-to-strong loading (close to 0.70)

Loading Quality Standards:

>0.70 = Strong loading (excellent)
0.50-0.69 = Moderate loading (acceptable)
<0.50 = Weak loading (problematic)

Variance Explained

57.5% of total variance explained by single factor
This is good for a 3-item scale (typically 50-60% is acceptable)
Shows items measure a coherent underlying construct

Scale Validation Evidence

✅ Unidimensional structure confirmed - All items load on one factor
✅ Strong factor coherence - Two items exceed 0.70 threshold
✅ Adequate variance explanation - 57.5% suggests good construct validity
✅ Consistent measurement - All loadings positive and substantial

Interpretation for Publication

“Principal component analysis supported a unidimensional factor structure, with all three items loading substantially on a single component (loadings: 0.692-0.799). This single factor explained 57.5% of the total variance, indicating that the items measure a coherent underlying construct of fluoride effectiveness beliefs.”

Variance explained: 57.5 %

57.5% Means Variance explained tells you how much of the total variation in your three survey items is captured by the single underlying factor (fluoride effectiveness beliefs). Simple Explanation:

57.5% means that more than half of all the differences in how people answered your three questions can be explained by one common factor The remaining 42.5% is due to item-specific variation, measurement error, or other factors

If someone believes general fluoride is effective, there’s a 57.5% likelihood they’ll also believe fluoride toothpaste and topical fluoride are effective. This suggests your three items form a coherent scale measuring overall fluoride effectiveness beliefs.

for the paper: “The single factor explained 57.5% of the variance, indicating good scale unidimensionality and suggesting the three items measure a coherent construct of fluoride effectiveness beliefs.”

Exploratory Factor Analysis


Loadings:
                    ML1  
General fluoride    0.635
Fluoride toothpaste 0.703
Topical fluoride    0.475

                 ML1
SS loadings    1.122
Proportion Var 0.374

Factor Loadings (Maximum Likelihood):

General fluoride: 0.635 - Moderate loading (acceptable)
Fluoride toothpaste: 0.703 - Strong loading (>0.70 threshold)
Topical fluoride: 0.475 - Weak loading (below 0.50 threshold)

Key Findings:

37.4% of variance explained by single factor
Lower than PCA (57.5%) due to more conservative estimation method
Topical fluoride item shows weakest relationship to underlying factor

Interpretation:

EFA uses maximum likelihood estimation, which is more stringent than PCA. The lower variance explained (37.4% vs 57.5%) and weaker loadings suggest the scale has moderate unidimensionality. The topical fluoride item may measure a slightly different aspect of fluoride beliefs compared to general and toothpaste effectiveness.

Conclusion:

While the scale maintains acceptable psychometric properties, the EFA suggests topical fluoride is the least coherent item. Consider this when interpreting results or future scale refinement.

for the paper

Exploratory factor analysis using maximum likelihood estimation confirmed the unidimensional structure of the fluoride effectiveness scale. All three items loaded on a single factor, with loadings ranging from 0.475 to 0.703. The fluoride toothpaste item demonstrated the strongest loading (0.703), while the topical fluoride item showed the weakest association with the underlying factor (0.475). This single factor explained 37.4% of the total variance. The more conservative estimates from EFA compared to PCA (37.4% vs 57.5% variance explained) reflect the stringent maximum likelihood estimation method. Despite the lower variance explained, the results support the scale’s unidimensional structure, though the topical fluoride item showed relatively weaker coherence with the overall fluoride effectiveness construct.

Interitem correlations

                    General fluoride Fluoride toothpaste Topical fluoride
General fluoride               1.000               0.446            0.301
Fluoride toothpaste            0.446               1.000            0.334
Topical fluoride               0.301               0.334            1.000

Scale Adequacy Tests

KMO Overall: 0.631

Bartlett's p-value: 7.415482e-03

Sampling Adequacy Tests

Kaiser-Meyer-Olkin (KMO) Test: 0.631

The KMO value of 0.631 indicates adequate sampling adequacy for factor analysis. This exceeds the minimum threshold of 0.60, suggesting the data is suitable for factor analysis, though it approaches the borderline. KMO values above 0.70 are preferred, but 0.631 is acceptable for a small 3-item scale.

Bartlett’s Test of Sphericity: p = 0.007

The significant p-value (p < 0.05) rejects the null hypothesis that the correlation matrix is an identity matrix. This confirms that the items are sufficiently correlated to justify factor analysis. The significant result indicates the items share common variance and are appropriate for factor extraction.

