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Use the attached data set to answer the questions.  To earn full credit show all of your calculations and other work. Explain your answers. Don’t just write a number. Use the below link to download JASP software https://jasp-stats.org/download/ Use the following data set to answer the following questions. To earn full credit show all of your calculations and other work. Explain your answers. Don’t just write a number. The 26 students who signed up for General Psychology reported their GPA. Each person was matched with another person on the basis of the GPAs, and two groups were formed. One group was taught with the traditional lecture method by Professor Nouveau. The other class could access the Web for the same lectures whenever they wished. At the end of the term, both classes took the same comprehensive final exam, and they also filled out a Satisfaction Questionnaire. Scores on both measures are shown below. Analyze the data with t tests and effect size indexes. Write a conclusion. You can use the JASP Software to perform your analysis. Make sure you include the analysis output in your submission. Also, explain your results in detail. Comprehensive Final Exam Scores Satisfaction Scores Traditional Section Online Section Traditional Section Online Section 50 56 25 31 72 75 18 19 64 62 40 38 82 90 31 35 89 91 17 24 65 65 22 20 74 72 14 18 85 87 36 35 80 76 27 31 65 79 22 27 82 77 23 27 75 78 28 28 64 70 20 23 DOI: 10.6084/m9.figshare.9980744 4th Edition JASP v0.14 2020 Copyright © 2020 by Mark A Goss-Sampson. Licenced as CC BY 4.0 All rights reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the author except for research, education or private study. CONTENTS PREFACE .................................................................................................................................................. 1 USING THE JASP ENVIRONMENT ............................................................................................................ 2 DATA HANDLING IN JASP ........................................................................................................................ 8 JASP ANALYSIS MENU ........................................................................................................................... 11 DESCRIPTIVE STATISTICS ....................................................................................................................... 14 DESCRIPTIVE PLOTS IN JASP .............................................................................................................. 19 SPLITTING DATA FILES ....................................................................................................................... 23 EXPLORING DATA INTEGRITY ................................................................................................................ 25 DATA TRANSFORMATION ..................................................................................................................... 34 EFFECT SIZE ........................................................................................................................................... 38 ONE SAMPLE T-TEST ............................................................................................................................. 40 BINOMIAL TEST ..................................................................................................................................... 43 MULTINOMIAL TEST .............................................................................................................................. 46 CHI-SQUARE ‘GOODNESS-OF-FIT’ TEST............................................................................................. 48 MULTINOMIAL AND Χ2 ‘GOODNESS-OF-FIT’ TEST. ........................................................................... 49 COMPARING TWO INDEPENDENT GROUPS .......................................................................................... 50 INDEPENDENT T-TEST ....................................................................................................................... 50 MANN-WITNEY U TEST ..................................................................................................................... 54 COMPARING TWO RELATED GROUPS ................................................................................................... 56 PAIRED SAMPLES T-TEST ................................................................................................................... 56 WILCOXON’S SIGNED RANK TEST...................................................................................................... 59 CORRELATION ANALYSIS ....................................................................................................................... 61 REGRESSION .......................................................................................................................................... 67 SIMPLE REGRESSION ......................................................................................................................... 70 MULTIPLE REGRESSION ..................................................................................................................... 73 LOGISTIC REGRESSION .......................................................................................................................... 80 COMPARING MORE THAN TWO INDEPENDENT GROUPS .................................................................... 85 ANOVA .............................................................................................................................................. 