Projektseminar

Datenaufbereitung II

Julius Klingelhoefer

2022-12-03

Aufgabe der letzten Woche

Fragen zur R-Übung der letzten Sitzung?

Erhebungs-Updates

Aktueller Stand der Erhebung



Screenshot des movisensXS-Dashboards, das zeigt, dass in der Version ohne Logging 79, in der Version mit Logging 94 Personen teilgenommen haben

Teilnehmer*innenanzahl Experience Sampling, Stand 15.11.22, 11:40

Graph, welcher zeigt, dass am 14. 11. knapp 200 vollständige Fragebägen und am 15.11. deutlich unter 50 Fragebögen volldtändig ausgefüllt wurden.

Teilnehmer*innenanzahl in der Vorbefragung, Stand 15.11.22, 11:44

Kursanforderungen

  • Aktive Rekrutierung von Studienteilnehmer*innen

Wozu laden Sie ein?

  • Befragungs-Studie der FAU Erlangen-Nürnberg (FB WiSo)

  • Sie haben die Studie im Rahmen Ihres Studiums in einem Kurs unter Betreuung von Julius Klingelhöfer entwickelt

  • Die Befragung untersucht Wohlbefinden und (nicht-)Nutzung digitaler/sozialer Medien im Alltag

  • Ziel der Studie ist, die Zusammenhänge zwischen selbstgesteuerter Mediennutzung und Wohlbefinden besser zu verstehen, um daraus Empfehlungen abzuleiten

  • Die Studie besteht aus zwei Teilen:

    • Vorbefragung (ca. 15 Min.)

    • 5 Kurzfragebögen pro Tag, je max. 1 Minute lang für 14 Tage (insg. max. 70 Minuten), zugestellt per Studien-App

  • Alle Studienabschnitte sind vollständig anonym

  • Alle Daten werden konform zur DSGVO, also nach höchsten deutschen/europäischen

    Datenschutzstandards, anonym erhoben und dienen nur der Forschung (keine kommerzielle Verwendung)

Zielgruppe

  • 18-35 Jahre alt

  • Idealerweise (halbwegs) geregelte Arbeitszeiten (Ausfüllen könnte schwierig für Schichtarbeiter*innen, o.Ä. sein) - aber kein Ausschlusskriterium

  • Besitzen ein Android-Smartphone

  • Idealerweise Bereit zur Teilnahme an der gesamten Studie (Vor-, ESM- & Nachbefragung)

    • Gesamtaufwand max. 90 Minuten (realistischerweise wahrscheinlich eher 60 min.)

Wichtigste Teilnahmeanreize

  • Interesse am Thema wecken ➡️ intrinsische Motivation

  • Persönliche Beziehung zum/r Teilnehmer*in; persönlicher Gefallen/Unterstützung des Studiums

  • Beitrag zur Forschung: besseres Verständnis von Detox, Wohlbefinden, & Mediennutzung

  • Implikationen für die Praxis

  • Monetäre Incentives

    • Als Gutschein für beliebige Online-Shops (über Wunschgutschein.de)

    • 15€ p.P. bei vollständiger Teilnahme

    • Verlosung von 100€ + 2*50€ Gutscheinen

  • Nicht-monetäre Incentives (bei Interesse)

    • Individuelles Feedback, grafisch aufbereitet (per Shiny-App)

    • Zusammenfassung der Studienergebnisse &/| Tipps rund um selbstregulierte Mediennutzung

Dos and Dont’s bei der Rekrutierung

Dos

  • Divers rekrutieren

  • Gezielte, persönliche Ansprache

  • Zentrale Teilnahmevoraussetzungen im Gespräch prüfen

  • Teilnahmeanreize nennen ➡️ Persuasion, aber keine Nötigung

  • Zusenden/Teilen des Fragebogens über Link (+Flyer)

Don’ts

  • Teilnahmevoraussetzungen ignorieren ➡️ macht allen Beteiligten Arbeit, bringt letztlich aber nichts

  • konkrete Forschungsfragen oder Hypothesen nennen ➡️ gefährdet Validität der Daten

  • Personen einladen, bei denen die Teilnahmechance sehr gering ist ➡️ Nachrekrutierungsaufwand

Wie Rekrutieren?

  • SoSci-Panel ✅

  • WiSo-Verteiler 🔜

  • Flyer drucken 🔜 (+ verteilen)

  • Persönliches Umfeld (FtF, Messenger, E-Mail, …)

  • Soziale Netzwerke (Instagram, Facebook, …)

  • Gruppen in sozialen Netzwerken (z. B. lokale Kleinanzeigen Facebook-Gruppen, …)

  • Umfragenetzwerke, z. B. Surveycircle

  • …

red arrows pointing up

CC0, KazuN, pixabay.com

Sharepic

Gruppenarbeit

Weitere Ideen?

  • Gruppenarbeit: Brainstorming: Ideen für die Rekrutierung

  • Welche Arten der Rekrutierung können Sie sich zusätzlich vorstellen?

  • Ordnen Sie die Rekrutierungsmöglichkeiten nach der angenommenen Effektivität (Sie können dafür Teams nutzen)

  • Zeit: 15 min.

Input: Datenaufbereitung II

Ziel der Sitzungen

  1. Darstellung der grundlegenden Schritte der Datenaufbereitung (im Kontext eines Forschungsprojektes)
  2. Hinweis auf spezifische Heraus- bzw. Anforderungen von ESM-Datensätzen
  3. Vermittlung der notwendigen RFunktionen zur selbstständigen Bearbeitung der Daten

Rückblick: Typisches Data-Science Projekt

Wickham & Grolemund (2016)

Inhalte heute

  • Letzte Woche: Fokus auf den “ersten Schritt”, d.h. auf

    • importieren

    • zusammenfügen

    • oberflächlich kontrollieren

  • Heute: “zweiter Schritt”:

    • Variablen über- & bearbeiten z. B.:

      • recodieren oder

      • neu erstellen (z. B. berechnen)

@dejonge

Jonge & Loo (n.d.)

Grundlagen der Variablenüberarbeitung in R

Reise durch das tidyverse & angrenzende Galaxien (sjmisc)

🦠 mutate() ⚔️ across() 🗃️ group_by() ✨ rec() 1️⃣ dicho()

Bearbeitung von Fällen

Fälle auswählen

Quelle: Posit Software (2021)

Bearbeitung von Fällen

Fälle sortieren

Quelle: Posit Software (2021)

Bearbeitung von Variablen

Variablen auswählen und sortieren

Quelle: Posit Software (2021)

Beispiel: Filterung nach Datentyp

Basisdaten

dl %>% 

  nrow()
[1] 25624

Anwendung von filter()