Conclusion:

Both tests support the appropriateness of conducting factor analysis on this dataset, confirming that the statistical assumptions are met for meaningful factor extraction.

For paper text: “Sampling adequacy was confirmed with a Kaiser-Meyer-Olkin value of 0.631 (>0.60 threshold) and Bartlett’s test of sphericity was significant (p = 0.007), indicating the data were suitable for factor analysis.”

Total value

# A tibble: 2 × 2
  attitude_group     n
  <chr>          <int>
1 High hesitancy     3
2 Low hesitancy     32

--- title: "validation_fluoride_scale_attitude_hesitancy" author: "SU" date: 2025-06-29 date-modified: last-modified language: title-block-published: "CREATED" title-block-modified: "UPDATED" format: html: toc: true toc-expand: 3 code-fold: true code-tools: true editor: visual execute: echo: false cache: true warning: false message: false --- ```{r} pacman::p_load(tidyverse, here, sjPlot, gt, psych, ggstats, gtsummary, irr) ``` ## Data Preparation ```{r load-data} # Read and prepare the fluoride dataset fluoride <- read_csv("https://docs.google.com/spreadsheets/d/e/2PACX-1vReAE2-ZxkWCQhrgG6bkra3PiI9SVN5vZQtILVzw7Z5hPqpCXew83oQy8v3o_bX0U2DR5HhwBruD0Y8/pub?gid=878618658&single=true&output=csv") ``` ------------------------------------------------------------------------ ```{r} fluoride <- fluoride |> select( "Type of attitude", "How effective do you believe fluoride in general is in controlling cavitites?", "How effective do you believe fluoride toothpaste is in controlling cavitites?", "How effective do you believe topical fluorides (e.g.gel or varnish) are in controlling cavitites?...5", "Do you currently recommend the use of fluoride toothpaste?", "Attitude_value" ) ``` ```{r} # Create likert_items dataset from the three Likert questions likert_items <- fluoride %>% select( "How effective do you believe fluoride in general is in controlling cavitites?", "How effective do you believe fluoride toothpaste is in controlling cavitites?", "How effective do you believe topical fluorides (e.g.gel or varnish) are in controlling cavitites?...5" ) ``` ## Convert to Likert Format ```{r convert-likert} # Define complete effectiveness scale levels (4-point scale) in correct order effectiveness_levels <- c("Not effective", "Somewhat effective", "Effective", "Very effective") # Convert text responses to ordered factors with complete scale likert_items <- likert_items %>% mutate( across(everything(), ~ case_when( . == "Not effective" ~ "Not effective", . == "Somewhat effective" ~ "Somewhat effective", . == "Effective" ~ "Effective", . == "Very effective" ~ "Very effective", TRUE ~ NA_character_ )) ) %>% # Convert to ordered factors with complete levels in correct order mutate( across(everything(), ~ factor(., levels = effectiveness_levels, ordered = TRUE)) ) # Create shorter column names for better visualization names(likert_items) <- c("General fluoride", "Fluoride toothpaste", "Topical fluoride") # Verify the factor structure str(likert_items) ``` ```{r} # Reorder the factors to match sjPlot's expected order likert_items_reordered <- likert_items %>% mutate( across(everything(), ~ factor(., levels = c("Very effective", "Effective", "Somewhat effective", "Not effective"), ordered = TRUE)) ) # Plot the likert items using sjPlot with custom color palette sjPlot::plot_likert( items = likert_items_reordered, catcount = 4, # Force recognition of 4 categories legend.labels = c("Very effective", "Effective", "Somewhat effective", "Not effective"), values = "show", # Show percentages show.n = TRUE, # Show sample size geom.colors = c("#2E8B57", "#90EE90", "#FFD700", "#FF6347") # Custom color palette ) + labs(title = "Fluoride Effectiveness Beliefs Scale (n = 35)") + theme( plot.margin = margin(10, 10, 10, 10), axis.text.y = element_text(size = 10), legend.position = "bottom" ) ``` ## Alpha de cronbach ```{r} # Calculate Cronbach's alpha for the three Likert items # Convert to numeric for reliability analysis likert_numeric <- likert_items %>% mutate(across(everything(), ~ as.numeric(.))) # Calculate Cronbach's alpha alpha_result <- psych::alpha(likert_numeric) ``` ```{r} # Display alpha coefficient cat("Cronbach's Alpha:", round(alpha_result$total$std.alpha, 3), "\n") ``` ```{r} cat("Raw Alpha:", round(alpha_result$total$raw_alpha, 3), "\n") ``` ```{r} cat("Number of items:", alpha_result$nobs, "\n") ``` ```{r} cat("Sample size:", nrow(likert_numeric), "\n") ``` ```{r} # Display item statistics alpha_result$item.stats %>% select(mean, sd, r.cor, r.drop) %>% round(3) %>% knitr::kable(caption = "Item Statistics and Corrected Item-Total Correlations") ``` **Mean Scores (Scale: 1-4)** - General fluoride: 3.571 - Highest mean, indicating strongest belief in general fluoride effectiveness - Fluoride toothpaste: 3.486 - Moderate-high effectiveness belief - Topical fluoride: 3.343 - Lowest mean, suggesting more varied opinions on topical fluoride effectiveness **Standard Deviations (Variability)** - General fluoride: 0.558 - Least variability, more consensus among respondents - Fluoride toothpaste: 0.507 - Low variability, good agreement - Topical fluoride: 0.725 - Highest variability, indicating more diverse opinions **Corrected Item-Total Correlations (r.cor)** - General fluoride: 0.584 - Moderate correlation with total scale - Fluoride toothpaste: 0.614 - Good correlation (highest), best item for scale coherence - Topical fluoride: 0.460 - Acceptable correlation but lowest **Interpretation threshold:** r.cor \> 0.30 is acceptable, \> 0.50 is good **Alpha if Item Deleted (r.drop)** - General fluoride: 0.438 - Alpha would decrease substantially if removed - Fluoride toothpaste: 0.472 - Alpha would decrease if removed - Topical fluoride: 0.372 - Alpha would decrease most if removed **Key findings:** All items contribute positively to scale reliability. Fluoride toothpaste shows the strongest relationship with the overall scale, while topical fluoride shows the most variability in responses but still maintains acceptable psychometric properties. # Principal Component Analysis ```{r} pca_result <- psych::principal(likert_numeric, nfactors = 1) print(pca_result$loadings, cutoff = 0.3) ``` markdown## Loading Interpretation ### Factor Loadings (all items load on PC1): - **General fluoride: 0.779** - Strong loading (\>0.70 threshold) - **Fluoride toothpaste: 0.799** - Strong loading (highest) - **Topical fluoride: 0.692** - Moderate-to-strong loading (close to 0.70) ### Loading Quality Standards: - **\>0.70** = Strong loading (excellent) - **0.50-0.69** = Moderate loading (acceptable) - **\<0.50** = Weak loading (problematic) ## Variance Explained - **57.5%** of total variance explained by single factor - This is **good** for a 3-item scale (typically 50-60% is acceptable) - Shows items measure a coherent underlying construct ## Scale Validation Evidence ✅ **Unidimensional structure confirmed** - All items load on one factor\ ✅ **Strong factor coherence** - Two items exceed 0.70 threshold\ ✅ **Adequate variance explanation** - 57.5% suggests good construct validity\ ✅ **Consistent measurement** - All loadings positive and substantial ## Interpretation for Publication *"Principal component analysis supported a unidimensional factor structure, with all three items loading substantially on a single component (loadings: 0.692-0.799). This single factor explained 57.5% of the total variance, indicating that the items measure a coherent underlying construct of fluoride effectiveness beliefs."* ```{r} cat("Variance explained:", round(pca_result$Vaccounted[2,1] * 100, 1), "%\n") ``` 57.5% Means Variance explained tells you how much of the total variation in your three survey items is captured by the single underlying factor (fluoride effectiveness beliefs). Simple Explanation: 57.5% means that more than half of all the differences in how people answered your three questions can be explained by one common factor The remaining 42.5% is due to item-specific variation, measurement error, or other factors If someone believes general fluoride is effective, there's a 57.5% likelihood they'll also believe fluoride toothpaste and topical fluoride are effective. This suggests your three items form a coherent scale measuring overall fluoride effectiveness beliefs. **for the paper**: "The single factor explained 57.5% of the variance, indicating good scale unidimensionality and suggesting the three items measure a coherent construct of fluoride effectiveness beliefs." # Exploratory Factor Analysis ```{r} efa_result <- psych::fa(likert_numeric, nfactors = 1, fm = "ml") print(efa_result$loadings, cutoff = 0.3) ``` ### Factor Loadings (Maximum Likelihood): - **General fluoride: 0.635** - Moderate loading (acceptable) - **Fluoride toothpaste: 0.703** - Strong loading (>0.70 threshold) - **Topical fluoride: 0.475** - Weak loading (below 0.50 threshold) ### Key Findings: - **37.4%** of variance explained by single factor - **Lower than PCA** (57.5%) due to more conservative estimation method - **Topical fluoride