# Techniques

In our work we use a wide array of statistical and psychometric techniques. An overview and a short description of those techniques organised by categories can be found below. If you cannot find the technique you’re interested in, please send an inquiry to info@psihometar.hr to see if Psihometar can conduct the said analysis.

## Basic statistical techniques

### Descriptive statistics

We offer the services of calculating mean, standard deviation, median (central value), semi-interquartile range and mod (dominant value).

### Distribution shape assessment

We assess if your distribution deviates from the normal distribution using the Anderson-Darling or Kolmogorov-Smirnov test. We describe the shape of your distribution using statistical parameters (skewness and kurtosis) or descriptively, depending on the degree of deviation from the normal distribution (e.g. bimodal distribution).

### Comparison of differences between groups or situations

We use t-test to compare if there are statistically significant differences between two groups or situations (e.g. before and after the application of a certain treatment). If the variances of the two groups/situations are not the same, we apply Welch’s correction to the t-test. We quantify the effect size using the Cohen’s d index.

If there are more than two groups or situations in the data, we use independent, dependent or mixed analysis of variance (ANOVA). We also offer the services of analysis of covariance (ANCOVA). We quantify the effect size using the η2 index.

If the data does not meet the assumptions for parametric statistical procedures, we will apply the adequate nonparametric procedure, such as Mann-Whitney’s U test, Wilcoxon’s test, Kruskal-Wallis’ test etc. We also offer the services of chi-square test, including the McNemar test.

Furthermore, we assess differences between group variances using Levene’s variance homogeneity test.

### Correlations

We calculate all types of correlations, such as Pearson’s r, Spearman’s ρ, Cramér’s φ ili Kendall’s τ. We calculate the multiple correlation coefficient (R). If possible, we compare if the two correlation coefficients are statistically significantly different.

### Regression analysis

We conduct bivariate and multivariate linear or logistic regression analysis on your data. We assess the significance of the model and single predictors and quantify the amount of explained variance. We conduct complete or stepwise regression.

We offer the analysis of moderation/interaction effects using Johnson-Neyman intervals. We also conduct hierarchical regression analysis. If the sample size is big enough, we perform cross-validation.

Additionaly, we offer the services of cosinor rhythmometry, which is basically sinusoidal regression analysis and can be used to detect seasonal trends in the data.

### Cluster analysis

We offer the services of grouping clients, products or other statistical units using cluster analysis. We determine the optimal number of clusters using 30 indices that suggest the most probable number of clusters. We use agglomerative clustering methods or the k-means method.

### Factor analysis

We perform exploratory or confirmatory factor analysis on your data. We determine the optimal number of factors by using the Kaiser-Guttman or Jolliffe’s criterion, parallel analysis, Velicer’s MAP or exploratory graph analysis (EGA). We use orthogonal or oblique rotations. We report the factor saturation coefficients to you.

We assess the fit of model to the data using the chi-square test, CFI, TLI, RMSEA and SRMR. We compare the fit of concurrent models using the chi-square test, information criteria or Vuong’s test. We assess measurement invariance. We calculate the reliability of the instrument under the assumption of tau-congenericity.

### Structural equation modeling

We assess complex relations among variables with structural equation modeling (SEM). We report the value and significance of all model coefficients to you.

We assess the fit of model to the data by using the chi-square test, CFI, TLI, RMSEA and SRMR. We compare the fit of concurrent models using the chi-square test, information criteria or Vuong’s test.

### Item Response Theory

We apply Item Response Theory models to your data: 1-, 2-, 3- or 4-parameter logistic model, graded response model, generalized graded unfolding model. We report the model coefficients to you. We assess the fit of the model to the data using the G2 or M2 indices, along with supplementary indices.

We analyse the amount of information provided by the instrument (test or questionnaire) and the ability level at which the instrument is the most informative. We compare concurrent models by comparison of log-likelihoods or by using information criteria (Akaike information criteria, Bayesian information criteria). We assess the differential functioning of items or the test.

We conduct all statistical tests using the R programming language. In extraordinary circumstances we may use other freeware programs to conduct the analyses.

Disclaimer of liability: Psihometar, craft for data analysis, owner Augustin Mutak is not liable in the event of impossibility of performing certain analyses due to the nature of the data, inadequacy of data for some of the statistical analyses, insufficient number of subjects or variables, technical problems in the data or errors or faults in the software packages used to analyse the data.

Graphs shown at this page were generated using the ggplot2, semPlot and lattice packages, with additional usage of functions from lavaan, mirt and cluster packages.