dl %>% 
  filter(form == "a Situational Survey") %>% 
  nrow()
[1] 10632

Beispiel: Drop der Variable version

Basisdaten

dl %>% 

  colnames()
  [1] "probe_id"                       "id"                            
  [3] "probe_start"                    "trigger_time_internal"         
  [5] "probe_time"                     "date_day_hm"                   
  [7] "probe_num"                      "trigger"                       
  [9] "valid_probe"                    "date_day"                      
 [11] "time_day"                       "trigger_date"                  
 [13] "trigger_time"                   "trigger_counter"               
 [15] "form"                           "form_start_date"               
 [17] "form_start_time"                "form_finish_date"              
 [19] "form_finish_time"               "form_upload_date"              
 [21] "form_upload_time"               "missing"                       
 [23] "wb_ge"                          "wb_energy"                     
 [25] "wb_stress"                      "wb_connect"                    
 [27] "procra"                         "screentime_work"               
 [29] "screentime_leisure"             "disco_1"                       
 [31] "disco_2"                        "disco_3"                       
 [33] "disco_4"                        "disco_5"                       
 [35] "disco_6"                        "disco_sd"                      
 [37] "motivation_distraction"         "motivation_wellbeing"          
 [39] "motivation_social"              "ns_autonomy"                   
 [41] "ns_competence"                  "ns_relatedness"                
 [43] "media_category_1"               "media_category_2"              
 [45] "media_category_3"               "media_category_4"              
 [47] "media_category_5"               "media_category_6"              
 [49] "media_category_7"               "goal_conf"                     
 [51] "missed_alarm"                   "missed_time"                   
 [53] "disco_1_daily_alarm_1"          "disco_1_daily_alarm_2"         
 [55] "disco_1_daily_alarm_3"          "disco_1_daily_alarm_4"         
 [57] "disco_1_daily_alarm_5"          "disco_1_daily_alarm_6"         
 [59] "disco_1_daily_time_1"           "disco_1_daily_time_2"          
 [61] "disco_1_daily_time_3"           "disco_1_daily_time_4"          
 [63] "disco_1_daily_time_5"           "disco_1_daily_time_6"          
 [65] "motivation_distraction_day"     "motivation_well_being_day"     
 [67] "motivation_social_day"          "conscientiousness"             
 [69] "disco_thoughts"                 "final_feedback"                
 [71] "participation_n_1"              "participation_n"               
 [73] "text_comment"                   "reward_choice"                 
 [75] "bold_check"                     "feedback"                      
 [77] "feedback_pin"                   "feedback_study_results"        
 [79] "day_n"                          "daily_forms"                   
 [81] "participation_number"           "final_day"                     
 [83] "finished"                       "end_of_day_fillout"            
 [85] "day_min"                        "day_newest"                    
 [87] "day_start"                      "dur"                           
 [89] "logging"                        "case_pre"                      
 [91] "serial_pre"                     "ref_pre"                       
 [93] "questnnr_pre"                   "mode_pre"                      
 [95] "started_pre"                    "availability_preference_01_pre"
 [97] "availability_preference_02_pre" "availability_preference_03_pre"
 [99] "availability_preference_04_pre" "disco_tech_w_1_pre"            
[101] "disco_tech_w_2_pre"             "disco_tech_w_3_pre"            
[103] "disco_tech_w_4_pre"             "disco_tech_w_5_pre"            
[105] "disco_tech_w_6_pre"             "disco_level_w_1_pre"           
[107] "disco_level_w_2_pre"            "disco_level_w_3_pre"           
[109] "disco_level_w_4_pre"            "disco_level_w_5_pre"           
[111] "disco_level_w_6_pre"            "disco_thoughts_pre"            
[113] "disco_practice_other_pre"       "disco_context_text_pre"        
[115] "disco_context_1_pre"            "disco_context_2_pre"           
[117] "disco_context_3_pre"            "disco_context_4_pre"           
[119] "disco_context_5_pre"            "disco_context_6_pre"           
[121] "disco_context_7_pre"            "disco_context_8_pre"           
[123] "disco_context_9_pre"            "disco_context_10_pre"          
[125] "disco_context_11_pre"           "disco_context_other_pre"       
[127] "logging_choice_pre"             "comment_pre_survey_pre"        
[129] "fomo_01_pre"                    "fomo_02_pre"                   
[131] "fomo_03_pre"                    "fomo_04_pre"                   
[133] "fomo_05_pre"                    "fomo_06_pre"                   
[135] "fomo_07_pre"                    "fomo_08_pre"                   
[137] "fomo_09_pre"                    "fomo_10_pre"                   
[139] "consent_pre"                    "ic03_04_pre"                   
[141] "ic03_03_pre"                    "ic03_01_pre"                   
[143] "ic03_02_pre"                    "android_pre"                   
[145] "consent_part_2_pre"             "md_work_seconds_pre"           
[147] "md_private_seconds_pre"         "mindfulness_01_pre"            
[149] "mindfulness_02_pre"             "mindfulness_03_pre"            
[151] "mindfulness_04_pre"             "mindfulness_05_pre"            
[153] "pdo_01_pre"                     "pdo_02_pre"                    
[155] "pdo_03_pre"                     "rsd_01_pre"                    
[157] "rsd_02_pre"                     "rsd_03_pre"                    
[159] "rsd_04_pre"                     "rsd_05_pre"                    
[161] "rsd_06_pre"                     "sc_res_1_pre"                  
[163] "sc_res_3_pre"                   "sc_imp_1_pre"                  
[165] "sc_res_4_pre"                   "sc_res_2_pre"                  
[167] "sc_imp_2_pre"                   "sc_imp_3_pre"                  
[169] "sc_imp_4_pre"                   "sd_gender_pre"                 
[171] "sd_gender_custom_pre"           "age_pre"                       
[173] "work_hours_pre"                 "sd_edu_pre"                    
[175] "sd_education_text_pre"          "sd_living_arrangement_pre"     
[177] "sd_living_not_own_kids_pre"     "sd_living_own_kids_pre"        
[179] "sd_living_arrangement_text_pre" "sd_household_size_pre"         
[181] "sd_occupation_pre"              "sd_occupation_text_pre"        
[183] "device_type_pre"                "swl_01_pre"                    
[185] "swl_02_pre"                     "swl_03_pre"                    
[187] "swl_04_pre"                     "swl_05_pre"                    
[189] "pa_01_pre"                      "pa_02_pre"                     
[191] "pa_03_pre"                      "pa_04_pre"                     
[193] "pa_05_pre"                      "na_01_pre"                     
[195] "na_02_pre"                      "na_03_pre"                     
[197] "na_04_pre"                      "na_05_pre"                     
[199] "positive_arousal_pre"           "negative_arousal_pre"          
[201] "connectedness_pre"              "wb_ge_pre"                     
[203] "procra_01_pre"                  "procra_02_pre"                 
[205] "procra_03_pre"                  "procra_04_pre"                 
[207] "procra_05_pre"                  "time001_pre"                   
[209] "time002_pre"                    "time003_pre"                   
[211] "time004_pre"                    "time005_pre"                   
[213] "time006_pre"                    "time007_pre"                   
[215] "time008_pre"                    "time009_pre"                   
[217] "time010_pre"                    "time011_pre"                   
[219] "time012_pre"                    "time013_pre"                   
[221] "time014_pre"                    "time015_pre"                   
[223] "time016_pre"                    "time017_pre"                   
[225] "time018_pre"                    "time019_pre"                   
[227] "time020_pre"                    "time021_pre"                   
[229] "time_sum_pre"                   "mailsent_pre"                  
[231] "lastdata_pre"                   "finished_pre"                  
[233] "q_viewer_pre"                   "lastpage_pre"                  
[235] "maxpage_pre"                    "missing_pre"                   
[237] "missrel_pre"                    "time_rsi_pre"                  
[239] "deg_time_pre"                   "valid_probes_sum"              
[241] "compliance"                     "date_diff"                     
[243] "max_participation"              "total_valid"                   
[245] "total_missed"

Anwendung von select()

