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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title></title>
<meta charset="utf-8" />
<link href="Intro_to_R_files/remark-css-0.0.1/default.css" rel="stylesheet" />
<link href="Intro_to_R_files/remark-css-0.0.1/default-fonts.css" rel="stylesheet" />
</head>
<body>
<textarea id="source">
.pull-right[
# Introduction to R
Hannah Coyle
20th August 2020
ECIMH Professional Development Session]
<center><img src="images/welcome_to_R.jpeg" height="400px" /></center>
.pull-right[@allison.horst]
---
## Introduction to R
- There are so many cool things you can do
- Today is not an exhaustive list, more about dipping your toes in the water
- Won't be a deep dive into *how* to use R, more *what* you can use it for
- Hopefully once inspired you will be motivated to go out on your own
.center[
]
---
## Lets start at the very beginning...
- *R* is the language *R Studio* is the IDE
- It is open-source (i.e. free) and available at http://www.rstudio.com/
<center><img src="./images/rstudio_ed.jpeg" height="450px" width="650px" /></center>
---
## A quick look see
<center><img src="images/rstudio.jpeg" height="450px" width="650px" /></center>
- To learn how to navigate R studio I think the best place to start is this video (https://rstudio.com/resources/webinars/a-gentle-introduction-to-tidy-statistics-in-r/)
---
## Packages
- The real power of R comes through it's packages
- Packages are fundamental units of reproducible R code.
- They include reusable R functions, the documentation that describes how to use them, and sample data
<center><img src="images/R_packages.jpeg" height="250px" width="500px"/></center>
- Step 1: Look on CRAN (https://cran.r-project.org/)
- Step 2: See if the author wrote a package vignette
- Step 3: Google it (always your friend!)
---
## Tidyverse
- The Tidyverse is created by Hadley Wickham ( R Pirate Captain!)
- Collection of packages designed with the sole purpose of making your life easier.
```r
install.packages("tidyverse")
library (tidyverse)
```
The goal of tidyr is to help you create tidy data. Tidy data is data where:
- Every column is variable.
- Every row is an observation.
- Every cell is a single value.
<center><img src="images/data_struc.jpeg" height="250px" width="500px"/></center>
---
## Data types and structure
- Everything in R is an object.
<center><img src="images/data_type.jpeg" height="350px" width="500px"/></center>
- Lots of useful functions to check what you are working with
+ class() - what kind of object is it (high-level)?
+ typeof() - what is the object’s data type (low-level)?
+ length() - how long is it? What about two dimensional objects?
+ attributes() - does it have any metadata?
---
## Import your data
- R can import data from lots of existing formats
+ **haven** for SPSS, Stata, and SAS data.
+ **httr** for web APIs.
+ **readxl** for .xls and .xlsx sheets.
+ **rvest** for web scraping.
+ **jsonlite** for JSON.
- Once in R, it is called a dataframe
<center><img src="images/data_frame1.jpeg" height="300px" width="550px" /></center>
---
## Wrangle your data
- No matter how much effort we put into database design the nature of data is that it is often messy
- The tidyverse includes packages specifically designed to help with the job
+ lubridate for dates and date-times.
+ stringr for working with strings
+ forcats for working with categorical variables
+ hms for time-of-day values.
- Helps clean/organise your data into the right format prior to plotting/analysis
.center[
]
---
# Wrangle your data (cont)...
- It's likely you will be working with a big dataset
```
## [1] 56 236
```
```
