Contents

Therefore, the GMM can provide a reliable connection for the monitored traffic data and the probabilistic modeling of structural fatigue stress range. Furthermore, most dynamic analyses reported in this area have focused on time domain analysis, because of the nature of time-varying differential equations in the interaction system, while very limited developments have been done in the frequency domain. However, incorporating the random vibration in the aforementioned coupled system, which requires and necessitates the use of spectral analysis, is more important and results in more valuable information in the frequency domain. This includes defining each construct and identifying their constituent domains and/or dimensions. Next, we select items or indicators for each construct based on our conceptualization of these construct, as described in the scaling procedure in Chapter 5.

By increasing variability in observations, random error reduces the reliability of measurement. In contrast, by shifting the central tendency measure, systematic error reduces the validity of measurement. Systematic error is an error that is introduced by factors that systematically affect all observations of a construct across an entire sample in a systematic manner. Unlike random error, which may be positive negative, or zero, across observation in a sample, systematic errors tends to be consistently positive or negative across the entire sample. Hence, systematic error is sometimes considered to be “bias” in measurement and should be corrected. Split-half reliability is a measure of consistency between two halves of a construct measure.

## Using And Interpreting Cronbachs Alpha

If the construct measures satisfy most or all of the requirements of reliability and validity described in this chapter, we can be assured that our operationalized measures are reasonably adequate and accurate. Herein, a prototype steel box-girder bridge was introduced to illustrate the feasibility of the proposed framework. Parametric studies demonstrated the accuracy and the efficiency of the framework. Influence of an increase in the traffic volume and vehicle weight on the fatigue reliability of the bridge was investigated. The ultimate goal of this study was to apply the stochastic fatigue truck model for probabilistic modeling of fatigue damage and the reliability assessment of welded steel bridge decks. An alternative and more common statistical method used to demonstrate convergent and discriminant validity is exploratory factor analysis .

The printed output facilitates the identification of dispensable variable by listing down the deleted variables in the first column together with the expected resultant alpha in the same row in the third column. For this example, the table indicates that if SB8 were to be deleted then the value of raw alpha will increase from the current .77 to .81. Note that the same variable has the lowest item-total correlation value (.185652). This indicates that SB8 is not measuring the same construct as the rest of the items in the scale are measuring. With this process alone, not only was the author able to come up with the reliability index of the “REGULATE” construct but he also managed to improve on it. What this means is that removal SB8 from the scale will make the construct more reliable for use as a predictor variable.

The integrated approach to measurement validation discussed here is quite demanding of researcher time and effort. Nonetheless, this elaborate multi-stage process is needed to ensure that measurement scales used in our research meets the expected norms of scientific research. Because inferences drawn using flawed or compromised scales are meaningless, scale validation and measurement remains one of the most important and involved phase of empirical research. Criterion-related validity can also be assessed based on whether a given measure relate well with a current or future criterion, which are respectively called concurrent and predictive validity. Predictive validity is the degree to which a measure successfully predicts a future outcome that it is theoretically expected to predict. For instance, can standardized test scores (e.g., Scholastic Aptitude Test scores) correctly predict the academic success in college (e.g., as measured by college grade point average)?

This is a data reduction technique which aggregates a given set of items to a smaller set of factors based on the bivariate correlation structure discussed above using a statistical technique called principal components analysis. These factors should ideally correspond to the underling theoretical constructs that we are trying to measure. The general norm for factor extraction is that each extracted factor should have an eigenvalue greater than 1.0.

## What Is Reliability Analysis?

If the observations have not changed substantially between the two tests, then the measure is reliable. The correlation in observations between the two tests is an estimate of test-retest reliability. Generally, the longer is the time gap, the greater is the chance that the two observations may change during this time , and the lower will be the test-retest reliability. Inter-rater reliability, also called inter-observer reliability, is a measure of consistency between two or more independent raters of the same construct. Usually, this is assessed in a pilot study, and can be done in two ways, depending on the level of measurement of the construct. If the measure is categorical, a set of all categories is defined, raters check off which category each observation falls in, and the percentage of agreement between the raters is an estimate of inter-rater reliability.

