SMHS Cronbachs - Revision history

Dinov: /* Software */

2026-02-10T21:30:57Z

‎Software

Dinov: /* Software */

2026-02-10T21:30:41Z

‎Software

Dinov at 18:57, 8 December 2025

2025-12-08T18:57:15Z

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Dinov: /* Software */

2015-11-23T18:52:52Z

‎Software

Dinov: /* Problems */

2015-11-23T18:30:53Z

‎Problems

Dinov: /* Problems */

2015-11-23T18:30:22Z

‎Problems

Dinov: /* Problems */

2015-11-23T18:29:36Z

‎Problems

Dinov: /* Cronbach’s Alpha */

2015-11-19T20:30:29Z

‎Cronbach’s Alpha

Dinov: /* Cronbach’s Alpha */

2015-11-19T20:29:30Z

‎Cronbach’s Alpha

Dinov: /* Cronbach's $\alpha$ inference */

2015-05-04T15:50:11Z

‎Cronbach's $\alpha$ inference

@@ Line 267: / Line 267: @@
 </pre>
-The '''coefficientalpha'' R package offers robust estimation with missing data and non-normality, including standard errors and confidence intervals.
+The '''coefficientalpha''' R package offers robust estimation with missing data and non-normality, including standard errors and confidence intervals.
 === Cronbach's <math>\alpha</math> Calculations ===

@@ Line 267: / Line 267: @@
 </pre>
-The `coefficientalpha` R package offers robust estimation with missing data and non-normality, including standard errors and confidence intervals.
+The '''coefficientalpha'' R package offers robust estimation with missing data and non-normality, including standard errors and confidence intervals.
 === Cronbach's <math>\alpha</math> Calculations ===

@@ Line 241: / Line 241: @@
   ## extract the revised data into a new dataset named ‘datafile’
   library(boot)
-  cronbach.boot <- function(data,x) {cronbach(data[x,])[[3]]}
+  cronbach.boot <- function(data,x) {cronbach(data[x,])\([[3]]\)}
   res <- boot(datafile,cronbach.boot,1000)
   res

@@ Line 317: / Line 317: @@
 ===Problems===
-* Use the [[SOCR_TurkiyeStudentEvalData| Turkiye Student Course Evaluation survey (N=5,000)]] to compute the ICC ad Cronbach's alpha.
+* Use the [[SOCR_TurkiyeStudentEvalData| Turkiye Student Course Evaluation survey (N=5,000)]] to compute the ICC and Cronbach's alpha.
 ===References===

@@ Line 317: / Line 317: @@
 ===Problems===
-* Use the [[SOCR_TurkiyeStudentEvalData| Turkiye Student Course Evaluation survey (N=5,000)] to compute the ICC ad Cronbach's alpha.
+* Use the [[SOCR_TurkiyeStudentEvalData| Turkiye Student Course Evaluation survey (N=5,000)]] to compute the ICC ad Cronbach's alpha.
 ===References===

@@ Line 14: / Line 14: @@
 *Suppose we measure a quantity X, which is a sum of K components: $X=Y_{1}+ Y_{2}+⋯+Y_{k}$, then Cronbach’s alpha is defined as $\alpha =\frac{K}{K-1}$  $\left( 1-\frac{\sum_{i=1}^{K}\sigma^{2}_{{Y}_{i}}} {\sigma_{X}^{2}}\right)$, where $\sigma_{X}^{2}$ is the variance of the observed total test scores, and $ \sigma^{2}_{{Y}_{i}} $ is the variance of component $i$ for the current sample.
-: If items are scored from 0 to 1, then $\alpha =\frac{K}{K-1}$ $\left( 1-\frac{\sum_{i=1}^{K}P_{i}Q_{i}} {\sigma_{X}^{2}} \right)$, where $P_{i}$ is the proportion scoring 1 on item $i$ and $Q_{i}=1-P_{i}$, alternatively, Cronbach’s alpha can be defined as $\alpha$=$\frac{K\bar c}{(\bar v +(K-1) \bar c )}$,where K is as above, $\bar v$ is the average variance of each component and $\bar c$ is the average of all covariance between the components across the current sample of persons.
+: If items are scored from 0 to 1, then $\alpha =\frac{K}{K-1}$ $\left( 1-\frac{\sum_{i=1}^{K}P_{i}Q_{i}} {\sigma_{X}^{2}} \right)$, where $P_{i}$ is the proportion scoring 1 on item $i$ and $Q_{i}=1-P_{i}$. Alternatively, Cronbach’s alpha can be defined as $\alpha$=$\frac{K\bar c}{(\bar v +(K-1) \bar c )}$,where K is as above, $\bar v$ is the average variance of each component and $\bar c$ is the average of all covariance between the components across the current sample of persons.
 *The standardized Cronbach’s alpha can be defined as $\alpha_{standardized}=\frac{K\bar r}  {(1+(K-1)\bar r )}$, $\bar r$ is the mean of $\frac {K(K-1)}{2}$ non redundant correlation coefficients (i.e., the mean of an upper triangular, or lower triangular, correlation matrix).

@@ Line 314: / Line 314: @@
 : Thus [[SMHS_HypothesisTesting#Testing_a_claim_about_a_mean_with_large_sample_size |the $(1-\gamma)100\%$ confidence interval for $\alpha$]] is:
 $$\left ( \hat{\alpha} - z_{\frac{\gamma}{2}}\hat{\sigma}_{\hat{\alpha}}, \hat{\alpha} + z_{\frac{\gamma}{2}}\hat{\sigma}_{\hat{\alpha}} \right ), $$
-: where $z_{\frac{\gamma}{2}}$ is the normal distribution critical value corresponding to false-positive error rate $\gamma$.
+: where $z_{\frac{\gamma}{2}}$ is the [[EBook#The_Standard_Normal_Distribution |normal distribution critical value]] corresponding to false-positive error rate $\gamma$.
 ===Problems===