## Rows: 56
## Columns: 236
## $ code <dbl> 1, 10, 101, 102, 103, 104, 105, 106…
## $ group <chr> "control", "control", "mtbi", "mtbi…
## $ initals <chr> "LNo", "CRo", "AHa", "ASu", "KGa", …
## $ ur_number <dbl> NA, NA, 7038891, 7038256, 6202556, …
## $ sex <chr> "female", "female", "female", "male…
## $ d.o.b <chr> "20.12.88", "14.03.94", "28.07.69",…
## $ age <dbl> 28, 22, 47, 53, 28, 29, 30, 41, 49,…
## $ notes <chr> "", "", "", "", "", "", "", "", "3r…
## $ dateofinjury <date> NA, NA, 2017-01-21, 2017-01-18, 20…
## $ baseline <date> 2017-12-22, 2017-02-01, 2017-02-15…
## $ t1 <date> 2017-03-23, 2017-05-08, 2017-05-23…
## $ t2 <date> 2017-06-27, 2017-08-07, 2017-08-21…
## $ headinjury_hx <chr> "no", "no", "yes", "yes", "yes", "y…
## $ gcs <dbl> NA, NA, NA, 15, NA, 15, 15, NA, 13,…
## $ loc <chr> NA, NA, "yes", "no", "no", "no", "n…
## $ loc_dur <dbl> NA, NA, 2.0, NA, NA, 0.0, 0.0, NA, …
## $ amnesia <chr> "NA", "NA", "retrograde", NA, "retr…
## $ injury_notes <chr> "", "", "MBA, approx 60km/h, H/S, a…
## $ injury_class <chr> "", "", "MVA", "HS", "Other", "PBA"…
## $ days_post <dbl> NA, NA, 25, 32, 19, 13, 23, 12, 25,…
## $ ct_pathology <fct> NA, NA, nill, nill, nill, nill, nil…
## $ ct_notes <chr> "", "", "clear", "clear", "clear", …
## $ prior_injury <chr> "", "", "One other MBA, 1986/87, no…
## $ other_injury <chr> "", "", "right leg, look up on cern…
## $ ageofinjury <dbl> NA, NA, 47, 53, 28, 29, 30, 41, 49,…
## $ education <dbl> 21, 17, 16, 16, 15, 19, 12, 26, 16,…
## $ hand <chr> "1", "1", "1", "1", "1", "1", "1", …
## $ percent <dbl> 70, 100, 100, 100, 80, 100, 100, 10…
## $ mddiagnosis <dbl> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,…
## $ mdmel <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,…
## $ dysthymia <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,…
## $ mania <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
## $ panicagor <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ social <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ ocd <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ ptsd <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ alcohol <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ subst <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ anorexia <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ bulimia <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ anxiety <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ hads_anxiety_bl <dbl> NA, NA, NA, NA, NA, 0, 2, 1, 7, 0, …
## $ hads_depression_bl <dbl> NA, NA, NA, NA, NA, 2, 8, 0, 1, 2, …
## $ hads_total_bl <dbl> NA, NA, NA, NA, 30, 2, 10, 1, 8, 2,…
## $ sf36_pf_bl <dbl> 100, 100, 30, 100, 35, 80, 100, 95,…
## $ sf36_rphys_bl <dbl> 100, 100, 0, 0, 25, 0, 75, 0, 0, 10…
## $ sf36_remo_bl <dbl> 100, 100, 100, 33, 0, 100, 100, 100…
## $ sf36_energy_bl <dbl> 75, 85, 55, 85, 10, 85, 60, 80, 30,…
## $ sf36_mh_bl <dbl> 92, 96, 56, 96, 8, 84, 76, 88, 80, …
## $ sf36_sf_bl <dbl> 100, 100, 75, 25, 0, 75, 88, 75, 0,…
## $ sf36_pain_bl <dbl> 90.0, 90.0, 58.0, 45.0, 23.0, 45.0,…
## $ sf36_gh_bl <dbl> 90, 70, 80, 100, 65, 85, 100, 100, …
## $ rpq_3_bl <dbl> 0, 0, 1, 2, 9, 0, 2, 0, 3, 1, 2, 0,…
## $ rpq_13_bl <dbl> 3, 1, 0, 1, 30, 0, 0, 1, 18, 0, 18,…
## $ rpq_16_bl <dbl> 3, 1, 1, 3, 39, 0, 2, 1, 21, 1, 20,…
## $ mfi_gf_bl <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 13,…
## $ mfi_pf_bl <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 12,…
## $ mfi_ra_bl <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 16,…
## $ mfi_rm_bl <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 11,…
## $ mfi_mf_bl <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 16,…
## $ wtar <dbl> 44, 49, 32, 43, 21, 45, 37, 48, 45,…
## $ tma_bl <dbl> 16.53, 18.97, 26.00, 36.12, 24.00, …
## $ tmb_bl <dbl> 23.16, 29.37, 44.00, 47.00, 113.00,…
## $ ravlt_t1_bl <dbl> 10, 10, 7, 5, 6, 7, 6, 6, 4, 9, 9, …
## $ ravl_t2_bl <dbl> 14, 12, 13, 8, 8, 9, 11, 8, 6, 13, …
## $ ravlt_t3_bl <dbl> 15, 15, 13, 11, 8, 8, 12, 