dl %>% 
  select(-id) %>% 
  colnames()
  [1] "probe_id"                       "probe_start"                   
  [3] "trigger_time_internal"          "probe_time"                    
  [5] "date_day_hm"                    "probe_num"                     
  [7] "trigger"                        "valid_probe"                   
  [9] "date_day"                       "time_day"                      
 [11] "trigger_date"                   "trigger_time"                  
 [13] "trigger_counter"                "form"                          
 [15] "form_start_date"                "form_start_time"               
 [17] "form_finish_date"               "form_finish_time"              
 [19] "form_upload_date"               "form_upload_time"              
 [21] "missing"                        "wb_ge"                         
 [23] "wb_energy"                      "wb_stress"                     
 [25] "wb_connect"                     "procra"                        
 [27] "screentime_work"                "screentime_leisure"            
 [29] "disco_1"                        "disco_2"                       
 [31] "disco_3"                        "disco_4"                       
 [33] "disco_5"                        "disco_6"                       
 [35] "disco_sd"                       "motivation_distraction"        
 [37] "motivation_wellbeing"           "motivation_social"             
 [39] "ns_autonomy"                    "ns_competence"                 
 [41] "ns_relatedness"                 "media_category_1"              
 [43] "media_category_2"               "media_category_3"              
 [45] "media_category_4"               "media_category_5"              
 [47] "media_category_6"               "media_category_7"              
 [49] "goal_conf"                      "missed_alarm"                  
 [51] "missed_time"                    "disco_1_daily_alarm_1"         
 [53] "disco_1_daily_alarm_2"          "disco_1_daily_alarm_3"         
 [55] "disco_1_daily_alarm_4"          "disco_1_daily_alarm_5"         
 [57] "disco_1_daily_alarm_6"          "disco_1_daily_time_1"          
 [59] "disco_1_daily_time_2"           "disco_1_daily_time_3"          
 [61] "disco_1_daily_time_4"           "disco_1_daily_time_5"          
 [63] "disco_1_daily_time_6"           "motivation_distraction_day"    
 [65] "motivation_well_being_day"      "motivation_social_day"         
 [67] "conscientiousness"              "disco_thoughts"                
 [69] "final_feedback"                 "participation_n_1"             
 [71] "participation_n"                "text_comment"                  
 [73] "reward_choice"                  "bold_check"                    
 [75] "feedback"                       "feedback_pin"                  
 [77] "feedback_study_results"         "day_n"                         
 [79] "daily_forms"                    "participation_number"          
 [81] "final_day"                      "finished"                      
 [83] "end_of_day_fillout"             "day_min"                       
 [85] "day_newest"                     "day_start"                     
 [87] "dur"                            "logging"                       
 [89] "case_pre"                       "serial_pre"                    
 [91] "ref_pre"                        "questnnr_pre"                  
 [93] "mode_pre"                       "started_pre"                   
 [95] "availability_preference_01_pre" "availability_preference_02_pre"
 [97] "availability_preference_03_pre" "availability_preference_04_pre"
 [99] "disco_tech_w_1_pre"             "disco_tech_w_2_pre"            
[101] "disco_tech_w_3_pre"             "disco_tech_w_4_pre"            
[103] "disco_tech_w_5_pre"             "disco_tech_w_6_pre"            
[105] "disco_level_w_1_pre"            "disco_level_w_2_pre"           
[107] "disco_level_w_3_pre"            "disco_level_w_4_pre"           
[109] "disco_level_w_5_pre"            "disco_level_w_6_pre"           
[111] "disco_thoughts_pre"             "disco_practice_other_pre"      
[113] "disco_context_text_pre"         "disco_context_1_pre"           
[115] "disco_context_2_pre"            "disco_context_3_pre"           
[117] "disco_context_4_pre"            "disco_context_5_pre"           
[119] "disco_context_6_pre"            "disco_context_7_pre"           
[121] "disco_context_8_pre"            "disco_context_9_pre"           
[123] "disco_context_10_pre"           "disco_context_11_pre"          
[125] "disco_context_other_pre"        "logging_choice_pre"            
[127] "comment_pre_survey_pre"         "fomo_01_pre"                   
[129] "fomo_02_pre"                    "fomo_03_pre"                   
[131] "fomo_04_pre"                    "fomo_05_pre"                   
[133] "fomo_06_pre"                    "fomo_07_pre"                   
[135] "fomo_08_pre"                    "fomo_09_pre"                   
[137] "fomo_10_pre"                    "consent_pre"                   
[139] "ic03_04_pre"                    "ic03_03_pre"                   
[141] "ic03_01_pre"                    "ic03_02_pre"                   
[143] "android_pre"                    "consent_part_2_pre"            
[145] "md_work_seconds_pre"            "md_private_seconds_pre"        
[147] "mindfulness_01_pre"             "mindfulness_02_pre"            
[149] "mindfulness_03_pre"             "mindfulness_04_pre"            
[151] "mindfulness_05_pre"             "pdo_01_pre"                    
[153] "pdo_02_pre"                     "pdo_03_pre"                    
[155] "rsd_01_pre"                     "rsd_02_pre"                    
[157] "rsd_03_pre"                     "rsd_04_pre"                    
[159] "rsd_05_pre"                     "rsd_06_pre"                    
[161] "sc_res_1_pre"                   "sc_res_3_pre"                  
[163] "sc_imp_1_pre"                   "sc_res_4_pre"                  
[165] "sc_res_2_pre"                   "sc_imp_2_pre"                  
[167] "sc_imp_3_pre"                   "sc_imp_4_pre"                  
[169] "sd_gender_pre"                  "sd_gender_custom_pre"          
[171] "age_pre"                        "work_hours_pre"                
[173] "sd_edu_pre"                     "sd_education_text_pre"         
[175] "sd_living_arrangement_pre"      "sd_living_not_own_kids_pre"    
[177] "sd_living_own_kids_pre"         "sd_living_arrangement_text_pre"
[179] "sd_household_size_pre"          "sd_occupation_pre"             
[181] "sd_occupation_text_pre"         "device_type_pre"               
[183] "swl_01_pre"                     "swl_02_pre"                    
[185] "swl_03_pre"                     "swl_04_pre"                    
[187] "swl_05_pre"                     "pa_01_pre"                     
[189] "pa_02_pre"                      "pa_03_pre"                     
[191] "pa_04_pre"                      "pa_05_pre"                     
[193] "na_01_pre"                      "na_02_pre"                     
[195] "na_03_pre"                      "na_04_pre"                     
[197] "na_05_pre"                      "positive_arousal_pre"          
[199] "negative_arousal_pre"           "connectedness_pre"             
[201] "wb_ge_pre"                      "procra_01_pre"                 
[203] "procra_02_pre"                  "procra_03_pre"                 
[205] "procra_04_pre"                  "procra_05_pre"                 
[207] "time001_pre"                    "time002_pre"                   
[209] "time003_pre"                    "time004_pre"                   
[211] "time005_pre"                    "time006_pre"                   
[213] "time007_pre"                    "time008_pre"                   
[215] "time009_pre"                    "time010_pre"                   
[217] "time011_pre"                    "time012_pre"                   
[219] "time013_pre"                    "time014_pre"                   
[221] "time015_pre"                    "time016_pre"                   
[223] "time017_pre"                    "time018_pre"                   
[225] "time019_pre"                    "time020_pre"                   
[227] "time021_pre"                    "time_sum_pre"                  
[229] "mailsent_pre"                   "lastdata_pre"                  
[231] "finished_pre"                   "q_viewer_pre"                  
[233] "lastpage_pre"                   "maxpage_pre"                   
[235] "missing_pre"                    "missrel_pre"                   
[237] "time_rsi_pre"                   "deg_time_pre"                  
[239] "valid_probes_sum"               "compliance"                    
[241] "date_diff"                      "max_participation"             
[243] "total_valid"                    "total_missed"

Bearbeitung und Erstellung von Variablen

Erstellung neuer Variablen

Quelle: Posit Software (2021)

Bearbeitung und Erstellung von Variablen

Fälle zusamenfassen

Quelle: Posit Software (2021)

Bearbeitung und Erstellung von Variablen

Hilfreiche Selektoren

Quelle: Posit Software (2021)

Beispiel: Anpassen der ID-Variable

Basisdaten

# Note: IDs are arlready removed, see connecting_data.qmd for more details
dl %>% 
  colnames() %>%
  tail(., n = 1)

Anwendung von select()

# Note: IDs are arlready removed, see connecting_data.qmd for more details
dl_plus = dl %>% 
  mutate(id_plus = ur01+9) 
dl_plus %>% 
  colnames() %>%
  tail(., n = 1)
mean(dl_plus$id_plus, na.rm = T)

mutate(): Neu oder überarbeiten

Zusätzliche Variable(n) erstellen

# Note: IDs are arlready removed, see connecting_data.qmd for more details
dl %>% 
  mutate(id_plus = ur01+9) %>%   
  colnames() %>% 
  length

Bestehende Variablen transformieren

# Note: IDs are arlready removed, see connecting_data.qmd for more details
dl %>% 
  mutate(ur01 = ur01+9) %>% 
  colnames() %>% 
  length(.)

Beispiel: Variablenausprägungen “zählen”

Einfaches Zählen mit count()

dl %>% 
  count()
# A tibble: 1 × 1
      n
  <int>
1 25624

Komfortable Lösung: frq()

dl %>% 
  frq(id)
id <integer> 
# total N=25624 valid N=25624 mean=375.61 sd=248.11