85 KRUSKAL-WALLIS .............................................................................................................................. 92 COMPARING MORE THAN TWO RELATED GROUPS ............................................................................. 95 RMANOVA ......................................................................................................................................... 95 FRIEDMAN’S REPEATED MEASURES ANOVA .................................................................................. 100 COMPARING INDEPENDENT GROUPS AND THE EFFECTS OF COVARIATES ........................................ 103 ANCOVA .......................................................................................................................................... 103 TWO-WAY INDEPENDENT ANOVA ...................................................................................................... 111 TWO-WAY REPEATED MEASURES ANOVA ........................................................................................ 119 MIXED FACTOR ANOVA ....................................................................................................................... 127 CHI-SQUARE TEST FOR ASSOCIATION ................................................................................................. 135 META-ANALYSIS .................................................................................................................................. 142 EXPERIMENTAL DESIGN AND DATA LAYOUT IN EXCEL FOR JASP IMPORT. ........................................ 150 Independent t-test .......................................................................................................................... 150 Paired samples t-test ...................................................................................................................... 151 Correlation ...................................................................................................................................... 152 Logistic Regression .......................................................................................................................... 154 One-way Independent ANOVA ....................................................................................................... 155 One-way repeated measures ANOVA ............................................................................................. 156 Two-way Independent ANOVA ....................................................................................................... 157 Two-way Repeated measures ANOVA ............................................................................................ 158 Two-way Mixed Factor ANOVA ....................................................................................................... 159 Chi-squared - Contingency tables ................................................................................................... 160 SOME CONCEPTS IN FREQUENTIST STATISTICS .................................................................................. 161 WHICH TEST SHOULD I USE? ............................................................................................................... 165 Comparing one sample to a known or hypothesized population mean. ........................................ 165 Testing relationships between two or more variables ................................................................... 165 Predicting outcomes ....................................................................................................................... 166 Testing for differences between two independent groups ............................................................ 166 Testing for differences between two related groups ..................................................................... 167 Testing for differences between three or more independent groups ............................................ 167 Testing for differences between three or more related groups ..................................................... 168 Test for interactions between 2 or more independent variables ................................................... 168 1 | P a g e JASP 0.14 - Dr Mark Goss-Sampson PREFACE JASP stands for Jeffrey’s Amazing Statistics Program in recognition of the pioneer of Bayesian inference Sir Harold Jeffreys. This is a free multi-platform open-source statistics package, developed and continually updated by a group of researchers at the University of Amsterdam. They aimed to develop a free, open-source programme that includes both standard and more advanced statistical techniques with a major emphasis on providing a simple intuitive user interface. In contrast to many statistical packages, JASP provides a simple drag and drop interface, easy access menus, intuitive analysis with real-time computation and display of all results. All tables and graphs are presented in APA format and can be copied directly and/or saved independently. Tables can also be exported from JASP in LaTeX format JASP can be downloaded free from the website https://jasp-stats.org/ and is available for Windows, Mac OS X and Linux. You can also download a pre-installed Windows version that will run directly from a USB or external hard drive without the need to install it locally. The WIX installer for Windows enables you to choose a path for the installation of JASP – however, this may be blocked in some institutions by local Administrative rights. The programme also includes a data library with an initial collection of over 50 datasets from Andy Fields book, Discovering Statistics using IBM SPSS statistics1 and The Introduction to the Practice of Statistics2 by Moore, McCabe and Craig. Since May 2018 JASP can also be run directly in your browser via rollApp™ without having to install it on your computer (https://www.rollapp.com/app/jasp). However, this may not be the latest version of JASP. Keep an eye on the JASP site since there are regular updates as well as helpful videos and blog posts!! This book is a collection of standalone handouts covering the most common standard (frequentist) statistical analyses used by students studying Biological Sciences. Datasets used in this document are available for download from https://osf.io/bx6uv/ Dr Mark Goss-Sampson Centre for Science and Medicine in Sport & Exercise University of Greenwich 2020 1 A Field. (2017) Discovering Statistics Using IBM SPSS Statistics (5th Ed.) SAGE Publications. 