10, 8, 12…
## $ ravlt_t4_bl <dbl> 15, 15, 14, 11, 9, 10, 12, 11, 9, 1…
## $ ravlt_t5_bl <dbl> 15, 15, 14, 11, 9, 13, 12, 12, 13, …
## $ ravlt_t_bl <dbl> 69, 67, 61, 46, 40, 47, 53, 47, 40,…
## $ ravlt_a6a5_bl <dbl> 0, 0, -2, -5, 0, -3, -1, -1, -2, 0,…
## $ ravlt_d_bl <dbl> 15, 15, 12, 5, 10, 9, 12, 11, 7, 14…
## $ bvmt_t1_bl <dbl> 8, 9, 7, 6, 3, 6, 9, 7, 5, 5, 9, 2,…
## $ bvmt_t2_bl <dbl> 11, 10, 10, 11, 6, 8, 10, 12, 9, 10…
## $ bvmt_t3_bl <dbl> 11, 11, 11, 11, 11, 10, 11, 12, 12,…
## $ totalbvmt_bl <dbl> 30, 30, 28, 28, 20, 24, 30, 31, 26,…
## $ ds_fwd_bl <dbl> 11, 11, 9, 9, 12, 15, 14, 9, 13, 12…
## $ ds_bwd_bl <dbl> 10, 6, 6, 7, 7, 8, 8, 8, 10, 9, 6, …
## $ ds_total_bl <dbl> 21, 17, 15, 16, 19, 23, 22, 17, 23,…
## $ lns_bl <dbl> 13, 11, NA, 15, 9, 14, 12, 14, NA, …
## $ coding_bl <dbl> 70, 78, 75, 61, 56, 52, 50, 61, 54,…
## $ symbolsearch_bl <dbl> 45, 36, 35, 34, 26, 39, 32, 36, 22,…
## $ ravlt_recognition_bl <dbl> 47, 38, NA, 35, 36, 36, 37, 30, NA,…
## $ arithmetic_bl <dbl> 20, 17, 13, 20, 7, 11, 17, 16, 20, …
## $ cowat_bl <dbl> 56, 59, NA, 53, 47, 34, 42, 42, NA,…
## $ bvmt_delay_recall <dbl> 10, 11, NA, NA, 11, 8, 11, 12, 12, …
## $ bvmt_recognition <dbl> 12, 12, NA, 12, 11, 11, 12, 12, 12,…
## $ rmt <dbl> 49, 55, 46, 55, 41, 46, 39, 52, 50,…
## $ rmt_110 <dbl> 54, 61, 52, 61, 45, 51, 43, 57, 55,…
## $ rmt_70 <dbl> 34, 39, 32, 39, 29, 32, 26, 36, 35,…
## $ dsb_eeg_t_bl_pre <dbl> 10, 8, 6, 5, 5, 11, 11, 8, 8, 7, 9,…
## $ dsb_eeg_ldb_bl_pre <dbl> 6, 4, 4, 2, 4, 5, 5, 4, 4, 4, 5, 6,…
## $ dsb_eeg_t_bl_post <dbl> 8, 12, 2, 7, 5, 13, 11, 8, 10, 7, 1…
## $ dsb_eeg_ldb_bl_post <dbl> 4, 8, 2, 4, 3, 8, 6, 5, 6, 5, 7, 5,…
## $ dsb_eeg_t_bl_delay <dbl> 9, 11, NA, 7, 5, 13, 0, NA, NA, 10,…
## $ dsb_eeg_ldb_bl_delay <dbl> 5, 6, NA, 5, 3, 8, 0, NA, NA, 6, NA…
## $ teps_p2p_n100_negclus_amp_bl_pre <dbl> 1.4697246, 3.9677563, 0.4663457, 99…
## $ teps_p2p_n100_negclus_lat_bl_pre <dbl> 99, 0, 104, 999, 0, 0, 0, 118, 0, 1…
## $ teps_p2p_n100_posclus_amp_bl_pre <dbl> -2.5754220, -3.0335369, -3.0797581,…
## $ teps_p2p_n100_posclus_lat_bl_pre <dbl> 131, 118, 123, 999, 111, 113, 115, …
## $ teps_p2p_p60_posclus_amp_bl_pre <dbl> 1.36602658, 1.00471604, -1.09753984…
## $ teps_p2p_p60_posclus_lat_bl_pre <dbl> 64, 51, 0, 999, 0, 0, 52, 56, 64, 6…
## $ teps_p2p_n100_posclus_amp_bl_post <dbl> -3.1906658, -3.0217492, -3.3839027,…
## $ teps_p2p_n100_posclus_lat_bl_post <dbl> 119, 117, 111, 999, 97, 115, 118, 1…
## $ teps_p2p_n100_negclus_amp_bl_post <dbl> 5.7612603, 3.5404475, 1.8448407, 99…
## $ teps_p2p_n100_negclus_lat_bl_post <dbl> 0, 0, 0, 999, 0, 0, 111, 125, 0, 11…
## $ crt_go_acc <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA,…
## $ crt_go_rt <dbl> 315.746, 279.443, 999.000, 999.000,…
## $ crt_nogo_acc <dbl> 268.000, 218.500, NA, NA, NA, NA, N…
## $ crt_nogo_rt <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA,…
## $ gfp_first_win_preitbs <dbl> 1.8388496, 1.7561099, NA, 1.4917429…
## $ gfp_sec_win_preitbs <dbl> 2.0689890, 2.4071061, NA, 1.8387612…
## $ gfp_first_win_postitbs <dbl> 1.2000022, 1.3953458, NA, 2.3673882…
## $ gfp_sec_win_postitbs <dbl> 1.482913, 2.998014, NA, 2.680385, N…
## $ alpha_power_ec_bl <dbl> 0.14933330, 0.05639068, 2.19738956,…
## $ hads_depression_t1 <dbl> 0, 0, 3, 3, 16, NA, 1, NA, 6, NA, 1…
## $ hads_anxiety_t1 <dbl> 2, 1, 3, 1, 18, NA, 9, NA, 3, NA, 7…
## $ hads_total_t1 <dbl> 2, 1, 6, 4, 34, NA, 9, NA, 9, NA, 8…
## $ mfi_gf_t1 <dbl> NA, NA, 13, 7, NA, NA, 11, NA, 12, …
## $ mfi_pf_t1 <dbl> NA, NA, 14, 9, NA, NA, 9, NA, 8, NA…
## $ mfi_ra_t1 <dbl> NA, NA, 16, 5, NA, NA, 4, NA, 11, N…
## $ mfi_rm_t1 <dbl> NA, NA, 11, 10, NA, NA, 5, NA, 7, N…
## $ mfi_mf_t1 <dbl> NA, NA, 16, 5, NA, NA, 13, NA, 11, …
## $ sf36_pf_t1 <dbl> 100, 100, 29, NA, 19, NA, 90, NA, 1…
## $ sf36_rphys_t1 <dbl> 100, 100, 8, NA, 4, NA, 25, NA, 100…
## $ sf36_remo_t1 <dbl> 100, 100, 6, NA, 3, NA, 67, NA, 100…
## $ sf36_energy_t1 <dbl> 75, 90, 12, NA, 13, NA, 65, NA, 40,…
## $ sf36_mh_t1 <dbl> 92, 96, 21, NA, 14, NA, 76, NA, 80,…
## $ sf36_sf_t1 <dbl> 100, 100, 5, NA, 5, NA, 75, NA, 100…
## $ sf36_pain_t1 <dbl> 90, 100, 5, NA, 9, NA, 45, NA, 90, …
## $ sf36_gh_t1 <dbl> 95, 85, 15, NA, 18, NA, 85, NA, 95,…
## $ rpq_3_t1_control <dbl> 0, 1, NA, NA, NA, NA, NA, NA, NA, N…
## $ rpq_16_t1 <dbl> 4, 0, NA, NA, NA, NA, NA, NA, NA, N…
## $ rpq_10_t1 <dbl> NA, NA, 0, 0, 12, NA, 2, NA, 25, NA…
## $ rpq_10_mtbi_notes <chr> "", "", "", "", "", "", "", "", "\"…
## $ tma_t1 <dbl> 13.00, 20.00, 23.00, 23.00, 17.00, …
## $ tmb_t1 <dbl> 17.00, 33.00, 31.00, 43.00, 54.00, …
## $ ravlt_t1_t1 <dbl> NA, 14, 4, 5, 6, NA, 10, NA, 5, NA,…
## $ ravl_t2_t1 <dbl> NA, 15, 12, 8, 8, NA, 15, NA, 8, NA…
## $ ravlt_t3_t1 <dbl> NA, 15, 14, 9, 11, NA, 14, NA, 10, …
## $ ravlt_t4_t1 <dbl> NA, 15, 14, 8, 12, NA, 14, NA, 14, …
## $ ravlt_t5_t1 <dbl> NA, 15, 12, 9, 11, NA, 15, NA, 14, …
## $ ravlt_t_t1 <dbl> NA, 74, 56, 39, 48, NA, 68, NA, 51,…
## $ ravlt_a6a5_t1 <dbl> NA, 15, NA, -3, 2, NA, -2, NA, -4, …
## $ ravlt_d_t1 <dbl> NA, 15, 9, 6, 13, NA, 14, NA, 9, NA…
## $ bvmt_t1_t1 <dbl> 10, 8, 6, 2, 5, NA, 5, NA, 4, NA, 8…
## $ bvmt_t2_t1 <dbl> 11, 12, 10, 7, 8, NA, 10, NA, 10, N…
## $ bvmt_t3_t1 <dbl> 11, 12, 11, 7, 11, NA, 11, NA, 10, …
## $ ds_fwd_t1 <dbl> 13, 11, 11, 10, 9, NA, 13, NA, 15, …
## $ ds_bwd_t1 <dbl> 8, 10, 12, 8, 2, NA, 12, NA, 12, NA…
## $ ds_total_t1 <dbl> 21, 21, 23, 18, 11, NA, 25, NA, 27,…
## $ lns_t1 <dbl> 13, 11, NA, 13, 6, NA, 14, NA, NA, …
## $ coding_t1 <dbl> 72, 84, 75, 65, 52, NA, 53, NA, 57,…
## $ symbolsearch_t1 <dbl> 41, 46, 38, 37, 37, NA, 38, NA, 29,…
## $ ravlt_recognition_t1 <dbl> NA, 47, NA, 36, 39, NA, 43, NA, NA,…
## $ arithmetic_t1 <dbl> 21, 17, 15, 19, 8, NA, 15, NA, 20, …
## $ cowat_t1 <dbl> 45, 64, NA, 55, 58, NA, 45, NA, NA,…
## $ bvmt_delayrecall_t1 <dbl> 12, 12, NA, 6, 11, NA, 11, NA, 10, …
## $ bvmt_recognition_t1 <dbl> 12, 12, NA, 12, 12, NA, 12, NA, 12,…
## $ rmt_t1 <dbl> 50, 51, 47, 56, 39, NA, 39, NA, 48,…
## $ rmt_110_t1 <dbl> 55, 56, 53, 62, 43, NA, 43, NA, 53,…
## $ rmt_70_t1 <dbl> 35, 36, 32, 39, 27, NA, 27, NA, 34,…
## $ alpha_power_ec_t1 <dbl> 0.09483792, 0.04889328, 1.30195586,…
## $ hads_depression_t2 <dbl> 0, 1, 1, 0, NA, NA, 2, NA, 5, NA, 2…
## $ hads_anxiety_t2 <dbl> 1, 0, 4, 2, NA, NA, 8, NA, 3, NA, 6…
## $ hads_total_t2 <dbl> 1, 1, 5, 2, NA, NA, 10, NA, 8, NA, …
## $ sf36_pf_t2 <dbl> 100, 100, 90, 95, NA, NA, 100, NA, …
## $ sf36_rphys_t2 <dbl> 100, 100, 100, 100, NA, NA, 100, NA…
## $ sf36_remo_t2 <dbl> 100, 100, 100, 100, NA, NA, 100, NA…
## $ sf36_energy_t2 <dbl> 85, 90, 95, 85, NA, NA, 85, NA, 70,…
## $ sf36_mh_t2 <dbl> 100, 100, 92, 96, NA, NA, 76, NA, 7…
## $ sf36_sf_t2 <dbl> 100.0, 100.0, 62.5, 100.0, NA, NA, …
## $ sf36_pain_t2 <dbl> 100, 100, 100, 80, NA, NA, 100, NA,…
## $ sf36_gh_t2 <dbl> 95, 85, 80, 90, NA, NA, 85, NA, 90,…
## $ rpq_3_t2_control <dbl> 0, 0, NA, NA, NA, NA, NA, NA, NA, N…
## $ rpq_16_t2 <dbl> 0, 0, NA, NA, NA, NA, NA, NA, NA, N…
## $ rpq_10_t2 <dbl> NA, NA, 0, 0, NA, NA, 0, NA, 14, NA…
## $ rpq_mtbi_t2_notes <chr> "", "", "", "", "", "", "", "", "",…
## $ mfi_gf_t2 <dbl> NA, 6, 10, 6, NA, NA, 11, NA, 10, N…
## $ mfi_pf_t2 <dbl> NA, 4, 7, 8, NA, NA, 9, NA, 8, NA, …
## $ mfi_ra_t2 <dbl> NA, 4, 12, 8, NA, NA, 4, NA, 9, NA,…
## $ mfi_rm_t2 <dbl> NA, 4, 5, 4, NA, NA, 5, NA, 6, NA, …
## $ mfi_mf_t2 <dbl> NA, 4, 7, 9, NA, NA, 13, NA, 5, NA,…
## $ tma_t2 <dbl> 11.00, 18.81, 18.22, 17.44, NA, NA,…
## $ tmb_t2 <dbl> 16.000, 28.530, 35.160, 50.530, NA,…
## $ ravlt_t1_t2 <dbl> 9, NA, 5, 8, NA, NA, 10, NA, 7, NA,…
## $ ravl_t2_t2 <dbl> 14, NA, 9, 7, NA, NA, 12, NA, 10, N…
## $ ravlt_t3_t2 <dbl> 15, NA, 8, 9, NA, NA, 12, NA, 12, N…
## $ ravlt_t4_t2 <dbl> 15, NA, 13, 11, NA, NA, 