Value |   N | Raw % | Valid % | Cum. %
--------------------------------------
    1 |  54 |  0.21 |    0.21 |   0.21
    2 | 115 |  0.45 |    0.45 |   0.66
    3 |   2 |  0.01 |    0.01 |   0.67
    4 |  25 |  0.10 |    0.10 |   0.76
    5 |   4 |  0.02 |    0.02 |   0.78
    6 | 122 |  0.48 |    0.48 |   1.26
    7 |  56 |  0.22 |    0.22 |   1.48
    8 |  26 |  0.10 |    0.10 |   1.58
    9 |   2 |  0.01 |    0.01 |   1.58
   10 |  41 |  0.16 |    0.16 |   1.74
   11 | 112 |  0.44 |    0.44 |   2.18
   12 |  94 |  0.37 |    0.37 |   2.55
   13 |  67 |  0.26 |    0.26 |   2.81
   14 |  86 |  0.34 |    0.34 |   3.15
   15 |  52 |  0.20 |    0.20 |   3.35
   16 |  78 |  0.30 |    0.30 |   3.65
   17 |   1 |  0.00 |    0.00 |   3.66
   18 |  57 |  0.22 |    0.22 |   3.88
   19 |  14 |  0.05 |    0.05 |   3.93
   20 |  80 |  0.31 |    0.31 |   4.25
   21 |  73 |  0.28 |    0.28 |   4.53
   22 |   1 |  0.00 |    0.00 |   4.53
   23 |  28 |  0.11 |    0.11 |   4.64
   24 |  16 |  0.06 |    0.06 |   4.71
   25 |  99 |  0.39 |    0.39 |   5.09
   26 |  81 |  0.32 |    0.32 |   5.41
   27 |  10 |  0.04 |    0.04 |   5.45
   28 |  80 |  0.31 |    0.31 |   5.76
   29 | 125 |  0.49 |    0.49 |   6.25
   30 |  22 |  0.09 |    0.09 |   6.33
   31 |  61 |  0.24 |    0.24 |   6.57
   32 |   4 |  0.02 |    0.02 |   6.59
   33 |   8 |  0.03 |    0.03 |   6.62
   34 |  57 |  0.22 |    0.22 |   6.84
   35 | 110 |  0.43 |    0.43 |   7.27
   36 |   9 |  0.04 |    0.04 |   7.31
   37 |  29 |  0.11 |    0.11 |   7.42
   38 |  61 |  0.24 |    0.24 |   7.66
   39 |   1 |  0.00 |    0.00 |   7.66
   40 |  71 |  0.28 |    0.28 |   7.94
   41 |   1 |  0.00 |    0.00 |   7.94
   42 |   2 |  0.01 |    0.01 |   7.95
   43 |  23 |  0.09 |    0.09 |   8.04
   44 |   1 |  0.00 |    0.00 |   8.04
   45 |  87 |  0.34 |    0.34 |   8.38
   46 |  23 |  0.09 |    0.09 |   8.47
   47 |  23 |  0.09 |    0.09 |   8.56
   48 |  83 |  0.32 |    0.32 |   8.89
   49 |  43 |  0.17 |    0.17 |   9.05
   50 |  88 |  0.34 |    0.34 |   9.40
   51 |  22 |  0.09 |    0.09 |   9.48
   52 |  53 |  0.21 |    0.21 |   9.69
   53 |  19 |  0.07 |    0.07 |   9.76
   54 |  76 |  0.30 |    0.30 |  10.06
   55 |  18 |  0.07 |    0.07 |  10.13
   56 | 145 |  0.57 |    0.57 |  10.70
   57 |  74 |  0.29 |    0.29 |  10.99
   58 |   5 |  0.02 |    0.02 |  11.01
   59 |   3 |  0.01 |    0.01 |  11.02
   60 |   1 |  0.00 |    0.00 |  11.02
   61 |  57 |  0.22 |    0.22 |  11.24
   62 |  37 |  0.14 |    0.14 |  11.39
   63 |   6 |  0.02 |    0.02 |  11.41
   64 | 101 |  0.39 |    0.39 |  11.81
   65 |  91 |  0.36 |    0.36 |  12.16
   66 |  79 |  0.31 |    0.31 |  12.47
   67 |  62 |  0.24 |    0.24 |  12.71
   68 |  82 |  0.32 |    0.32 |  13.03
   69 |   1 |  0.00 |    0.00 |  13.03
   70 |  67 |  0.26 |    0.26 |  13.30
   71 |   3 |  0.01 |    0.01 |  13.31
   72 |   1 |  0.00 |    0.00 |  13.31
   73 |  48 |  0.19 |    0.19 |  13.50
   74 |   1 |  0.00 |    0.00 |  13.50
   75 |   3 |  0.01 |    0.01 |  13.51
   76 |   1 |  0.00 |    0.00 |  13.52
   77 |  69 |  0.27 |    0.27 |  13.79
   78 |  80 |  0.31 |    0.31 |  14.10
   79 |   3 |  0.01 |    0.01 |  14.11
   80 |  63 |  0.25 |    0.25 |  14.36
   81 |  74 |  0.29 |    0.29 |  14.65
   82 |   3 |  0.01 |    0.01 |  14.66
   83 |  84 |  0.33 |    0.33 |  14.99
   84 |   3 |  0.01 |    0.01 |  15.00
   85 |  14 |  0.05 |    0.05 |  15.05
   86 | 130 |  0.51 |    0.51 |  15.56
   87 |  56 |  0.22 |    0.22 |  15.78
   88 |   7 |  0.03 |    0.03 |  15.81
   89 |  39 |  0.15 |    0.15 |  15.96
   90 |  69 |  0.27 |    0.27 |  16.23
   91 |  49 |  0.19 |    0.19 |  16.42
   92 |  79 |  0.31 |    0.31 |  16.73
   93 |   3 |  0.01 |    0.01 |  16.74
   94 | 127 |  0.50 |    0.50 |  17.23
   95 |  20 |  0.08 |    0.08 |  17.31
   96 |  10 |  0.04 |    0.04 |  17.35
   97 | 117 |  0.46 |    0.46 |  17.81
   98 |  61 |  0.24 |    0.24 |  18.05
   99 |  63 |  0.25 |    0.25 |  18.29
  100 |   1 |  0.00 |    0.00 |  18.30
  101 |   1 |  0.00 |    0.00 |  18.30
  102 |   3 |  0.01 |    0.01 |  18.31
  103 |  71 |  0.28 |    0.28 |  18.59
  104 | 102 |  0.40 |    0.40 |  18.99
  105 |  57 |  0.22 |    0.22 |  19.21
  106 |   2 |  0.01 |    0.01 |  19.22
  107 |  76 |  0.30 |    0.30 |  19.51
  108 |   2 |  0.01 |    0.01 |  19.52
  109 |  64 |  0.25 |    0.25 |  19.77
  110 |  89 |  0.35 |    0.35 |  20.12
  111 |   4 |  0.02 |    0.02 |  20.13
  112 | 129 |  0.50 |    0.50 |  20.64
  113 |  59 |  0.23 |    0.23 |  20.87
  114 |   9 |  0.04 |    0.04 |  20.90
  115 |   2 |  0.01 |    0.01 |  20.91
  116 |  41 |  0.16 |    0.16 |  21.07
  117 |   1 |  0.00 |    0.00 |  21.07
  118 |  72 |  0.28 |    0.28 |  21.35
  119 |  54 |  0.21 |    0.21 |  21.57
  120 |  94 |  0.37 |    0.37 |  21.93
  121 |  92 |  0.36 |    0.36 |  22.29
  122 |   3 |  0.01 |    0.01 |  22.30
  123 |   8 |  0.03 |    0.03 |  22.33
  124 | 119 |  0.46 |    0.46 |  22.80
  125 |  85 |  0.33 |    0.33 |  23.13
  126 |  88 |  0.34 |    0.34 |  23.47
  127 |  46 |  0.18 |    0.18 |  23.65
  128 |  91 |  0.36 |    0.36 |  24.01
  129 |  67 |  0.26 |    0.26 |  24.27
  130 |  70 |  0.27 |    0.27 |  24.54
  131 |  34 |  0.13 |    0.13 |  24.68
  132 | 118 |  0.46 |    0.46 |  25.14
  133 |  64 |  0.25 |    0.25 |  25.39
  134 |   2 |  0.01 |    0.01 |  25.39
  135 |  89 |  0.35 |    0.35 |  25.74
  136 |   1 |  0.00 |    0.00 |  25.75
  137 |  62 |  0.24 |    0.24 |  25.99
  138 |  22 |  0.09 |    0.09 |  26.07
  139 |  59 |  0.23 |    0.23 |  26.30
  140 | 113 |  0.44 |    0.44 |  26.74
  141 |  45 |  0.18 |    0.18 |  26.92
  142 |  68 |  0.27 |    0.27 |  27.19
  143 |  83 |  0.32 |    0.32 |  27.51
  144 |  82 |  0.32 |    0.32 |  27.83
  145 |   3 |  0.01 |    0.01 |  27.84
  146 |  48 |  0.19 |    0.19 |  28.03
  147 |   3 |  0.01 |    0.01 |  28.04
  148 |   1 |  0.00 |    0.00 |  28.04
  149 |  90 |  0.35 |    0.35 |  28.40
  150 |  76 |  0.30 |    0.30 |  28.69
  151 |  67 |  0.26 |    0.26 |  28.95
  152 |  10 |  0.04 |    0.04 |  28.99
  153 |  80 |  0.31 |    0.31 |  29.30
  154 |   2 |  0.01 |    0.01 |  29.31
  155 | 101 |  0.39 |    0.39 |  29.71
  156 |  18 |  0.07 |    0.07 |  29.78
  157 | 137 |  0.53 |    0.53 |  30.31
  158 |   2 |  0.01 |    0.01 |  30.32
  159 |  82 |  0.32 |    0.32 |  30.64
  160 |  52 |  0.20 |    0.20 |  30.84
  161 |  98 |  0.38 |    0.38 |  31.22
  162 |   5 |  0.02 |    0.02 |  31.24
  163 |   2 |  0.01 |    0.01 |  31.25
  164 |   7 |  0.03 |    0.03 |  31.28
  165 |  83 |  0.32 |    0.32 |  31.60
  166 |   5 |  0.02 |    0.02 |  31.62
  167 | 162 |  0.63 |    0.63 |  32.25
  168 |  84 |  0.33 |    0.33 |  32.58
  169 |  25 |  0.10 |    0.10 |  32.68
  170 |  74 |  0.29 |    0.29 |  32.97
  171 |  13 |  0.05 |    0.05 |  33.02
  172 |   1 |  0.00 |    0.00 |  33.02
  173 |  93 |  0.36 |    0.36 |  33.39
  174 |   8 |  0.03 |    0.03 |  33.42
  175 |  34 |  0.13 |    0.13 |  33.55
  176 |   7 |  0.03 |    0.03 |  33.58
  177 |   3 |  0.01 |    0.01 |  33.59
  178 |   2 |  0.01 |    0.01 |  33.60
  179 |   3 |  0.01 |    0.01 |  33.61