- By increasing variability in observations, random error reduces the reliability of measurement.
- This book is suitable for adoption as a text book or a reference book in an advanced structural reliability analysis course.
- In the proposed study, the alpha coefficient obtained is 0.869, which indicates a good ability of the items of the questionnaire to evaluate the same latent factor in subjects, neuroticism in our case.
- Likewise, a measure can be valid but not reliable if it is measuring the right construct, but not doing so in a consistent manner.
- To estimate the Cronbach’s alpha of the BSS, go to the Analyze menu and select Scale → Reliability Analysis….
- Herein, we will present how the stochastic fatigue truck load model was established based on site-specific WIM measurements.
- This is a data reduction technique which aggregates a given set of items to a smaller set of factors based on the bivariate correlation structure discussed above using a statistical technique called principal components analysis.

This is further combined with the first- and second-order reliability methods to create a unique reliability analysis framework. To assess this approach, the deterministic computational homogenisation method is combined with the Monte Carlo method as an alternative reliability method. Numerical examples are used to demonstrate the capability of the proposed method in measuring the safety of composite structures. The paper shows that it provides estimates very close to those from Monte Carlo method, but is significantly more efficient in terms of computational time. It is advocated that this new method can be a fundamental element in the development of stochastic multi-scale design methods for composite structures.

## Applied Mathematical Modelling

Their correlations with the total scale are respectively 0.451 and 0.342, while all other questions are correlated at least to a value of 0.55. Since the number of items in the questionnaire is low, we choose the Enumeration method, which performs an exhaustive search among all the possible partitions. The Type of reliability selected is Internal Model, which means that we will study the contribution of each item assuming a single independent test. This personality trait is evaluated by means of 10 items for which each person expresses his degree of agreement or disagreement with a statement . In this tutorial, we will focus on the computation and interpretation of indices relative to the internal model, while mentioning indices from the split-half reliability. The correlation between the question and the result of the total sum of the remaining questions.

The reliability analysis will allow you to assess how well the items work together to assess the variable of interest in your sample. Researchers commonly calculate the Cronbach’s alpha to evaluate the reliability of the items comprising a composite score. This statistic allows you to make a statement regarding the acceptability of the combination of items to represent your variable. Cronbach’s alphas of at least 0.7 indicate that the combination of items has acceptable reliability (George & Mallery, 2016).

In other words, if we use this scale to measure the same construct multiple times, do we get pretty much the same result every time, assuming the underlying phenomenon is not changing? Quite likely, people will guess differently, the different measures will be inconsistent, and therefore, the “guessing” technique of measurement is unreliable. A more reliable measurement may be to use a weight scale, where you are likely to get the same value every time you step on the scale, unless your weight has actually changed between measurements. In the proposed study, the alpha coefficient obtained is 0.869, which indicates a good ability of the items of the questionnaire to evaluate the same latent factor in subjects, neuroticism in our case. The internal consistency itself , based on the scores between each measure/item and the sum of all the others (Cronbach’s Alpha, Guttman indices L1 and L6) which assumes a good homogeneity among the items. To make the demonstration on Cronbach’s alpha possible, SB8, which was a variable previously deleted during factor analysis, was restored in the data set.

The best items (say 10-15) for each construct are selected for further analysis. Each of the selected items is reexamined by judges for face validity and content validity. If an adequate set of items is not achieved at this stage, new items may have to be created based on the conceptual definition of the intended https://wizardsdev.com/ construct. Two or three rounds of Q-sort may be needed to arrive at reasonable agreement between judges on a set of items that best represents the constructs of interest. Reliability comes to the forefront when variables developed from summated scales are used as predictor components in objective models.

Bucher and Macke , introduced the solutions to the first-passage problem by importance sampling. A probability density evolution method which was capable of capturing the instantaneous PDF and its evolution of the responses was developed by Chen and Li . Applications of first-passage reliability to engineering structures are very interesting since safety assessment and design can be put forward to guarantee the structural safety. Park and Ang assessed the probability of damage for a reinforced concrete structure under the seismic load. Zhang et al. adopted a pseudo-excitation method and a precise integration method to compute the non-stationary random response of 3-D train-bridge systems subjects to lateral horizontal earthquakes. Significant progress in structural reliability evaluation has been achieved in the last decades utilizing nonlinear stochastic structural dynamics .

