class: center, middle, inverse, title-slide # Article presentation ## Statistical technique: <i>t</i>-student ### Jorge Sinval ### 05 April, 2019 --- class: center, middle  --- class: inverse, center, middle # The article --- # Description of the [article](https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00353/full) -- **The aim** Present the psychometric properties of a Portuguese version of the UWES-9. -- **Sample** <table> <thead> <tr> <th style="text-align:left;"> Country </th> <th style="text-align:right;"> Frequency </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Brazil </td> <td style="text-align:right;"> 524 </td> </tr> <tr> <td style="text-align:left;"> Portugal </td> <td style="text-align:right;"> 522 </td> </tr> </tbody> </table> -- **Data analysis** Confirmatory Factor Analysis Reliability Measurement invariance Group comparisons --- class: middle **Results** Invariance among countries. There were no statistically significant differences. -- **Conclusion** The instrument presents good validity evidence (internal structure). Portuguese and Brazilian works present similar work engagement levels¹. .footnote[ [1] dimensions (vigor, dedication, absorption)] --- class: inverse, center, middle #Statistical technique --- #**_t_-Student test (independent samples) ¹** -- **What is it for?** Compare means from two populations from which the independent samples were drawn (e.g. control group vs. experimental group; Brazil vs. Portugal) -- **When does it apply? (Assumptions)?** i) quantitative dependent variable; ii) independent samples; iii) `\(d.v. \sim N_i(\mu_i,\sigma_i)\)`, iv) `\(\sigma_1=\sigma_2\)` (homoscedasticity) .footnote[ [1] Marôco, J. (2018). _Análise estatística com o SPSS Statistics_ (7th ed.). Pêro Pinheiro, Portugal: ReportNumber] --- class: middle -- **A. Hypotheses** `\(H_0: \mu_1=\mu_2\)` vs. `\(H_1: \mu_1 \neq \mu_2\)` (B. T.) `\(H_0: \mu_1 \leq \mu_2\)` vs. `\(H_1: \mu_1 > \mu_2\)` (R. T. T.) `\(H_0: \mu_1 \geq \mu_2\)` vs. `\(H_1: \mu_1 < \mu_2\)` (L. T. T.) -- **B. Test statistic** `\(t = \frac{\bar {X}_1 - \bar{X}_2}{s_p \cdot \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\)` with `\(s_p = \sqrt{\frac{\left(n_1-1\right)s_{X_1}^2+\left(n_2-1\right)s_{X_2}^2}{n_1+n_2-2}}\)` --- class: middle **C. Decision** Reject `\(H_0\)` if `\(p-value (Sig.) \leq \alpha\)` For the unilateral tests case compare `\(Sig/2\)` with `\(\alpha\)`. **But beware**: the T.E. signal must be consistent with `\(H_1\)`: If `\(T.E.<0\)` the test must be left tailed to the left; if `\(T>0\)` the test must be right tailed. **_T.E._**: Relative distance (SD units) between the difference of samples' means and the populations' means defined on `\(H_0\)`. --- class: inverse, center, middle #Results interpretation --- #Sample ```r DT::datatable( head(df.UWES9[,c("Country","HPQC1","HPQC2","UWES9.UWES1.")], 8), fillContainer = FALSE, options = list(pageLength = 5)) ``` <div id="htmlwidget-044e7ef3ec1b2e66b4e3" style="width:100%;height:auto;" class="datatables html-widget"></div> <script type="application/json" data-for="htmlwidget-044e7ef3ec1b2e66b4e3">{"x":{"filter":"none","fillContainer":false,"data":[["1","6","11","13","17","18","20","22"],["Brazil","Brazil","Brazil","Brazil","Brazil","Brazil","Brazil","Brazil"],[38,29,null,null,57,60,28,45],["Male","Female","N/A","N/A","Female","Female","Female","Female"],[4,6,4,6,5,5,4,5]],"container":"<table class=\"display\">\n <thead>\n <tr>\n <th> <\/th>\n <th>Country<\/th>\n <th>HPQC1<\/th>\n <th>HPQC2<\/th>\n <th>UWES9.UWES1.