  180 |  46 |  0.18 |    0.18 |  33.79
  181 |  37 |  0.14 |    0.14 |  33.93
  182 |  87 |  0.34 |    0.34 |  34.27
  183 | 103 |  0.40 |    0.40 |  34.67
  184 |   7 |  0.03 |    0.03 |  34.70
  185 |   1 |  0.00 |    0.00 |  34.71
  186 |  81 |  0.32 |    0.32 |  35.02
  187 |  58 |  0.23 |    0.23 |  35.25
  188 |  28 |  0.11 |    0.11 |  35.36
  189 |  34 |  0.13 |    0.13 |  35.49
  190 |  44 |  0.17 |    0.17 |  35.66
  191 | 113 |  0.44 |    0.44 |  36.10
  192 |  62 |  0.24 |    0.24 |  36.34
  193 |  40 |  0.16 |    0.16 |  36.50
  194 |  99 |  0.39 |    0.39 |  36.89
  195 |  83 |  0.32 |    0.32 |  37.21
  196 |   8 |  0.03 |    0.03 |  37.24
  197 |  62 |  0.24 |    0.24 |  37.48
  198 |  29 |  0.11 |    0.11 |  37.60
  199 |  80 |  0.31 |    0.31 |  37.91
  200 |   2 |  0.01 |    0.01 |  37.92
  201 |  38 |  0.15 |    0.15 |  38.07
  202 | 100 |  0.39 |    0.39 |  38.46
  203 |  77 |  0.30 |    0.30 |  38.76
  204 |  80 |  0.31 |    0.31 |  39.07
  205 |  70 |  0.27 |    0.27 |  39.34
  206 |  18 |  0.07 |    0.07 |  39.41
  207 |  12 |  0.05 |    0.05 |  39.46
  208 |   1 |  0.00 |    0.00 |  39.46
  209 |  51 |  0.20 |    0.20 |  39.66
  210 | 110 |  0.43 |    0.43 |  40.09
  211 |  16 |  0.06 |    0.06 |  40.15
  212 |  65 |  0.25 |    0.25 |  40.41
  213 |   3 |  0.01 |    0.01 |  40.42
  214 |  85 |  0.33 |    0.33 |  40.75
  215 |   4 |  0.02 |    0.02 |  40.77
  216 |  90 |  0.35 |    0.35 |  41.12
  217 | 125 |  0.49 |    0.49 |  41.61
  218 |  93 |  0.36 |    0.36 |  41.97
  219 |  56 |  0.22 |    0.22 |  42.19
  220 |  25 |  0.10 |    0.10 |  42.28
  221 |  41 |  0.16 |    0.16 |  42.44
  222 |  46 |  0.18 |    0.18 |  42.62
  223 | 235 |  0.92 |    0.92 |  43.54
  224 | 102 |  0.40 |    0.40 |  43.94
  225 |  80 |  0.31 |    0.31 |  44.25
  226 |  83 |  0.32 |    0.32 |  44.58
  227 |   8 |  0.03 |    0.03 |  44.61
  228 |  65 |  0.25 |    0.25 |  44.86
  229 |  80 |  0.31 |    0.31 |  45.17
  230 |  91 |  0.36 |    0.36 |  45.53
  231 |   6 |  0.02 |    0.02 |  45.55
  232 |  88 |  0.34 |    0.34 |  45.89
  233 |  86 |  0.34 |    0.34 |  46.23
  234 |   1 |  0.00 |    0.00 |  46.23
  235 |  48 |  0.19 |    0.19 |  46.42
  236 |   2 |  0.01 |    0.01 |  46.43
  237 |  39 |  0.15 |    0.15 |  46.58
  238 |  79 |  0.31 |    0.31 |  46.89
  239 |  67 |  0.26 |    0.26 |  47.15
  240 |   8 |  0.03 |    0.03 |  47.18
  241 |   1 |  0.00 |    0.00 |  47.19
  242 |   1 |  0.00 |    0.00 |  47.19
  243 |   1 |  0.00 |    0.00 |  47.19
  244 |   1 |  0.00 |    0.00 |  47.20
  245 |   1 |  0.00 |    0.00 |  47.20
  246 |   1 |  0.00 |    0.00 |  47.21
  247 |   1 |  0.00 |    0.00 |  47.21
  248 |   1 |  0.00 |    0.00 |  47.21
  249 |   1 |  0.00 |    0.00 |  47.22
  250 |   1 |  0.00 |    0.00 |  47.22
  251 |   1 |  0.00 |    0.00 |  47.23
  252 |   1 |  0.00 |    0.00 |  47.23
  253 |   1 |  0.00 |    0.00 |  47.23
  254 |   1 |  0.00 |    0.00 |  47.24
  255 |   1 |  0.00 |    0.00 |  47.24
  256 |   1 |  0.00 |    0.00 |  47.24
  257 |   1 |  0.00 |    0.00 |  47.25
  258 |   1 |  0.00 |    0.00 |  47.25
  259 |   1 |  0.00 |    0.00 |  47.26
  260 |   1 |  0.00 |    0.00 |  47.26
  261 |   1 |  0.00 |    0.00 |  47.26
  262 |   1 |  0.00 |    0.00 |  47.27
  263 |   1 |  0.00 |    0.00 |  47.27
  264 |   1 |  0.00 |    0.00 |  47.28
  265 |   1 |  0.00 |    0.00 |  47.28
  266 |   1 |  0.00 |    0.00 |  47.28
  267 |   1 |  0.00 |    0.00 |  47.29
  268 |   1 |  0.00 |    0.00 |  47.29
  269 |   1 |  0.00 |    0.00 |  47.30
  270 |   1 |  0.00 |    0.00 |  47.30
  271 |   1 |  0.00 |    0.00 |  47.30
  272 |   1 |  0.00 |    0.00 |  47.31
  273 |   1 |  0.00 |    0.00 |  47.31
  274 |   1 |  0.00 |    0.00 |  47.32
  275 |   1 |  0.00 |    0.00 |  47.32
  276 |   1 |  0.00 |    0.00 |  47.32
  277 |   1 |  0.00 |    0.00 |  47.33
  278 |   1 |  0.00 |    0.00 |  47.33
  279 |   1 |  0.00 |    0.00 |  47.33
  280 |   1 |  0.00 |    0.00 |  47.34
  281 |   1 |  0.00 |    0.00 |  47.34
  282 |   1 |  0.00 |    0.00 |  47.35
  283 |   1 |  0.00 |    0.00 |  47.35
  284 |   1 |  0.00 |    0.00 |  47.35
  285 |   1 |  0.00 |    0.00 |  47.36
  286 |   1 |  0.00 |    0.00 |  47.36
  287 |   1 |  0.00 |    0.00 |  47.37
  288 |   1 |  0.00 |    0.00 |  47.37
  289 |   1 |  0.00 |    0.00 |  47.37
  290 |   1 |  0.00 |    0.00 |  47.38
  291 |   1 |  0.00 |    0.00 |  47.38
  292 |   1 |  0.00 |    0.00 |  47.39
  293 |   1 |  0.00 |    0.00 |  47.39
  294 |   1 |  0.00 |    0.00 |  47.39
  295 |   1 |  0.00 |    0.00 |  47.40
  296 |   1 |  0.00 |    0.00 |  47.40
  297 |   1 |  0.00 |    0.00 |  47.40
  298 |   1 |  0.00 |    0.00 |  47.41
  299 |   1 |  0.00 |    0.00 |  47.41
  300 |   1 |  0.00 |    0.00 |  47.42
  301 |   1 |  0.00 |    0.00 |  47.42
  302 |   1 |  0.00 |    0.00 |  47.42
  303 |   1 |  0.00 |    0.00 |  47.43
  304 |   1 |  0.00 |    0.00 |  47.43
  305 |   1 |  0.00 |    0.00 |  47.44
  306 |   1 |  0.00 |    0.00 |  47.44
  307 |   1 |  0.00 |    0.00 |  47.44
  308 |   1 |  0.00 |    0.00 |  47.45
  309 |   1 |  0.00 |    0.00 |  47.45
  310 |   1 |  0.00 |    0.00 |  47.46
  311 |   1 |  0.00 |    0.00 |  47.46
  312 |   1 |  0.00 |    0.00 |  47.46
  313 |   1 |  0.00 |    0.00 |  47.47
  314 |   1 |  0.00 |    0.00 |  47.47
  315 |   1 |  0.00 |    0.00 |  47.48
  316 |   1 |  0.00 |    0.00 |  47.48
  317 |   1 |  0.00 |    0.00 |  47.48
  318 |   1 |  0.00 |    0.00 |  47.49
  319 |   1 |  0.00 |    0.00 |  47.49
  320 |   1 |  0.00 |    0.00 |  47.49
  321 |   1 |  0.00 |    0.00 |  47.50
  322 |   1 |  0.00 |    0.00 |  47.50
  323 |   1 |  0.00 |    0.00 |  47.51
  324 |   1 |  0.00 |    0.00 |  47.51
  325 |   1 |  0.00 |    0.00 |  47.51
  326 |   1 |  0.00 |    0.00 |  47.52
  327 |   1 |  0.00 |    0.00 |  47.52
  328 |   1 |  0.00 |    0.00 |  47.53
  329 |   1 |  0.00 |    0.00 |  47.53
  330 |   1 |  0.00 |    0.00 |  47.53
  331 |   1 |  0.00 |    0.00 |  47.54
  332 |   1 |  0.00 |    0.00 |  47.54
  333 |   1 |  0.00 |    0.00 |  47.55
  334 |   1 |  0.00 |    0.00 |  47.55
  335 |   1 |  0.00 |    0.00 |  47.55
  336 |   1 |  0.00 |    0.00 |  47.56
  337 |   1 |  0.00 |    0.00 |  47.56
  338 |   1 |  0.00 |    0.00 |  47.56
  339 |   1 |  0.00 |    0.00 |  47.57
  340 |   1 |  0.00 |    0.00 |  47.57
  341 |   1 |  0.00 |    0.00 |  47.58
  342 |   1 |  0.00 |    0.00 |  47.58
  343 |   1 |  0.00 |    0.00 |  47.58
  344 |   1 |  0.00 |    0.00 |  47.59
  345 |   1 |  0.00 |    0.00 |  47.59
  346 |   1 |  0.00 |    0.00 |  47.60
  347 |   1 |  0.00 |    0.00 |  47.60
  348 |   1 |  0.00 |    0.00 |  47.60
  349 |   1 |  0.00 |    0.00 |  47.61
  350 |   1 |  0.00 |    0.00 |  47.61
  351 |   1 |  0.00 |    0.00 |  47.62
  352 |   1 |  0.00 |    0.00 |  47.62
  353 |   1 |  0.00 |    0.00 |  47.62
  354 |   1 |  0.00 |    0.00 |  47.63
  355 |   1 |  0.00 |    0.00 |  47.63
  356 |   1 |  0.00 |    0.00 |  47.64
  357 |   1 |  0.00 |    0.00 |  47.64
  358 |   1 |  0.00 |    0.00 |  47.64
  359 |   1 |  0.00 |    0.00 |  47.65
  360 |   1 |  0.00 |    0.00 |  47.65