2 D Moore, G McCabe, B Craig. (2011) Introduction to the Practice of Statistics (7th Ed.) W H Freeman. https://jasp-stats.org/ https://www.rollapp.com/app/jasp https://osf.io/bx6uv/ 2 | P a g e JASP 0.14 - Dr Mark Goss-Sampson USING THE JASP ENVIRONMENT Open JASP. The main menu can be accessed by clicking on the top-left icon. Open: JASP has its own .jasp format but can open a variety of different dataset formats such as: • .csv (comma separated values) can be saved in Excel • .txt (plain text) also can be saved in Excel • .tsv (tab-separated values) also can be saved in Excel • .sav (IBM SPSS data file) • .ods (Open Document spreadsheet) You can open recent files, browse your computer files, access the Open Science Framework (OSF) or open the wide range of examples that are packaged with the Data Library in JASP. 3 | P a g e JASP 0.14 - Dr Mark Goss-Sampson Save/Save as: Using these options the data file, any annotations and the analysis can be saved in the .jasp format Export: Results can be exported to either an HTML file or as a PDF Data can be exported to either a .csv, .tsv or .txt file Sync data: Used to synchronize with any updates in the current data file (also can use Ctrl-Y) Close: As it states - it closes the current file but not JASP Preferences: There are three sections that users can use to tweak JASP to suit their needs In the Data Preferences section users can: • Synchronize/update the data automatically when the data file is saved (default) • Set the default spreadsheet editor (i.e. Excel, SPSS etc) • Change the threshold so that JASP more readily distinguishes between nominal and scale data • Add a custom missing value code 4 | P a g e JASP 0.14 - Dr Mark Goss-Sampson In the Results Preferences section users can: • Set JASP to return exact p values i.e. P=0.00087 rather than P<.001 • Fix the number of decimals for data in tables – makes tables easier to read/publish • Change the pixel resolution of the graph plots • Select when copying graphs whether they have a white or transparent background. In the Interface Preferences section users can now define a user font and pick between two different themes; a light theme (default) and a dark theme. The preferred language currently supports English, 5 | P a g e JASP 0.14 - Dr Mark Goss-Sampson German and Dutch only. In this section, there is also the ability to change the system size (zoom) for accessibility and the scroll speeds. In the Advanced Preferences section, most users will probably never have to change any of the default settings. Comparison of the dark and light themes in JASP 6 | P a g e JASP 0.14 - Dr Mark Goss-Sampson JASP has a streamlined interface to switch between the spreadsheet, analysis and results views. The vertical bars highlighted above allows for the windows to be dragged right or left by clicking and dragging the three vertical dots The individual windows can also be completely collapsed using the right or left arrow icons If you click the Results icon a range of options is provided including: • Edit title • Copy • Export results • Add notes • Remove all • Refresh all The ‘add notes’ option allows the results output to be easily annotated and then exported to an HTML or PDF file by going to File > Export Results. 7 | P a g e JASP 0.14 - Dr Mark Goss-Sampson The Add notes menu provides many options to change text font, colour size etc. You can change the size of all the tables and graphs using ctrl+ (increase) ctrl- (decrease) ctrl= (back to default size). Graphs can also be resized by dragging the bottom right corner of the graph. As previously mentioned, all tables and figures are APA standard and can just be copied into any other document. Since all images can be copied/saved with either a white or transparent background. This can be selected in Preferences > Advanced as described earlier. There are many further resources on using JASP on the website https://jasp-stats.org/ https://jasp-stats.org/ 8 | P a g e JASP 0.14 - Dr Mark Goss-Sampson DATA HANDLING IN JASP For this section open England injuries.csv All files must have a header label in the first row. Once loaded, the dataset appears in the window: For large datasets, there is a hand icon which allows easy scrolling through the data. On import JASP makes a best guess at assigning data to the different variable types: Nominal Ordinal Continuous If JASP has incorrectly identified the data type just click on the appropriate variable data icon in the column title to change it to the correct format. If you have coded the data you can click on the variable name to open up the following window in which you can label each code. These labels now replace the codes in the spreadsheet view. If you save this as a .jasp file these codes, as well as all analyses and notes, will be saved automatically. This makes the data analysis fully reproducible. 