# Tagged Questions

Psychometrics has evolved as a subfield of psychology to become the science of measurement of unobservable individual characteristics.

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### Good internal factor structure but poor Cronbach's $\alpha$?

I am running a CFA and getting good fit indices (CFI = .99, RMSEA = .01) for a uni-dimensional scale. However, when I test for internal consistency, I get poor Cronbach's $\alpha$s ($\alpha = .6$). I ...
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### Map a normal distribution N(x,s) to an ordinal response variable

I am working on a simulation. I am going to extract a series of normally distributed values from a distribution $N(x,s)$ whose mean $x$ and variance $s$ is known. I want to pretend that such ...
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### How to check psychometric type of scales?

It is well known, that there are diffrent types of scales (see Wikipedia Level of measurement). In psycholinguistics there is Semantic Differential technique. It uses a scale (usually 5 or 7 grades) ...
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### Cronbach's alpha vs. KR20/KR21 in reliability studies

Should we calculate Cronbach's alpha instead of KR20/KR21 for measuring the reliability of an achievement test, or a test with dichotomous data?
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### Where do the descriptors for Cronbach's alpha values come from (e.g., poor, excellent)?

It seems fairly common to describe Cronbach's alpha values as follows: α ≥ 0.9 Excellent 0.7 ≤ α < 0.9 Good 0.6 ≤ α < 0.7 Acceptable 0.5 ≤ α < 0.6 Poor α < 0.5 Unacceptable Where ...
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### What is the correct use of Cronbach's alpha?

I am trying to use Cronbach's alpha in order to see if some variables are measuring the "same", but I have some doubts about the correct use: Can I compute alpha for numerical, ordinal or ...
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### Confirmatory factor analysis for a newly constructed questionnaire

I am about to develop a new questionnaire with 142 questions I have performed exploratory factor analysis and 30 latent factors were extracted. I was wondering if it is necessary to perform ...
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### Doing CFA on a known theoretical model, but having problems with convergent and discriminant validity

I did a survey based on the UTAUT model / theory with standard questions used. The N was 150. I am trying to validate the model for my survey with structural equation modeling (via the AMOS software). ...
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### Item response theory vs. summative Likert scale

If the items to be "summed" or combined to create an overall index are collectively the underlying construct (i.e. I am trying to measure compliance to an intervention which has different components), ...
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### Two treatments - How do I compute reliability estimates like Cronbach's $\alpha$?

I randomized my survey, and now I have my data on SPSS (and all cleaned up) but when trying to run my Cronbach's $\alpha$ I have a problem. Because I have two treatments (sexualised and normal) all ...
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### Should I run measurement invariance if confirmatory factor analysis is not affirmative?

I have a repeated measures design for a Likert scale with 10 items. This scale is assumed to be unidimensional and this is one of the research questions along with the scales measurement invariance (...
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### Should I use raw scores or profile scores for variables in a regression model?

I'm trying to build a regression model to predict subjective memory reports based on the following predictors: objective memory test, illness perceptions, verbal fluency, and mood. I also want to ...
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### Using existing questionnaire

I will be doing my colloquium and will be using existing questionnaires. I would like to know if there are authors/authorities who say that an existing questionnaire need not be validated. The ...
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### Summing up ordered items to a sum-score: implications?

It is common practice in psychology to add together ordered items to sum-scores, and then use these sum-scores for subsequent statistics. This is usually done without explicitly mentioning measurement ...
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### Cronbach's alpha negative result

What should I do if I am getting negative results for Cronbach's alpha? Is there anyway to adjust it?
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### Can I combine several ordinal questions to create an index and/or composite measure?

I am using a survey that contains several questions about various dimensions of performance for policy research institutes. Here, performance in the policy arena is unpacked into things like: ...
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### Is it appropriate to assess internal consistency on related items measured with different response formats within the same instrument?

In my survey, I grouped 67 unique counseling techniques that I thought were related to one another (based on theory and conceptual similarity) into six "counseling domains" using fairly intuitive, ...
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### IQ adaptive test items in 1pl, 2pl or 3pl IRT model?

Some adapative test systems (e.g. school assessment tools) use the 1pl IRT model, while others use the 2pl or the 3pl. When developing an adaptive IQ test, is there a rule of thumb about which model ...
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### How to calculate validity of questionnaire in SPSS?

I have 3 types of questionnaires, A 15 item scale with each item on a 7-point Likert type scale. Six subscales each containing different number of items 21 subscales each containing 4 items. ...
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### How to select next item in polytomous CAT / MIRT?

To make a Computerized Adaptive Test out of a sample of 20 dichotomous items a typical course of action would be to: 1) calibrate respondent data with a R package like mirt or ltm using Rasch, 2PL ...
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### How can there be a standard deviation of true scores?

Dudek (1979) describes the following formula as "the standard deviation of true scores when the observed score is held constant" (p. 337): $SE_{est} = SD \sqrt{(reliability × (1 - reliability))}$ ...
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### What is the reasoning behind the formulae for the different standard errors of measurement?

McManus (2012) discusses the three standard errors of measurement and provides the following definitions. $SE_{meas} = SD \sqrt{(1 - reliability)}$ The standard error of measurement is an estimate ...
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### Why don't we square the reliability correlation when calculating reliable variance?