  361 |   1 |  0.00 |    0.00 |  47.65
  362 |   1 |  0.00 |    0.00 |  47.66
  363 |   1 |  0.00 |    0.00 |  47.66
  364 |   1 |  0.00 |    0.00 |  47.67
  365 |   1 |  0.00 |    0.00 |  47.67
  366 |   1 |  0.00 |    0.00 |  47.67
  367 |   1 |  0.00 |    0.00 |  47.68
  368 |   1 |  0.00 |    0.00 |  47.68
  369 |   1 |  0.00 |    0.00 |  47.69
  370 |   1 |  0.00 |    0.00 |  47.69
  371 |   1 |  0.00 |    0.00 |  47.69
  372 |   1 |  0.00 |    0.00 |  47.70
  373 |   1 |  0.00 |    0.00 |  47.70
  374 |   1 |  0.00 |    0.00 |  47.71
  375 |   1 |  0.00 |    0.00 |  47.71
  376 |   1 |  0.00 |    0.00 |  47.71
  377 |   1 |  0.00 |    0.00 |  47.72
  378 |   1 |  0.00 |    0.00 |  47.72
  379 |   1 |  0.00 |    0.00 |  47.72
  380 |   1 |  0.00 |    0.00 |  47.73
  381 |   1 |  0.00 |    0.00 |  47.73
  382 |   1 |  0.00 |    0.00 |  47.74
  383 |   1 |  0.00 |    0.00 |  47.74
  384 |   1 |  0.00 |    0.00 |  47.74
  385 |   1 |  0.00 |    0.00 |  47.75
  386 |   1 |  0.00 |    0.00 |  47.75
  387 |   1 |  0.00 |    0.00 |  47.76
  388 |   1 |  0.00 |    0.00 |  47.76
  389 |   1 |  0.00 |    0.00 |  47.76
  390 |   1 |  0.00 |    0.00 |  47.77
  391 |   1 |  0.00 |    0.00 |  47.77
  392 |   1 |  0.00 |    0.00 |  47.78
  393 |   1 |  0.00 |    0.00 |  47.78
  394 |   1 |  0.00 |    0.00 |  47.78
  395 |   1 |  0.00 |    0.00 |  47.79
  396 |   1 |  0.00 |    0.00 |  47.79
  397 |   1 |  0.00 |    0.00 |  47.80
  398 |   1 |  0.00 |    0.00 |  47.80
  399 |   1 |  0.00 |    0.00 |  47.80
  400 |   1 |  0.00 |    0.00 |  47.81
  401 |   1 |  0.00 |    0.00 |  47.81
  402 |   1 |  0.00 |    0.00 |  47.81
  403 |   1 |  0.00 |    0.00 |  47.82
  404 |   1 |  0.00 |    0.00 |  47.82
  405 |   1 |  0.00 |    0.00 |  47.83
  406 |   1 |  0.00 |    0.00 |  47.83
  407 |   1 |  0.00 |    0.00 |  47.83
  408 |   1 |  0.00 |    0.00 |  47.84
  409 |   1 |  0.00 |    0.00 |  47.84
  410 |   1 |  0.00 |    0.00 |  47.85
  411 |   1 |  0.00 |    0.00 |  47.85
  412 |   1 |  0.00 |    0.00 |  47.85
  413 |   1 |  0.00 |    0.00 |  47.86
  414 |   1 |  0.00 |    0.00 |  47.86
  415 |   1 |  0.00 |    0.00 |  47.87
  416 |   1 |  0.00 |    0.00 |  47.87
  417 |   1 |  0.00 |    0.00 |  47.87
  418 |   1 |  0.00 |    0.00 |  47.88
  419 |   1 |  0.00 |    0.00 |  47.88
  420 |   1 |  0.00 |    0.00 |  47.88
  421 |   1 |  0.00 |    0.00 |  47.89
  422 |   1 |  0.00 |    0.00 |  47.89
  423 |   1 |  0.00 |    0.00 |  47.90
  424 |   1 |  0.00 |    0.00 |  47.90
  425 |   1 |  0.00 |    0.00 |  47.90
  426 |   1 |  0.00 |    0.00 |  47.91
  427 |   1 |  0.00 |    0.00 |  47.91
  428 |   1 |  0.00 |    0.00 |  47.92
  429 |   1 |  0.00 |    0.00 |  47.92
  430 |   1 |  0.00 |    0.00 |  47.92
  431 |   1 |  0.00 |    0.00 |  47.93
  432 |   1 |  0.00 |    0.00 |  47.93
  433 |   1 |  0.00 |    0.00 |  47.94
  434 |   1 |  0.00 |    0.00 |  47.94
  435 |   1 |  0.00 |    0.00 |  47.94
  436 |   1 |  0.00 |    0.00 |  47.95
  437 |   1 |  0.00 |    0.00 |  47.95
  438 |   1 |  0.00 |    0.00 |  47.96
  439 |   1 |  0.00 |    0.00 |  47.96
  440 |   1 |  0.00 |    0.00 |  47.96
  441 |   1 |  0.00 |    0.00 |  47.97
  442 |   1 |  0.00 |    0.00 |  47.97
  443 |   1 |  0.00 |    0.00 |  47.97
  444 |   1 |  0.00 |    0.00 |  47.98
  445 |   1 |  0.00 |    0.00 |  47.98
  446 |   1 |  0.00 |    0.00 |  47.99
  447 |   1 |  0.00 |    0.00 |  47.99
  448 |   1 |  0.00 |    0.00 |  47.99
  449 |   1 |  0.00 |    0.00 |  48.00
  450 |   1 |  0.00 |    0.00 |  48.00
  451 |   1 |  0.00 |    0.00 |  48.01
  452 |   1 |  0.00 |    0.00 |  48.01
  453 |   1 |  0.00 |    0.00 |  48.01
  454 |   1 |  0.00 |    0.00 |  48.02
  455 |   1 |  0.00 |    0.00 |  48.02
  456 |   1 |  0.00 |    0.00 |  48.03
  457 |   1 |  0.00 |    0.00 |  48.03
  458 |   1 |  0.00 |    0.00 |  48.03
  459 |   1 |  0.00 |    0.00 |  48.04
  460 |   1 |  0.00 |    0.00 |  48.04
  461 |   1 |  0.00 |    0.00 |  48.04
  462 |   1 |  0.00 |    0.00 |  48.05
  463 |   1 |  0.00 |    0.00 |  48.05
  464 |   1 |  0.00 |    0.00 |  48.06
  465 |   1 |  0.00 |    0.00 |  48.06
  466 |   1 |  0.00 |    0.00 |  48.06
  467 |   1 |  0.00 |    0.00 |  48.07
  468 |   1 |  0.00 |    0.00 |  48.07
  469 |   1 |  0.00 |    0.00 |  48.08
  470 |   1 |  0.00 |    0.00 |  48.08
  471 |   1 |  0.00 |    0.00 |  48.08
  472 |   1 |  0.00 |    0.00 |  48.09
  473 |   1 |  0.00 |    0.00 |  48.09
  474 |   1 |  0.00 |    0.00 |  48.10
  475 |   1 |  0.00 |    0.00 |  48.10
  476 |   1 |  0.00 |    0.00 |  48.10
  477 |   1 |  0.00 |    0.00 |  48.11
  478 |  91 |  0.36 |    0.36 |  48.46
  479 |  67 |  0.26 |    0.26 |  48.72
  480 |   9 |  0.04 |    0.04 |  48.76
  481 |  80 |  0.31 |    0.31 |  49.07
  482 |   8 |  0.03 |    0.03 |  49.10
  483 |   1 |  0.00 |    0.00 |  49.11
  484 |  37 |  0.14 |    0.14 |  49.25
  485 |  66 |  0.26 |    0.26 |  49.51
  486 |   7 |  0.03 |    0.03 |  49.54
  487 |  36 |  0.14 |    0.14 |  49.68
  488 |   1 |  0.00 |    0.00 |  49.68
  489 |   1 |  0.00 |    0.00 |  49.68
  490 |  77 |  0.30 |    0.30 |  49.98
  491 |  84 |  0.33 |    0.33 |  50.31
  492 |  90 |  0.35 |    0.35 |  50.66
  493 |   4 |  0.02 |    0.02 |  50.68
  494 |   4 |  0.02 |    0.02 |  50.69
  495 |   1 |  0.00 |    0.00 |  50.70
  496 |  80 |  0.31 |    0.31 |  51.01
  497 |  44 |  0.17 |    0.17 |  51.18
  498 |   1 |  0.00 |    0.00 |  51.19
  499 |  76 |  0.30 |    0.30 |  51.48
  500 |  26 |  0.10 |    0.10 |  51.58
  501 |   1 |  0.00 |    0.00 |  51.59
  502 |  93 |  0.36 |    0.36 |  51.95
  503 |   1 |  0.00 |    0.00 |  51.96
  504 |  86 |  0.34 |    0.34 |  52.29
  505 |  90 |  0.35 |    0.35 |  52.64
  506 |   9 |  0.04 |    0.04 |  52.68
  507 |   1 |  0.00 |    0.00 |  52.68
  508 |   1 |  0.00 |    0.00 |  52.68
  509 |  60 |  0.23 |    0.23 |  52.92
  510 |  46 |  0.18 |    0.18 |  53.10
  511 |  77 |  0.30 |    0.30 |  53.40
  512 |  62 |  0.24 |    0.24 |  53.64
  513 |  73 |  0.28 |    0.28 |  53.93
  514 |   1 |  0.00 |    0.00 |  53.93
  515 |   1 |  0.00 |    0.00 |  53.93
  516 |   1 |  0.00 |    0.00 |  53.94
  517 |   1 |  0.00 |    0.00 |  53.94
  518 |   1 |  0.00 |    0.00 |  53.95
  519 | 111 |  0.43 |    0.43 |  54.38
  520 | 101 |  0.39 |    0.39 |  54.77
  521 |  77 |  0.30 |    0.30 |  55.07
  522 |  58 |  0.23 |    0.23 |  55.30
  523 |  92 |  0.36 |    0.36 |  55.66
  524 |   1 |  0.00 |    0.00 |  55.66
  525 | 110 |  0.43 |    0.43 |  56.09
  526 |   1 |  0.00 |    0.00 |  56.10
  527 |  88 |  0.34 |    0.34 |  56.44
  528 |   3 |  0.01 |    0.01 |  56.45
  529 | 133 |  0.52 |    0.52 |  56.97
  530 |  38 |  0.15 |    0.15 |  57.12
  531 |  82 |  0.32 |    0.32 |  57.44
  532 |  14 |  0.05 |    0.05 |  57.49
  533 |  60 |  0.23 |    0.23 |  57.73
  534 |   2 |  0.01 |    0.01 |  57.73
  535 |  66 |  0.26 |    0.26 |  57.99
  536 | 140 |  0.55 |    0.55 |  58.54
  537 |  66 |  0.26 |    0.26 |  58.80
  538 |  69 |  0.27 |    0.27 |  59.07
  539 |  11 |  0.04 |    0.04 |  59.11
  540 |  72 |  0.28 |    0.28 |  59.39
  541 |   3 |  0.01 |    0.01 |  59.40