9 | P a g e JASP 0.14 - Dr Mark Goss-Sampson In this window, you can also carry out simple filtering of data, for example, if you untick the Wales label it will not be used in subsequent analyses. Clicking this icon in the spreadsheet window opens up a much more comprehensive set of data filtering options: Using this option will not be covered in this document. For detailed information on using more complex filters refer to the following link: https://jasp-stats.org/2018/06/27/how-to-filter-your-data- in-jasp/ https://jasp-stats.org/2018/06/27/how-to-filter-your-data-in-jasp/ https://jasp-stats.org/2018/06/27/how-to-filter-your-data-in-jasp/ 10 | P a g e JASP 0.14 - Dr Mark Goss-Sampson By default, JASP plots data in the Value order (i.e. 1-4). The order can be changed by highlighting the label and moving it up or down using the appropriate arrows: Move up Move down Reverse order Close If you need to edit the data in the spreadsheet just double click on a cell and the data should open up in the original spreadsheet i.e. Excel. Once you have edited your data and saved the original spreadsheet JASP will automatically update to reflect the changes that were made, provided that you have not changed the file name. 11 | P a g e JASP 0.14 - Dr Mark Goss-Sampson JASP ANALYSIS MENU The main analysis options can be accessed from the main toolbar. Currently, JASP offers the following frequentist (parametric and non-parametric standard statistics) and alternative Bayesian tests: Descriptives • Descriptive stats Regression • Correlation • Linear regression Logistic regression T-Tests • Independent • Paired • One sample Frequencies • Binomial test • Multinomial test • Contingency tables • Log-linear regression* ANOVA • Independent • Repeated measures • ANCOVA • MANOVA * Factor • Principal Component Analysis (PCA)* • Exploratory Factor Analysis (EFA)* • Confirmatory Factor Analysis (CFA)* Mixed Models* • Linear Mixed Models Generalised linear mixed models * Not covered in this document BY clicking on the + icon on the top-right menu bar you can also access advanced options that allow the addition of optional modules. Once ticked they will be added to the main analysis ribbon. These include; See the JASP website for more information on these advanced modules Audit Network analysis BAIN Reliability analysis Distributions SEM Equivalence tests Summary statistics JAGS Visual modelling Machine learning Learning Bayes Meta-analysis (included in this guide) R (beta) 12 | P a g e JASP 0.14 - Dr Mark Goss-Sampson Once you have selected your required analysis all the possible statistical options appear in the left window and output in the right window. JASP provides the ability to rename and ‘stack’ the results output thereby organising multiple analyses. The individual analyses can be renamed using the pen icon or deleted using the red cross. By clicking on the analysis in this list will then take you to the appropriate part of the results output window. They can also be rearranged by dragging and dropping each of the analyses. The green + icon produces a copy of the chosen analysis The blue information icon provides detailed information on each of the statistical procedures used and includes a search option. 13 | P a g e JASP 0.14 - Dr Mark Goss-Sampson 14 | P a g e JASP 0.14 - Dr Mark Goss-Sampson DESCRIPTIVE STATISTICS Presentation of all the raw data is very difficult for a reader to visualise or to draw any inference on. Descriptive statistics and related plots are a succinct way of describing and summarising data but do not test any hypotheses. There are various types of statistics that are used to describe data: • Measures of central tendency • Measures of dispersion • Percentile values • Measures of distribution • Descriptive plots To explore these measures, load Descriptive data.csv into JASP. Go to Descriptives > Descriptive statistics and move the Variable data to the Variables box on the right. The Statistics menu can now be opened to see the various options available. 15 | P a g e JASP 0.14 - Dr Mark Goss-Sampson CENTRAL TENDENCY. This can be defined as the tendency for variable values to cluster around a central value. The three ways of describing this central value are mean, median or mode. If the whole population is considered we the term population mean / median/mode is used. If a sample/subset of the population is being analysed the term sample mean/ median/mode is used. The measures of central tendency move toward a constant value when the sample size is sufficient to be representative of the population. In the Statistics options make sure that everything is unticked apart from mean, median and mode. The mean, M or x̅ (17.71) is equal to the sum of all the values divided by the number of values in the dataset i.e. the average of the values. It is used for describing continuous data. It provides a simple statistical model of the centre of distribution of the values and is a theoretical estimate of the ‘typical value’. However, it can be influenced heavily by ‘extreme’ scores. The median, Mdn (17.9) is the middle value in a dataset that has been ordered from the smallest to largest value and is the normal measure used for ordinal or non-parametric continuous data. Less sensitive to outliers and skewed data The mode (20.0) is the most frequent value in the dataset and is usually the highest bar in a distribution histogram DISPERSION In the Statistics options make sure that the following options are ticked Standard deviation, S or SD (6.94) is used to quantify the amount of dispersion of data values around the mean. A low standard deviation indicates that the values are close to the mean, while a high standard deviation indicates that the values are dispersed over a wider range. 