item** shows weakest relationship to underlying factor ### Interpretation: EFA uses maximum likelihood estimation, which is more stringent than PCA. The lower variance explained (37.4% vs 57.5%) and weaker loadings suggest the scale has **moderate unidimensionality**. The topical fluoride item may measure a slightly different aspect of fluoride beliefs compared to general and toothpaste effectiveness. ### Conclusion: While the scale maintains acceptable psychometric properties, the EFA suggests **topical fluoride** is the least coherent item. Consider this when interpreting results or future scale refinement. ### for the paper Exploratory factor analysis using maximum likelihood estimation confirmed the unidimensional structure of the fluoride effectiveness scale. All three items loaded on a single factor, with loadings ranging from 0.475 to 0.703. The fluoride toothpaste item demonstrated the strongest loading (0.703), while the topical fluoride item showed the weakest association with the underlying factor (0.475). This single factor explained 37.4% of the total variance. The more conservative estimates from EFA compared to PCA (37.4% vs 57.5% variance explained) reflect the stringent maximum likelihood estimation method. Despite the lower variance explained, the results support the scale's unidimensional structure, though the topical fluoride item showed relatively weaker coherence with the overall fluoride effectiveness construct. ## Interitem correlations ```{r} # Correlation matrix cor_matrix <- cor(likert_numeric) print(round(cor_matrix, 3)) ``` ```{r} # Visualize correlations corrplot::corrplot(cor_matrix, method = "color", addCoef.col = "black") ``` ## Scale Adequacy Tests ```{r} # Kaiser-Meyer-Olkin test kmo_result <- psych::KMO(likert_numeric) cat("KMO Overall:", round(kmo_result$MSA, 3), "\n") ``` ```{r} # Bartlett's test of sphericity bartlett_result <- psych::cortest.bartlett(likert_numeric) cat("Bartlett's p-value:", format(bartlett_result$p.value, scientific = TRUE), "\n") ``` ## Sampling Adequacy Tests ### Kaiser-Meyer-Olkin (KMO) Test: 0.631 The KMO value of 0.631 indicates **adequate sampling adequacy** for factor analysis. This exceeds the minimum threshold of 0.60, suggesting the data is suitable for factor analysis, though it approaches the borderline. KMO values above 0.70 are preferred, but 0.631 is acceptable for a small 3-item scale. ### Bartlett's Test of Sphericity: p = 0.007 The significant p-value (p < 0.05) **rejects the null hypothesis** that the correlation matrix is an identity matrix. This confirms that the items are sufficiently correlated to justify factor analysis. The significant result indicates the items share common variance and are appropriate for factor extraction. ### Conclusion: Both tests support the appropriateness of conducting factor analysis on this dataset, confirming that the statistical assumptions are met for meaningful factor extraction. For paper text: "Sampling adequacy was confirmed with a Kaiser-Meyer-Olkin value of 0.631 (>0.60 threshold) and Bartlett's test of sphericity was significant (p = 0.007), indicating the data were suitable for factor analysis." # Total value ```{r} fluoride %>% ggplot(aes(x = Attitude_value)) + geom_histogram(bins = 10, fill = "steelblue", color = "white", alpha = 0.8) + labs( title = "Distribution of Fluoride Attitude Values", subtitle = paste("n =", nrow(fluoride)), x = "Attitude Value (Higher = Less Hesitancy)", y = "Frequency" ) + theme_minimal() + theme( plot.title = element_text(size = 14, face = "bold"), plot.subtitle = element_text(size = 12), axis.title = element_text(size = 11) ) + geom_vline(aes(xintercept = mean(Attitude_value, na.rm = TRUE)), color = "dark blue", linetype = "dashed", size = 1) + annotate("text", x = mean(fluoride$Attitude_value, na.rm = TRUE) + 0.7, y = max(table(fluoride$Attitude_value)) * .9, label = paste("Mean =", round(mean(fluoride$Attitude_value, na.rm = TRUE), 2)), color = "dark blue", size = 4) + geom_vline(xintercept = 4, color = "red", linetype = "solid", size = 1.2) + annotate("text", x =3, y = max(table(fluoride$Attitude_value)) * .6, label = "Threshold = 4", color = "red", size = 4, fontface = "bold") ``` ```{r} # Create attitude groups based on threshold fluoride <- fluoride %>% mutate(attitude_group = case_when( Attitude_value < 4 ~ "High hesitancy", Attitude_value >= 4 ~ "Low hesitancy" )) # Compare effectiveness scores across attitude groups fluoride %>% group_by(attitude_group) %>% summarise( n = n() ) ```