  542 |   1 |  0.00 |    0.00 |  59.41
  543 |  23 |  0.09 |    0.09 |  59.50
  544 | 111 |  0.43 |    0.43 |  59.93
  545 |   1 |  0.00 |    0.00 |  59.93
  546 |  72 |  0.28 |    0.28 |  60.21
  547 |  39 |  0.15 |    0.15 |  60.37
  548 |  67 |  0.26 |    0.26 |  60.63
  549 |  63 |  0.25 |    0.25 |  60.87
  550 |  45 |  0.18 |    0.18 |  61.05
  551 |  78 |  0.30 |    0.30 |  61.35
  552 |   1 |  0.00 |    0.00 |  61.36
  553 |  74 |  0.29 |    0.29 |  61.65
  554 |  22 |  0.09 |    0.09 |  61.73
  555 | 117 |  0.46 |    0.46 |  62.19
  556 |   3 |  0.01 |    0.01 |  62.20
  557 | 103 |  0.40 |    0.40 |  62.60
  558 |  61 |  0.24 |    0.24 |  62.84
  559 |  90 |  0.35 |    0.35 |  63.19
  560 |  89 |  0.35 |    0.35 |  63.54
  561 |  77 |  0.30 |    0.30 |  63.84
  562 |  10 |  0.04 |    0.04 |  63.88
  563 |  39 |  0.15 |    0.15 |  64.03
  564 |  85 |  0.33 |    0.33 |  64.36
  565 |   1 |  0.00 |    0.00 |  64.37
  566 |   4 |  0.02 |    0.02 |  64.38
  567 |   2 |  0.01 |    0.01 |  64.39
  568 |  69 |  0.27 |    0.27 |  64.66
  569 | 122 |  0.48 |    0.48 |  65.13
  570 |  96 |  0.37 |    0.37 |  65.51
  571 |  74 |  0.29 |    0.29 |  65.80
  572 |  79 |  0.31 |    0.31 |  66.11
  573 |  75 |  0.29 |    0.29 |  66.40
  574 |  86 |  0.34 |    0.34 |  66.73
  575 | 100 |  0.39 |    0.39 |  67.12
  576 |  45 |  0.18 |    0.18 |  67.30
  577 |   1 |  0.00 |    0.00 |  67.30
  578 |   7 |  0.03 |    0.03 |  67.33
  579 |  74 |  0.29 |    0.29 |  67.62
  580 |  91 |  0.36 |    0.36 |  67.98
  581 |   1 |  0.00 |    0.00 |  67.98
  582 |  87 |  0.34 |    0.34 |  68.32
  583 | 104 |  0.41 |    0.41 |  68.72
  584 |  68 |  0.27 |    0.27 |  68.99
  585 |   1 |  0.00 |    0.00 |  68.99
  586 |  18 |  0.07 |    0.07 |  69.06
  587 |   1 |  0.00 |    0.00 |  69.07
  588 | 110 |  0.43 |    0.43 |  69.50
  589 |  64 |  0.25 |    0.25 |  69.75
  590 |  54 |  0.21 |    0.21 |  69.96
  591 |  46 |  0.18 |    0.18 |  70.14
  592 | 126 |  0.49 |    0.49 |  70.63
  593 |  63 |  0.25 |    0.25 |  70.87
  594 |  68 |  0.27 |    0.27 |  71.14
  595 |  50 |  0.20 |    0.20 |  71.34
  596 |  78 |  0.30 |    0.30 |  71.64
  597 |  95 |  0.37 |    0.37 |  72.01
  598 |  91 |  0.36 |    0.36 |  72.37
  599 |  80 |  0.31 |    0.31 |  72.68
  600 |  71 |  0.28 |    0.28 |  72.96
  601 |  82 |  0.32 |    0.32 |  73.28
  602 |  99 |  0.39 |    0.39 |  73.66
  603 |  82 |  0.32 |    0.32 |  73.98
  604 |  77 |  0.30 |    0.30 |  74.28
  605 |  94 |  0.37 |    0.37 |  74.65
  606 |  18 |  0.07 |    0.07 |  74.72
  607 |   1 |  0.00 |    0.00 |  74.72
  608 |  37 |  0.14 |    0.14 |  74.87
  609 |  86 |  0.34 |    0.34 |  75.20
  610 |  78 |  0.30 |    0.30 |  75.51
  611 |  83 |  0.32 |    0.32 |  75.83
  612 |   1 |  0.00 |    0.00 |  75.84
  613 |  62 |  0.24 |    0.24 |  76.08
  614 |  72 |  0.28 |    0.28 |  76.36
  615 |  84 |  0.33 |    0.33 |  76.69
  616 | 103 |  0.40 |    0.40 |  77.09
  617 |   1 |  0.00 |    0.00 |  77.09
  618 |  92 |  0.36 |    0.36 |  77.45
  619 | 107 |  0.42 |    0.42 |  77.87
  620 |  80 |  0.31 |    0.31 |  78.18
  621 |  70 |  0.27 |    0.27 |  78.45
  622 |  54 |  0.21 |    0.21 |  78.66
  623 |  33 |  0.13 |    0.13 |  78.79
  624 |  75 |  0.29 |    0.29 |  79.09
  625 |  83 |  0.32 |    0.32 |  79.41
  626 |  92 |  0.36 |    0.36 |  79.77
  627 |  79 |  0.31 |    0.31 |  80.08
  628 | 123 |  0.48 |    0.48 |  80.56
  629 |   4 |  0.02 |    0.02 |  80.57
  630 |   2 |  0.01 |    0.01 |  80.58
  631 |  85 |  0.33 |    0.33 |  80.91
  632 |   1 |  0.00 |    0.00 |  80.92
  633 | 105 |  0.41 |    0.41 |  81.33
  634 |   2 |  0.01 |    0.01 |  81.33
  635 |  86 |  0.34 |    0.34 |  81.67
  636 |  76 |  0.30 |    0.30 |  81.97
  637 |  21 |  0.08 |    0.08 |  82.05
  638 |  71 |  0.28 |    0.28 |  82.33
  639 |  68 |  0.27 |    0.27 |  82.59
  640 |  61 |  0.24 |    0.24 |  82.83
  641 |  48 |  0.19 |    0.19 |  83.02
  642 |   1 |  0.00 |    0.00 |  83.02
  643 |  67 |  0.26 |    0.26 |  83.28
  644 |  83 |  0.32 |    0.32 |  83.61
  645 |  82 |  0.32 |    0.32 |  83.93
  646 |  76 |  0.30 |    0.30 |  84.22
  647 |  88 |  0.34 |    0.34 |  84.57
  648 |  74 |  0.29 |    0.29 |  84.85
  649 |   1 |  0.00 |    0.00 |  84.86
  650 |   1 |  0.00 |    0.00 |  84.86
  651 |  73 |  0.28 |    0.28 |  85.15
  652 |  61 |  0.24 |    0.24 |  85.38
  653 |  53 |  0.21 |    0.21 |  85.59
  654 |  90 |  0.35 |    0.35 |  85.94
  655 |   1 |  0.00 |    0.00 |  85.95
  656 |  55 |  0.21 |    0.21 |  86.16
  657 |  41 |  0.16 |    0.16 |  86.32
  658 |   1 |  0.00 |    0.00 |  86.33
  659 | 100 |  0.39 |    0.39 |  86.72
  660 |  92 |  0.36 |    0.36 |  87.07
  661 | 100 |  0.39 |    0.39 |  87.46
  662 |  62 |  0.24 |    0.24 |  87.71
  663 |   1 |  0.00 |    0.00 |  87.71
  664 |  80 |  0.31 |    0.31 |  88.02
  665 |  93 |  0.36 |    0.36 |  88.39
  666 | 102 |  0.40 |    0.40 |  88.78
  667 |  86 |  0.34 |    0.34 |  89.12
  668 |  31 |  0.12 |    0.12 |  89.24
  669 |  78 |  0.30 |    0.30 |  89.54
  670 |  71 |  0.28 |    0.28 |  89.82
  671 |   3 |  0.01 |    0.01 |  89.83
  672 |  59 |  0.23 |    0.23 |  90.06
  673 |  37 |  0.14 |    0.14 |  90.21
  674 |   1 |  0.00 |    0.00 |  90.21
  675 |   1 |  0.00 |    0.00 |  90.22
  676 |  62 |  0.24 |    0.24 |  90.46
  677 |  79 |  0.31 |    0.31 |  90.77
  678 |  91 |  0.36 |    0.36 |  91.12
  679 |   1 |  0.00 |    0.00 |  91.13
  680 |  94 |  0.37 |    0.37 |  91.49
  681 |   1 |  0.00 |    0.00 |  91.50
  682 |  66 |  0.26 |    0.26 |  91.75
  683 |  82 |  0.32 |    0.32 |  92.07
  684 |  98 |  0.38 |    0.38 |  92.46
  685 |  66 |  0.26 |    0.26 |  92.71
  686 |   2 |  0.01 |    0.01 |  92.72
  687 |  80 |  0.31 |    0.31 |  93.03
  688 |  69 |  0.27 |    0.27 |  93.30
  689 |  65 |  0.25 |    0.25 |  93.56
  690 |  81 |  0.32 |    0.32 |  93.87
  691 |   1 |  0.00 |    0.00 |  93.88
  692 |  63 |  0.25 |    0.25 |  94.12
  693 |  15 |  0.06 |    0.06 |  94.18
  694 |  94 |  0.37 |    0.37 |  94.55
  695 |  33 |  0.13 |    0.13 |  94.68
  696 |  81 |  0.32 |    0.32 |  94.99
  697 | 109 |  0.43 |    0.43 |  95.42
  698 |   1 |  0.00 |    0.00 |  95.42
  699 |  94 |  0.37 |    0.37 |  95.79
  700 |  86 |  0.34 |    0.34 |  96.12
  701 |   1 |  0.00 |    0.00 |  96.13
  702 |  79 |  0.31 |    0.31 |  96.44
  703 |   1 |  0.00 |    0.00 |  96.44
  704 |  55 |  0.21 |    0.21 |  96.66
  705 |   5 |  0.02 |    0.02 |  96.67
  706 |  87 |  0.34 |    0.34 |  97.01
  707 |   1 |  0.00 |    0.00 |  97.02
  708 |   9 |  0.04 |    0.04 |  97.05
  709 |   1 |  0.00 |    0.00 |  97.06
  710 |   2 |  0.01 |    0.01 |  97.07
  711 |  71 |  0.28 |    0.28 |  97.34
  712 |  89 |  0.35 |    0.35 |  97.69
  713 |  82 |  0.32 |    0.32 |  98.01
  714 |  38 |  0.15 |    0.15 |  98.16
  715 |   4 |  0.02 |    0.02 |  98.17
  716 |  59 |  0.23 |    0.23 |  98.40
  717 |  80 |  0.31 |    0.31 |  98.72
  718 |  64 |  0.25 |    0.25 |  98.97
  719 |  64 |  0.25 |    0.25 |  99.22
  720 |  84 |  0.33 |    0.33 |  99.54
  721 | 117 |  0.46 |    0.46 | 100.00
 <NA> |   0 |  0.00 |    <NA> |   <NA>