14, NA, 13,…
## $ ravlt_t5_t2 <dbl> 15, NA, 11, 10, NA, NA, 13, NA, 13,…
## $ ravlt_t_t2 <dbl> 68, NA, 46, 45, NA, NA, 61, NA, 55,…
## $ ravlt_a6a5_t2 <dbl> 0, NA, -3, -2, NA, NA, 1, NA, -3, N…
## $ ravlt_d_t2 <dbl> 14, NA, 7, 8, NA, NA, 15, NA, 10, N…
## $ bvmt_t1_t2 <dbl> 10, 9, 5, 6, NA, NA, 7, NA, 7, NA, …
## $ bvmt_t2_t2 <dbl> 12, 12, 7, 9, NA, NA, 12, NA, 10, N…
## $ bvmt_t3_t2 <dbl> 12, 12, 10, 11, NA, NA, 11, NA, 10,…
## $ ds_fwd_t2 <dbl> 12, 11, 11, 8, NA, NA, 14, NA, 15, …
## $ ds_bwd_t2 <dbl> 8, 8, 11, 8, NA, NA, 10, NA, 11, NA…
## $ ds_total_t2 <dbl> 20, 19, 22, 16, NA, NA, 24, NA, 26,…
## $ lns_t2 <dbl> 14, 12, NA, 9, NA, NA, 14, NA, 14, …
## $ coding_t2 <dbl> 74, 86, 70, 64, NA, NA, 58, NA, 56,…
## $ symbolsearch_t2 <dbl> 48, 48, 42, 40, NA, NA, 38, NA, 19,…
## $ ravlt_recognition_t2 <dbl> 46, NA, NA, 40, NA, NA, 39, NA, NA,…
## $ arithmetic_t2 <dbl> 20, 15, 16, 18, NA, NA, 17, NA, 20,…
## $ cowat_t2 <dbl> 44, 61, NA, 52, NA, NA, 40, NA, NA,…
## $ bvmt_delayrecall_t2 <dbl> 12, 12, 8, 11, NA, NA, 12, NA, 10, …
## $ bvmt_recognition_t2 <dbl> 12, 12, 12, 12, NA, NA, 12, NA, 12,…
## $ rmt_t2 <dbl> 47, 51, NA, 56, NA, NA, 38, NA, 50,…
## $ rmt_110_t2 <dbl> 52, 56, 51, 62, NA, NA, 42, NA, 55,…
## $ rmt_70_t2 <dbl> 33, 36, 32, 39, NA, NA, 27, NA, 35,…
## $ alpha_power_ec_t2 <dbl> 0.09497454, 0.03579252, 1.21636692,…
## $ ztma_bl <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA,…
## $ bvmt_total <dbl> 30, 30, 28, 28, 20, 24, 30, 31, 26,…
## $ mfi_total_bl <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 68,…
## $ mfi_total_t1 <dbl> NA, NA, 70, 36, NA, NA, 42, NA, 49,…
## $ mfi_total_t2 <dbl> NA, 22, 41, 35, NA, NA, 42, NA, 38,…
## $ n100_bl <dbl> -2.5754220, -3.0335370, -3.0797580,…
## $ n100_t1 <dbl> -0.6292168, -2.6058410, -3.9175000,…
## $ n100_t2 <dbl> -1.885530, -1.852751, -4.940181, -1…
## $ alpha_bl <dbl> 0.11919471, 0.03767557, 1.68883536,…
## $ alpha_t1 <dbl> 0.07992500, 0.04556836, 1.19564393,…
## $ alpha_t2 <dbl> 0.07333200, 0.02657021, 1.13498800,…
## $ av_gfp_bl <dbl> 1.341457, 2.196680, 3.231449, 2.523…
## $ av_gfp_t1 <dbl> 2.7909408, 1.6109176, 1.7344729, NA…
## $ av_gfp_t2 <dbl> 1.443285, 1.754155, 2.445952, 1.179…
## $ p60_bl <dbl> 1.36602600, 1.00471600, -1.09754000…
## $ p60_t1 <dbl> 0.76626000, 1.27640400, -1.54978100…
## $ p60_t2 <dbl> 0.926337800, 1.372298000, -1.248625…
## $ rpq_perc_bl.x <dbl> 4.6875, 1.5625, 1.5625, 4.6875, 60.…
## $ rpq_perc_t1.x <dbl> 6.2500, 1.5625, 0.0000, 0.0000, 30.…
## $ rpq_perc_t2.x <dbl> 0.0, 0.0, 0.0, 0.0, NA, NA, 0.0, NA…
## $ rpq_bl_cat <fct> NA, NA, mild, mild, severe, nil, mi…
## $ rpq_t1_cat <fct> NA, NA, nil, nil, moderate, NA, mil…
## $ rpq_t2_cat <fct> NA, NA, nil, nil, NA, NA, nil, NA, …
## $ rpq_perc_bl.y <dbl> 4.6875, 1.5625, 1.5625, 4.6875, 60.…
## $ rpq_perc_t1.y <dbl> 6.2500, 1.5625, 0.0000, 0.0000, 30.…
## $ rpq_perc_t2.y <dbl> 0.0, 0.0, 0.0, 0.0, NA, NA, 0.0, NA…
```
<table>
<thead>
<tr>
<th style="text-align:right;"> code </th>
<th style="text-align:left;"> group </th>
<th style="text-align:left;"> initals </th>
<th style="text-align:right;"> ur_number </th>
<th style="text-align:left;"> sex </th>
<th style="text-align:left;"> d.o.b </th>
<th style="text-align:right;"> age </th>
<th style="text-align:left;"> notes </th>
<th style="text-align:left;"> dateofinjury </th>
<th style="text-align:left;"> baseline </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;"> 1 </td>
<td style="text-align:left;"> control </td>
<td style="text-align:left;"> LNo </td>
<td style="text-align:right;"> NA </td>
<td style="text-align:left;"> female </td>
<td style="text-align:left;"> 20.12.88 </td>
<td style="text-align:right;"> 28 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> NA </td>
<td style="text-align:left;"> 2017-12-22 </td>
</tr>
<tr>
<td style="text-align:right;"> 10 </td>