## Reliability Analysis

Remember that reliability is a number that ranges from 0 to 1, with values closer to 1 indicating higher reliability. Cronbach’s alpha coefficient, also known as α coefficient, is used to evaluate the internal consistency of the questions asked in this test . Its value generally lies between 0 and 1 and is considered as acceptable when it’s higher than 0.70. A complete and adequate assessment of validity must include both theoretical and multi-scale analysis empirical approaches. As shown in Figure 7.4, this is an elaborate multi-step process that must take into account the different types of scale reliability and validity. If employee morale in a firm is measured by watching whether the employees smile at each other, whether they make jokes, and so forth, then different observers may infer different measures of morale if they are watching the employees on a very busy day or a light day .

This type of reliability also assumes the equality of the true scores of each item measured (Tau-equivalence hypothesis) so that the different estimators of the internal coherence of the test have a minimal bias . High reliability suggests strong relationships between the measures/items within the measurement procedure. Concurrent validity examines how well one measure relates to other concrete criterion that is presumed to occur simultaneously. For instance, do students’ scores in a calculus class correlate well with their scores in a linear algebra class? These scores should be related concurrently because they are both tests of mathematics. Unlike convergent and discriminant validity, concurrent and predictive validity is frequently ignored in empirical social science research.

This book is suitable for adoption as a text book or a reference book in an advanced structural reliability analysis course. Abstract A large number of long-span bridges are under construction or have been constructed all over the world. The steady increase in traffic volume and gross vehicle weight has caused a threat to the serviceability or even safety of in-service bridges. Therefore, ensuring the safety and serviceability of these bridges has become a growing concern. In particular, long-span suspension bridges support heavy traffic volumes and experience considerable wind loads on the bridge deck on a regular basis. Excessive dynamic responses may cause large deformation and undesirable vibration of the stiffening girders.

Two observers may also infer different levels of morale on the same day, depending on what they view as a joke and what is not. Sometimes, reliability may be improved by using quantitative measures, for instance, by counting the number of grievances filed over one month as a measure of morale. Of course, grievances may or may not be a valid measure of morale, but it is less subject to human subjectivity, and therefore more reliable. A second source of unreliable observation is asking imprecise or ambiguous questions. For instance, if you ask people what their salary is, different respondents may interpret this question differently as monthly salary, annual salary, or per hour wage, and hence, the resulting observations will likely be highly divergent and unreliable. Reliability is the degree to which the measure of a construct is consistent or dependable.

Since summated scales are an assembly of interrelated items designed to measure underlying constructs, it is very important to know whether the same set of items would elicit the same responses if the same questions are recast and re-administered to the same respondents. Variables derived from test instruments are declared to be reliable only when they provide stable and reliable responses over a repeated administration of the test. Reliability analysis allows to study the properties of the scales of measurement and the elements that constitute them. The reliability analysis procedure provides several results to evaluate the internal consistency and also provides information on the relationships between the different elements composing the scale. Convergent validity refers to the closeness with which a measure relates to the construct that it is purported to measure, and discriminant validity refers to the degree to which a measure does not measure other constructs that it is not supposed to measure. Usually, convergent validity and discriminant validity are assessed jointly for a set of related constructs.

For instance, absorptive capacity of an organization has often been measured as research and development intensity (i.e., R&D expenses divided by gross revenues)! In the previous example of the weight scale, if the weight scale is calibrated incorrectly (say, to shave off ten pounds from your true weight, just to make you feel better!), it will not measure your true weight and is therefore not a valid measure. Nevertheless, the miscalibrated weight scale will still give you the same weight every time , and hence the scale is reliable. While labeling is critical, it definitely makes for an easy identification of which construct is running on what particular procedure. At this point, the named common factors can now be used as independent or predictor variables. However, most experienced researchers would insist on running a reliability test for all the factors before using them in subsequent analyses.