Beispiel: Neue Daten(sätze) “berechnen”

Eigene Auswertung mit summarise()

dl %>% 
  summarise(
    m_round = round(mean(screentime_work, na.rm = T), digits = 2),
    sd = sd(screentime_work, na.rm = T)
    )
# A tibble: 1 × 2
  m_round    sd
    <dbl> <dbl>
1    23.5  35.6

Komfortable Lösung: descr()

dl %>% 
  select(screentime_work) %>% 
  
  
  descr()

## Basic descriptive statistics

             var    type           label     n NA.prc  mean    sd   se md
 screentime_work numeric screentime_work 13473  47.42 23.49 35.57 0.31  2
 trimmed       range iqr skew
   15.88 120 (0-120)  36 1.48

Beispiel: Mehrere Variablen editieren (simultan)

Überarbeitung einer Variable

# Note: IDs are arlready removed, see connecting_data.qmd for more details
dl %>% 
  mutate(across(ur01, ~ .x+9)) %>% 
  select(ur01)

Überarbeitung mehrerer Variablen

dl %>% 
  mutate(across(media_category_1:media_category_7, as.factor)) %>% 
  select(media_category_5) %>% 
  descr()

## Basic descriptive statistics

              var        type            label    n NA.prc mean   sd   se md
 media_category_5 categorical media_category_5 5555  78.32 0.17 0.38 0.01  0
 trimmed   range iqr skew
    0.09 1 (0-1)   0 1.72

Gruppierung nach Variablen und Fällen

Variablen

Achtung: ungroup() nicht vergessen

Quelle: Posit Software (2021)

Fälle

Achtung: ungroup() nicht vergessen

Quelle: Posit Software (2021)

Beispiel: Gruppierung nach Variable

Ungruppierte Auswrtung der NAs

dl %>%
  filter(form == "a Situational Survey") %>%
  
  miss_case_summary()
# A tibble: 10,632 × 3
    case n_miss pct_miss
   <int>  <int>    <dbl>
 1  1831    215     87.8
 2  2648    215     87.8
 3  7711    215     87.8
 4  8611    215     87.8
 5  8903    215     87.8
 6  8914    215     87.8
 7  9782    215     87.8
 8 10251    215     87.8
 9 10556    215     87.8
10  8124    214     87.3
# … with 10,622 more rows

Gruppierte Auswertung der NAs pro Fall

dl %>%
  filter(form == "a Situational Survey") %>%
  group_by(id) %>% 
  miss_case_summary()
# A tibble: 10,632 × 4
# Groups:   id [368]
      id  case n_miss pct_miss
   <int> <int>  <int>    <dbl>
 1     1     4    196     80.3
 2     1     6    196     80.3
 3     1    10    196     80.3
 4     1    11    196     80.3
 5     1    14    196     80.3
 6     1    21    196     80.3
 7     1     1    190     77.9
 8     1     2    190     77.9
 9     1     3    190     77.9
10     1     5    190     77.9
# … with 10,622 more rows

Beispiel: Gruppierung nach Fällen

  • Häufig sind fall- bzw. personenspezfische Mittel- oder Summewerte von Interesse

  • rowwise() ist vergleichsweise “kompliziert”, erlaubt aber im Gegensatz zu anderen Funktionen die direkte Umsetzung von mehreren Arbeitsschritten gleichzeitig (bezogen auf Fälle / Reihen)

z. B. Index für disconnection

dl %>%
  select(disco_1:disco_5) %>% 
  rowwise() %>% 
  mutate(disco_index = mean(c_across(starts_with("disco_")), na.rm = T)) %>% 
  frq(disco_index)
disco_index <numeric> 
# total N=25624 valid N=13449 mean=0.38 sd=0.39

Value |     N | Raw % | Valid % | Cum. %
----------------------------------------
 0.00 |  5512 | 21.51 |   40.98 |  40.98
 0.20 |  1377 |  5.37 |   10.24 |  51.22
 0.40 |  1528 |  5.96 |   11.36 |  62.58
 0.60 |  1517 |  5.92 |   11.28 |  73.86
 0.80 |  1186 |  4.63 |    8.82 |  82.68
 1.00 |  2329 |  9.09 |   17.32 | 100.00
 <NA> | 12175 | 47.51 |    <NA> |   <NA>

Weitere nützliche tidyverse-Befehle

Quelle: Posit Software (2021)

R-Aufgabe

  1. Nutzen Sie die kennengelernten tidyverse-Funktionen, um

    1. …interessierende Variablen zu erstellen

    2. …die Messungen oder Personen in Gruppen zu unterteilen und zu vergleichen

Literatur

Jonge, E. de, & Loo, M. van der. (n.d.). An introduction to data cleaning with R. https://cran.r-project.org/doc/contrib/de_Jonge+van_der_Loo-Introduction_to_data_cleaning_with_R.pdf
Posit Software. (2021). Data-Transformation. https://posit.co/wp-content/uploads/2022/10/data-transformation-1.pdf
Wickham, H., & Grolemund, G. (2016). R for data science: Import, tidy, transform, visualize, and model data (First edition). O’Reilly.