This question relates to situations where we apply some test to the same people at Time 1 and Time 2, and then calculate the correlation between scores at Time 1 and Time 2. I am reading the book ...
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### Cronbach's Alpha on true and false data?

I have a 10 item knowledge scale (true/false). Can I do Cronbach alpha test?
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### how to analyze necessary/sufficient relationship?

Good day! I'm a second year psych grad student. From my fascination with formal logic, I wondered (just personal; not homework) about how to statistically establish necessary/sufficient ...
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### What coefficient could I use to calculate the relative difficulty of a test in relation to others using only mean and population standard deviation?

I have a series of tests, all of them of different difficulty, and from each of them I get an average score and a population standard deviation; e.g: ...
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### IRT/Rasch modeling with very large N

I want to fit a 1-parameter IRT model on a questionaire with 15 questions and about six million people. Considering the large N, standard errors aren't essential. It looks like the IRT world is sort ...
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### EFA on R: Classifying Observations

I am newbie for R and Stats. I am using EFA in R [psych library] to identify the latent factors underlying my data. I got a reasonable amount of factors matching my purpose. My question is once I ...
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### What factors do I have to consider when deciding if creating a composite score using four t-scores is defensible psychometrically?

Edit: I've conducted an item analysis on four variables - two quizzes and two psychological attributes, namely emotional intelligence and happiness. Its a within-subject design with students as ...
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### EFA clearly supports one-factor, measure is internally consistent, but CFA has poor fit?

I am exploring the psychometric properties of a 10-item self-report measure. I have about 400 cases in two independent samples. The items are completed on 4-point Likert scales. An EFA clearly ...
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### Comparing two logit or probit curves using a single parameter

I've conducted a psychological experiment on the same subject, under two different condition. For each condition I've collected the number of correct and wrong answer for each stimulus (number of ...
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### How do I analyze a z-score to determine a difference?

My data are in SPSS. I teach in a nursing program. During their junior year, 68 students participated in a simulation scenario for heart failure. They were by rated by observers (0/1, did not do/did ...
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### IRT in R: Does anyone know of an IRT item calibration function that can cope with NA's?

I have a dataset that looks like this. ...
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### 4 point and 5 point Likert scales in a new questionnaire

I'm looking to confirm whether having a 4 point Likert Scale for some constructs, and a 5 point Likert scale for other constructs will be suitable when developing a questionnaire? I have 7 constructs ...
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### Error message from grm() in ltm: subscript out of bounds

I am analyzing a survey data set. One of the items in the survey is: ...
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### Which correlation analysis is appropriate for binary and ordinal variables?

Violin players were asked to rate 5 violins from least to most rich on a [0 1], 0.05-increment scale, ...
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### Omega H asymptotic

In the omega function in the psych package for R, we have several outputs including Hierarchical omega, Asymptotic omega and Total omega. I was reading about the outputs, but I find nothing about ...
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### Understanding signficant interaction with non-significant main effects [duplicate]

Possible Duplicate: How to compute significant interaction estimates when main effect is not significant? I am an applied linguist and I am modelling responses to a vocabulary test taken by ...
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### Likert scale and yes/no calculation of one score

My survey is based on observations and interviews. The observation questions are yes/no type questions and interview questions are 4 points. $1=$ never, $2=$ sometimes, $3=$ usually, and $4=$ ...
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### How to validate a survey when using Likert scale?

I have developed a very simple survey to measure the attitudes of students toward science fairs. It makes use of the Likert Scale and Open Ended Questions. Do you have a recommendation for the type ...
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### How to equate questionnaires with different response scales

I'm trying to help out a not-for-profit organization and made an error that I'm trying to fix. They've been doing a non scientific survey of their Board of Directors for a number of years regarding ...
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### How to deal with the cases when participants gave rating of 2.5 or 4.5 on a 1-5 scale?

Because this was done during the interview, the participants just spoke out their rating rather than marked it done on the paper: they sometimes say "I think it is between 2 and 3" or "I give it 4 or ...
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### How is Item Response Theory (IRT) called for continuous response?

I would like to model my problem using something similar to Item Response Theory - but my responses are not binary - they are continuous in [0;1]. How are these models/the research field called?
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### Item information in IRT with item covariates (linear logistic test model)

Short question: How does the calculation and interpretation of IRT item information and test information change in the presence of item properties? Long question: There's a variation on IRT called ...
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### Item information in IRT

According to item information curves, item information for a 2PL IRT model is $I(\theta)=a^2_i p_i(\theta) q_i(\theta)$ To determine $p_i(\theta)$ and $q_i(\theta)$, do you just use the observed ...
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### Internal consistency reliability in item response theory models

How can internal consistency reliability of a test and of individual test items be quantified in Item Response Theory models? I know I can resort to Classical Test Theory, Cronbach's alpha, and other ...
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### Test of symptom severity equality / symptom configuration equality

We have a questionnaire measuring 9 clinical symptoms. The sum scores simply adds all these symptoms up. Symptoms are ordered (0,1,2,3), and pretty strongly skewed (lots of 0s). 1) First, we want to ...
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### Omega vs. alpha reliability

I wonder if someone can explain what is the main difference between omega and alpha reliabilities? I understand an omega reliability is based on hierarchical factor model as shown in the following ...