<td style="text-align:left;"> control </td>
<td style="text-align:left;"> CRo </td>
<td style="text-align:right;"> NA </td>
<td style="text-align:left;"> female </td>
<td style="text-align:left;"> 14.03.94 </td>
<td style="text-align:right;"> 22 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> NA </td>
<td style="text-align:left;"> 2017-02-01 </td>
</tr>
<tr>
<td style="text-align:right;"> 101 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> AHa </td>
<td style="text-align:right;"> 7038891 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:left;"> 28.07.69 </td>
<td style="text-align:right;"> 47 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> 2017-01-21 </td>
<td style="text-align:left;"> 2017-02-15 </td>
</tr>
<tr>
<td style="text-align:right;"> 102 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> ASu </td>
<td style="text-align:right;"> 7038256 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:left;"> 31.10.63 </td>
<td style="text-align:right;"> 53 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> 2017-01-18 </td>
<td style="text-align:left;"> 2017-02-24 </td>
</tr>
<tr>
<td style="text-align:right;"> 103 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> KGa </td>
<td style="text-align:right;"> 6202556 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:left;"> 16.11.89 </td>
<td style="text-align:right;"> 28 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> 2017-03-02 </td>
<td style="text-align:left;"> 2017-03-21 </td>
</tr>
<tr>
<td style="text-align:right;"> 104 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> TDe </td>
<td style="text-align:right;"> 6252414 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:left;"> 08.02.88 </td>
<td style="text-align:right;"> 29 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> 2017-04-05 </td>
<td style="text-align:left;"> 2017-04-18 </td>
</tr>
<tr>
<td style="text-align:right;"> 105 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> JMo </td>
<td style="text-align:right;"> 1229531 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:left;"> 28.09.86 </td>
<td style="text-align:right;"> 30 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> 2017-03-27 </td>
<td style="text-align:left;"> 2017-04-19 </td>
</tr>
<tr>
<td style="text-align:right;"> 106 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> PPr </td>
<td style="text-align:right;"> 6065121 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:left;"> 10.02.76 </td>
<td style="text-align:right;"> 41 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> 2017-04-18 </td>
<td style="text-align:left;"> 2017-05-01 </td>
</tr>
<tr>
<td style="text-align:right;"> 107 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> DBe </td>
<td style="text-align:right;"> 7061598 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:left;"> 08.03.68 </td>
<td style="text-align:right;"> 49 </td>
<td style="text-align:left;"> 3rd session out of +/- 7 day window due to holidays </td>
<td style="text-align:left;"> 2017-05-20 </td>
<td style="text-align:left;"> 2017-06-14 </td>
</tr>
<tr>
<td style="text-align:right;"> 108 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> JMi </td>
<td style="text-align:right;"> 7063069 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:left;"> 21.03.92 </td>
<td style="text-align:right;"> 25 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> 2017-05-31 </td>
<td style="text-align:left;"> 2017-06-27 </td>
</tr>
<tr>
<td style="text-align:right;"> 109 </td>
<td style="text-align:left;"> mtbi </td>
<td style="text-align:left;"> JDu </td>
<td style="text-align:right;"> 1143545 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:left;"> 15.08.82 </td>
<td style="text-align:right;"> 34 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> 2017-06-13 </td>