<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"pageLength":5,"columnDefs":[{"className":"dt-right","targets":[2,4]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":[],"jsHooks":[]}</script> --- ``` ## ## Attaching package: 'skimr' ``` ``` ## The following object is masked from 'package:stats': ## ## filter ``` Skim summary statistics n obs: 1046 n variables: 9 Variable type: numeric variable missing complete n mean sd p0 p25 p50 p75 p100 hist mode SEM sk ku ---------- --------- ---------- ------ ------ ------ ---- ----- ----- ----- ------ ---------- ------ ------ ------- ------- UWES1 0 1046 1046 4.14 1.38 0 3 5 5 6 ▁▁▂▃▁▃▇▃ 5.00 0.04 -0.73 -0.09 UWES2 0 1046 1046 4.14 1.42 0 3 5 5 6 ▁▁▂▃▁▅▇▃ 5.00 0.04 -0.77 -0.04 UWES3 0 1046 1046 4.31 1.54 0 3 5 5 6 ▁▁▂▃▁▅▇▆ 5.00 0.05 -0.84 -0.15 UWES4 0 1046 1046 4.05 1.72 0 3 4 5 6 ▁▂▃▅▁▅▇▇ 5.00 0.05 -0.66 -0.59 UWES5 0 1046 1046 3.74 1.78 0 3 4 5 6 ▂▃▃▅▁▅▇▅ 5.00 0.05 -0.53 -0.77 UWES6 0 1046 1046 4.54 1.54 0 4 5 6 6 ▁▁▂▂▁▃▇▇ 6.00 0.05 -1.13 0.56 UWES7 0 1046 1046 4.72 1.53 0 4 5 6 6 ▁▁▁▂▁▂▆▇ 6.00 0.05 -1.37 1.26 UWES8 0 1046 1046 4.44 1.51 0 4 5 6 6 ▁▁▂▂▁▅▇▇ 5.00 0.05 -1.04 0.45 UWES9 0 1046 1046 3.98 1.71 0 3 4 5 6 ▂▂▃▅▁▆▇▆ 5.00 0.05 -0.70 -0.40 --- class: center, middle <img src="Article_presentation_files/figure-html/vigor raw-1.png" width="90%" /> --- class: center, middle <img src="Article_presentation_files/figure-html/dedication raw-1.png" width="90%" /> --- class: center, middle <img src="Article_presentation_files/figure-html/absortion raw-1.png" width="90%" /> --- class:center, middle <div id="htmlwidget-6d989307c85f1796fe5d" style="width:90%;height:504px;" class="plotly html-widget"></div> <script type="application/json" data-for="htmlwidget-6d989307c85f1796fe5d">{"x":{"data":[{"orientation":"v","width":[0.45,0.45,0.45],"base":[0,0,0],"x":[0.775,1.775,2.775],"y":[4.01590330788804,4.38867684478372,4.33396946564886],"text":["variable: vig_brt<br />mean: 4.015903<br />factor(Group.1): Brazil","variable: ded_brt<br />mean: 4.388677<br />factor(Group.1): Brazil","variable: abs_brt<br />mean: 4.333969<br />factor(Group.1): Brazil"],"type":"bar","marker":{"autocolorscale":false,"color":"rgba(248,118,109,1)","line":{"width":1.88976377952756,"color":"transparent"}},"name":"Brazil","legendgroup":"Brazil","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"orientation":"v","width":[0.45,0.45,0.45],"base":[0,0,0],"x":[1.225,2.225,3.225],"y":[3.99744572158365,4.33780332056194,4.30523627075351],"text":["variable: vig_brt<br />mean: 3.997446<br />factor(Group.1): Portugal","variable: ded_brt<br />mean: 4.337803<br />factor(Group.1): Portugal","variable: abs_brt<br />mean: 4.305236<br />factor(Group.1): Portugal"],"type":"bar","marker":{"autocolorscale":false,"color":"rgba(0,191,196,1)","line":{"width":1.88976377952756,"color":"transparent"}},"name":"Portugal","legendgroup":"Portugal","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[0.775,1.775,2.775],"y":[4.01590330788804,4.38867684478372,4.33396946564886],"text":["mean - 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J., & DiStefano, C. (2013). Non-normal and categorical data in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), _Structural equation modeling: A second course_ (2nd ed., pp. 439–492). Charlotte, NC, USA: Information Age Publishing. [2] Cohen, J. (1988). _Statistical power analysis for the behavioral sciences_ (2nd ed.). Hillsdale, NJ, USA: Lawrence Erlbaum Associates. ] --- class: center, middle # Thanks!