16 | P a g e JASP 0.14 - Dr Mark Goss-Sampson Variance (S2 = 48.1) is another estimate of how far the data is spread from the mean. It is also the square of the standard deviation. The standard error of the mean, SE (0.24) is a measure of how far the sample mean of the data is expected to be from the true population mean. As the size of the sample data grows larger the SE decreases compared to S and the true mean of the population is known with greater specificity. MAD, median absolute deviation, a robust measure of the spread of data. It is relatively unaffected by data that is not normally distributed. Reporting median +/- MAD for data that is not normally distributed is equivalent to mean +/- SD for normally distributed data. MAD Robust: Median absolute deviation of the data points, adjusted by a factor for asymptotically normal consistency. IQR - Interquartile Range is similar to the MAD but is less robust (see Boxplots). Confidence intervals (CI), although not shown in the general Descriptive statistics output, these are used in many other statistical tests. When sampling from a population to get an estimate of the mean, confidence intervals are a range of values within which you are n\% confident the true mean is included. A 95\% CI is, therefore, a range of values that one can be 95\% certain contains the true mean of the population. This is not the same as a range that contains 95\% of ALL the values. For example, in a normal distribution, 95\% of the data are expected to be within ± 1.96 SD of the mean and 99\% within ± 2.576 SD. 95\% CI = M ± 1.96 * the standard error of the mean. Based on the data so far, M = 17.71, SE = 0.24, this will be 17.71 ± (1.96 * 0.24) or 17.71 ± 0.47. Therefore the 95\% CI for this dataset is 17.24 - 18.18 and suggests that the true mean is likely to be within this range 95\% of the time QUARTILES In the Statistics options make sure that everything is unticked apart from Quartiles. Quartiles are where datasets are split into 4 equal quarters, normally based on rank ordering of median values. For example, in this dataset 17 | P a g e JASP 0.14 - Dr Mark Goss-Sampson 1 1 2 2 3 3 4 4 4 4 5 5 5 6 7 8 8 9 10 10 10 25\% 50\% 75\% The median value that splits data by 50\% = 50th percentile = 5 The median value of left side = 25th percentile = 3 The median value of right side = 75th percentile = 8 From this the Interquartile range (IQR) range can be calculated, this is the difference between the 75th and 25th percentiles i.e. 5. These values are used to construct the descriptive boxplots later. The IQR can also be shown by ticking this option in the Dispersion menu. DISTRIBUTION Skewness describes the shift of the distribution away from a normal distribution. Negative skewness shows that the mode moves to the right resulting in a dominant left tail. Positive skewness shows that the mode moves to the left resulting in a dominant right tail. Kurtosis describes how heavy or light the tails are. Positive kurtosis results in an increase in the “pointiness” of the distribution with heavy (longer) tails while negative kurtosis exhibit a much more uniform or flatter distribution with light (shorter) tails. Negative skewness Positive skewness + kurtosis Normal - kurtosis 18 | P a g e JASP 0.14 - Dr Mark Goss-Sampson In the Statistics options make sure that everything is unticked apart from skewness, kurtosis and Shapiro-Wilk test. We can use the Descriptives output to calculate skewness and kurtosis. For a normal data distribution, both values should be close to zero. The Shapiro-Wilk test is used to assess whether or not the data is significantly different from a normal distribution. (see - Exploring data integrity in JASP for more details). 19 | P a g e JASP 0.14 - Dr Mark Goss-Sampson DESCRIPTIVE PLOTS IN JASP Currently, JASP produces a range of descriptive plots: Again, using Descriptive data.csv with the variable data in the Variables box, go to the statistics options and under Plots tick Distribution plots, Boxplots – Boxplot Element and Q-Q plots. The Distribution plot is based on splitting the data into frequency bins, this is then overlaid with the distribution curve. As mentioned before, the highest bar is the mode (most frequent value of the dataset. In this case, the curve looks approximately symmetrical suggesting that the data is approximately normally distributed. The second distribution plot is from another dataset which shows that the data is positively skewed. 20 | P a g e JASP 0.14 - Dr Mark Goss-Sampson The boxplots visualise several statistics described above in one plot: • Median value • 25 and 75\% quartiles • Interquartile range (IQR) i.e. 75\% - 25\% quartile values • Maximum and minimum values plotted with outliers excluded • Outliers are shown if requested Maximum value Median value Minimum value 75\% quartile 25\% quartile IQR Top 25\% Bottom 25\% Outlier 21 | P a g e JASP 0.14 - Dr Mark Goss-Sampson Go back to the statistics options, in Descriptive plots tick both Boxplot and Violin Element, look at how the plot has changed. Next tick Boxplot, Violin and Jitter Elements. The Violin plot has taken the smoothed distribution curve from the Distribution plot, rotated it 90o and superimposed it on the boxplot. The jitter plot has further added all the data points. A Q-Q plot (quantile-quantile plot) can be used to visually assess if a set of data comes from a normal distribution. Q-Q plots take the sample data, sort it in ascending order, and then plot them against quantiles (percentiles) calculated from a theoretical distribution. If the data is normally distributed, the points will fall on or close to the 45-degree reference line. If the data is not normally distributed, the points will deviate from the reference line. Boxplot + Violin plot Boxplot + Violin + Jitter plot 22 | P a g e JASP 0.14 - Dr Mark Goss-Sampson Scatter Plots JASP can produce scatterplots of various types and to be able to include …