<td style="text-align:left;"> 2017-07-07 </td>
</tr>
<tr>
<td style="text-align:right;"> 11 </td>
<td style="text-align:left;"> control </td>
<td style="text-align:left;"> SKa </td>
<td style="text-align:right;"> NA </td>
<td style="text-align:left;"> male </td>
<td style="text-align:left;"> 18.07.85 </td>
<td style="text-align:right;"> 31 </td>
<td style="text-align:left;"> </td>
<td style="text-align:left;"> NA </td>
<td style="text-align:left;"> 2017-03-09 </td>
</tr>
</tbody>
</table>
---
# So dplyr is your best of friends
<center><img src="images/dplyr.jpeg" height="500px" width="650px" /></center>
---
# For example...
- Say I wan't to look at just the mTBI participants
```r
COMBINED_COG_PhD %>%
dplyr::filter(group=="mtbi") %>%
dplyr::select(code, age, sex, education) %>%
knitr::kable("html")
```
<table>
<thead>
<tr>
<th style="text-align:right;"> code </th>
<th style="text-align:right;"> age </th>
<th style="text-align:left;"> sex </th>
<th style="text-align:right;"> education </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;"> 101 </td>
<td style="text-align:right;"> 47 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:right;"> 16.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 102 </td>
<td style="text-align:right;"> 53 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 16.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 103 </td>
<td style="text-align:right;"> 28 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:right;"> 15.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 104 </td>
<td style="text-align:right;"> 29 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:right;"> 19.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 105 </td>
<td style="text-align:right;"> 30 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 12.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 106 </td>
<td style="text-align:right;"> 41 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 26.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 107 </td>
<td style="text-align:right;"> 49 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 16.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 108 </td>
<td style="text-align:right;"> 25 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 17.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 109 </td>
<td style="text-align:right;"> 34 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 15.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 110 </td>
<td style="text-align:right;"> 27 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 12.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 111 </td>
<td style="text-align:right;"> 31 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 15.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 112 </td>
<td style="text-align:right;"> 23 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 15.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 113 </td>
<td style="text-align:right;"> 46 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 13.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 114 </td>
<td style="text-align:right;"> 29 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 17.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 115 </td>
<td style="text-align:right;"> 28 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:right;"> 14.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 116 </td>
<td style="text-align:right;"> 21 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 10.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 117 </td>
<td style="text-align:right;"> 26 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 12.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 118 </td>
<td style="text-align:right;"> 21 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 13.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 119 </td>
<td style="text-align:right;"> 31 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 9.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 120 </td>
<td style="text-align:right;"> 44 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:right;"> 15.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 121 </td>
<td style="text-align:right;"> 38 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 12.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 122 </td>
<td style="text-align:right;"> 49 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 16.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 123 </td>
<td style="text-align:right;"> 42 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 15.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 124 </td>
<td style="text-align:right;"> 32 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:right;"> 17.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 125 </td>
<td style="text-align:right;"> 55 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 18.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 126 </td>
<td style="text-align:right;"> 24 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 15.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 127 </td>
<td style="text-align:right;"> 33 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 16.5 </td>
</tr>
<tr>
<td style="text-align:right;"> 128 </td>
<td style="text-align:right;"> 40 </td>
<td style="text-align:left;"> female </td>
<td style="text-align:right;"> 19.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 129 </td>
<td style="text-align:right;"> 54 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 14.0 </td>
</tr>
<tr>
<td style="text-align:right;"> 130 </td>
<td style="text-align:right;"> 33 </td>
<td style="text-align:left;"> male </td>
<td style="text-align:right;"> 18.0 </td>
</tr>
</tbody>
</table>
---
# dplyr (cont)..
<center><img src="images/dplyr_2.jpeg" height="550px" width="700px" /></center>
https://rstudio.com/wp-content/uploads/2015/02/data-wrangling-cheatsheet.pdf
---
## Explore your data
- ggplot2 is a **magical** graphics package specifically built to help you iteratively create customized graphs.
<center><img src="images/ggplot2_exploratory_1.jpeg" height="400px" width="550px" /></center>
.pull-right[@allison.horst]
---
## The *plot*-abilities are endless..
<center><img src="images/ggplot_all.jpeg" height="450px" width="550px" /></center>
https://www.r-graph-gallery.com/all-graphs.html
https://serialmentor.com/dataviz/directory-of-visualizations.html
---
##
---
## Friends don't let friends make bar plots...
.center[
]
----
<center><img src="images/data_struc_show1.jpeg" height="650px" width="650px" /></center>
---
## The grammar of graphics..
To make the most basic graph, you need to tell R three things:
1. You're using ggplot
2. What data is used to create the graph
3. What type of graph you want to create
...everything beyond that is optional customization.
---
So code to make the most basic scatterplot for might look something like..
