Suppose that I performed a latent-class analysis on several "true-false" questions designed to measure students' engagement with school. I got the results presented in the table below:

\begin{array}{lccc}\text { Survey Questions } &\text { Class } 1(n=42) & \text { Class } 2(n=58) & \text { Class } 3(n=40)\\\\&30 \% & 41 \% & 29 \% \\\\\hline \text { 1. I usually pay close attention in class. } & .92 & .25 & .78 \\\\\text { 2. I participate often in class } &.45 & 75 & .72 \\\text {discussions. }\\\\\text { 3. I always bring my materials (book, } &.24 & .88 & .83 \\\text { pencils, paper) to class. }\\\\\text { 4. I'm often excited to be in class. } &.77 & .14 & .63 \\\\\text {5. I often talk with my friends and } &.85 & .32 & .61 \\\text { parents about ideas we learn about in }\\\text { school. }\\\\\text {6. I almost always turn in my } &.35 & .92 & .45\\\text { homework and other assignments on }\\\text { time. }\\\\\hline\end{array}

a. How would you describe these three latent classes?

What Is the Purpose of a Cluster Analysis

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