```r
ggplot(g, aes(x = year, y = visitors)) +
geom_point()
```
<img src="Intro_to_R_files/figure-html/dino_graph-1.png" style="display: block; margin: auto;" />
---
- Then you can customise your graph based on combining dplyr, the pipe operator and ggplot2
```r
np_visit %>% #
dplyr::filter(state == "CA" & type == "National Park") %>%
dplyr::arrange(park_name, year) %>%
ggplot(aes(x = year, y = visitors)) +
geom_point() +
xlab("Year") +
ylab("Annual Visitors") +
theme_bw() +
ggtitle("California National Parks Visitation") +
facet_wrap(~park_name)
```
---
<img src="Intro_to_R_files/figure-html/unnamed-chunk-6-1.png" style="display: block; margin: auto;" />
https://cedricscherer.netlify.app/2019/05/17/the-evolution-of-a-ggplot-ep.-1/
---
## The pipe operator %>%
- The "pipe" (%>%) is another friend well worth learning how to use
- The pipe will forward a value, or the result of an expression, into the next function call/expression.
```r
# For instance a function to filter data can be written as:
iris %>%
dplyr::group_by(Species) %>%
dplyr::summarize_if(is.numeric, mean) %>%
ungroup() %>%
gather(measure, value, -Species) %>%
dplyr::arrange(value)
```
```
## # A tibble: 12 x 3
## Species measure value
## <fct> <chr> <dbl>
## 1 setosa Petal.Width 0.246
## 2 versicolor Petal.Width 1.33
## 3 setosa Petal.Length 1.46
## 4 virginica Petal.Width 2.03
## 5 versicolor Sepal.Width 2.77
## 6 virginica Sepal.Width 2.97
## 7 setosa Sepal.Width 3.43
## 8 versicolor Petal.Length 4.26
## 9 setosa Sepal.Length 5.01
## 10 virginica Petal.Length 5.55
## 11 versicolor Sepal.Length 5.94
## 12 virginica Sepal.Length 6.59
```
Its legible in that you can read this as you would read normal prose (we read the %>% as “and then”): “take iris and then group by and then summarise and then ungroup and then arrange.
---
## Analysis: Write your own *fun*-ctions
- Make the computer do the hard work
- I.e take a manual job like extracting values from presentation output in excel
Turn this --> x 60 participants x 3 timepoints x 3 conditions
<center><img src="images/excel_sheet.jpeg" height="400px" width="550px" /></center>
---
## Using this....
```r
load_ds_behav <- function(filename) {
if (!file.exists(filename)) {
warning(paste("Missing", filename))
return(NULL)
}
pathA <- dirname(filename)
folder1 <- basename(pathA)
id<- folder1 ## pull apart file name with bash style
df <- read.table(filename,header = TRUE, sep = "\t",fileEncoding= "ASCII") # create a dataframe
df <- mutate(df, sourcefile=filename, id=id,
timepoint=timepoint, condition=condition)
acc_data<-sum(df$Accuracy=="Correct")
df<-mutate(df, accuracy=acc_data)
df<-select(df, id, timepoint, condition, accuracy)
df<-head(df,1)
return(df) } # Calculate accuracy and return df
## Now we have it working, instantly apply to everything
ds_df <- map_df(ds_behav_files, load_ds_behav)
```
---
## Into this.....
<table>
<thead>
<tr>
<th style="text-align:right;"> id </th>
<th style="text-align:left;"> group </th>
<th style="text-align:right;"> bl_pre </th>
<th style="text-align:right;"> bl_post </th>
<th style="text-align:right;"> bl_delay </th>
<th style="text-align:right;"> t1_pre </th>
<th style="text-align:right;"> t1_post </th>
<th style="text-align:right;"> t1_delay </th>
<th style="text-align:right;"> t2_pre </th>
<th style="text-align:right;"> t2_post </th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;"> 1 </td>
<td style="text-align:left;"> Control </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 8 </td>
<td style="text-align:right;"> 9 </td>
<td style="text-align:right;"> 8 </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 12 </td>
<td style="text-align:right;"> 14 </td>
<td style="text-align:right;"> 14 </td>
</tr>
<tr>
<td style="text-align:right;"> 2 </td>
<td style="text-align:left;"> Control </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 19 </td>
<td style="text-align:right;"> 14 </td>
<td style="text-align:right;"> 13 </td>
<td style="text-align:right;"> 13 </td>
<td style="text-align:right;"> 11 </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 10 </td>
</tr>
<tr>
<td style="text-align:right;"> 3 </td>
<td style="text-align:left;"> Control </td>
<td style="text-align:right;"> 12 </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 8 </td>
<td style="text-align:right;"> 9 </td>
<td style="text-align:right;"> 16 </td>
<td style="text-align:right;"> 13 </td>
<td style="text-align:right;"> 12 </td>
<td style="text-align:right;"> 12 </td>
</tr>
<tr>
<td style="text-align:right;"> 4 </td>
<td style="text-align:left;"> Control </td>
<td style="text-align:right;"> 11 </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 15 </td>
<td style="text-align:right;"> 11 </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 15 </td>
<td style="text-align:right;"> 18 </td>
<td style="text-align:right;"> 18 </td>
</tr>
<tr>
<td style="text-align:right;"> 5 </td>
<td style="text-align:left;"> Control </td>
<td style="text-align:right;"> 13 </td>
<td style="text-align:right;"> 12 </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 11 </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 10 </td>
<td style="text-align:right;"> 12 </td>
<td style="text-align:right;"> 12 </td>
</tr>
<tr>
<td style="text-align:right;"> 6 </td>
<td style="text-align:left;"> Control </td>
<td style="text-align:right;"> 12 </td>
<td style="text-align:right;"> 14 </td>
<td style="text-align:right;"> 14 </td>