Formal Methods
- 0.1 Overall change over time in the two broad families
- 0.2 Breaking things down by more specific methods
- 0.3 Breaking things down by level
- 0.4 Proportion of papers in 2010s in each family broken down by subdiscipline
- 0.5 Contingency table
- 0.6 Change over time in the two broad families
- 0.6.0.1 Logistic regression asking whether the proportion of papers that use logic is changing over time
- 0.6.0.2 Logistic regression asking whether the proportion of papers that use probability is changing over time
- 0.6.0.3 Is there still an increase over time in the probability family when we ignore the decision theory papers?
- 0.6.0.4 McNemar’s exact test asking whether the proportion of logic papers is higher than the proportion of probability papers in each time period
- 0.6.0.5 Is there still an increase over time in the probability family when we ignore the advanced papers?
- 0.7 Change over time in the individual methods
- 0.8 Interrater reliabilities
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] conflicted_1.0.4 forcats_0.5.0 stringr_1.4.0 dplyr_1.0.2
## [5] purrr_0.3.4 readr_1.4.0 tidyr_1.1.2 tibble_3.0.4
## [9] tidyverse_1.3.0 psych_2.0.9 exact2x2_1.6.5 exactci_1.3-3
## [13] ssanv_1.1 sjlabelled_1.1.7 sjmisc_2.8.6 sjPlot_2.8.9
## [17] knitr_1.36 nnet_7.3-15 MASS_7.3-53.1 scales_1.1.1
## [21] ggplot2_3.3.5
##
## loaded via a namespace (and not attached):
## [1] nlme_3.1-149 fs_1.5.0 lubridate_1.7.9 insight_0.14.5
## [5] httr_1.4.2 tools_4.0.3 backports_1.1.10 bslib_0.3.1
## [9] R6_2.5.0 DBI_1.1.0 colorspace_1.4-1 withr_2.4.2
## [13] tidyselect_1.1.0 mnormt_2.0.2 emmeans_1.6.2-1 compiler_4.0.3
## [17] cli_3.1.0 rvest_0.3.6 performance_0.8.0 xml2_1.3.2
## [21] sandwich_3.0-0 bayestestR_0.11.5 sass_0.4.0 mvtnorm_1.1-1
## [25] digest_0.6.27 minqa_1.2.4 rmarkdown_2.11 pkgconfig_2.0.3
## [29] htmltools_0.5.2 lme4_1.1-25 dbplyr_1.4.4 fastmap_1.1.0
## [33] rlang_0.4.12 readxl_1.3.1 rstudioapi_0.13 jquerylib_0.1.4
## [37] generics_0.0.2 zoo_1.8-8 jsonlite_1.7.1 magrittr_2.0.1
## [41] parameters_0.15.0 Matrix_1.2-18 Rcpp_1.0.7 munsell_0.5.0
## [45] lifecycle_1.0.1 stringi_1.5.3 multcomp_1.4-15 yaml_2.2.1
## [49] grid_4.0.3 blob_1.2.1 parallel_4.0.3 crayon_1.3.4
## [53] lattice_0.20-41 ggeffects_1.0.2 haven_2.4.3 splines_4.0.3
## [57] sjstats_0.18.0 hms_0.5.3 tmvnsim_1.0-2 pillar_1.4.6
## [61] boot_1.3-25 estimability_1.3 effectsize_0.5 codetools_0.2-16
## [65] reprex_0.3.0 glue_1.4.2 evaluate_0.14 modelr_0.1.8
## [69] vctrs_0.3.4 nloptr_1.2.2.2 cellranger_1.1.0 gtable_0.3.0
## [73] datawizard_0.2.1 assertthat_0.2.1 cachem_1.0.6 xfun_0.28
## [77] xtable_1.8-4 broom_0.7.10 coda_0.19-4 survival_3.2-7
## [81] memoise_2.0.0 statmod_1.4.35 TH.data_1.0-10 ellipsis_0.3.10.1 Overall change over time in the two broad families
0.2 Breaking things down by more specific methods
0.2.0.1 Proportion of logic papers using each more specific method
0.2.0.2 Proportion of probability papers using each more specific method
## # A tibble: 2 x 5
## Var1 Category No Yes Percent
## <fct> <chr> <int> <int> <dbl>
## 1 2005-2009 Statistics 369 1 0.00270
## 2 2015-2019 Statistics 532 7 0.0130
0.3 Breaking things down by level
0.3.0.1 Proportion of logic papers over time broken down by level
0.3.0.2 Proportion of probability papers over time broken down by level
0.4 Proportion of papers in 2010s in each family broken down by subdiscipline
0.5 Contingency table
## Log Mod Set Caus Prob
## Action 0.002702703 0.002702703 0.000000000 0.000000000 0.000000000
## Decision 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## Epistemology 0.008108108 0.024324324 0.000000000 0.000000000 0.010810811
## Language 0.029729730 0.013513514 0.005405405 0.000000000 0.002702703
## Logic 0.021621622 0.005405405 0.002702703 0.000000000 0.000000000
## Metaphysics 0.021621622 0.021621622 0.013513514 0.002702703 0.000000000
## Mind 0.002702703 0.002702703 0.002702703 0.000000000 0.000000000
## Science 0.002702703 0.000000000 0.000000000 0.000000000 0.008108108
## Value 0.005405405 0.008108108 0.002702703 0.000000000 0.000000000
## Dec Stats
## Action 0.000000000 0.000000000
## Decision 0.002702703 0.000000000
## Epistemology 0.000000000 0.002702703
## Language 0.000000000 0.000000000
## Logic 0.000000000 0.000000000
## Metaphysics 0.000000000 0.000000000
## Mind 0.000000000 0.000000000
## Science 0.000000000 0.000000000
## Value 0.002702703 0.000000000## Log Mod Set Caus Prob
## Action 0.001855288 0.001855288 0.000000000 0.003710575 0.000000000
## Decision 0.001855288 0.000000000 0.000000000 0.000000000 0.001855288
## Epistemology 0.012987013 0.018552876 0.001855288 0.000000000 0.025974026
## Language 0.022263451 0.001855288 0.003710575 0.000000000 0.000000000
## Logic 0.020408163 0.007421150 0.003710575 0.000000000 0.000000000
## Metaphysics 0.035250464 0.024118738 0.018552876 0.005565863 0.007421150
## Mind 0.001855288 0.001855288 0.001855288 0.001855288 0.000000000
## Science 0.001855288 0.003710575 0.001855288 0.001855288 0.011131725
## Value 0.007421150 0.003710575 0.005565863 0.000000000 0.003710575
## Dec Stats
## Action 0.001855288 0.003710575
## Decision 0.022263451 0.001855288
## Epistemology 0.005565863 0.000000000
## Language 0.000000000 0.000000000
## Logic 0.000000000 0.000000000
## Metaphysics 0.000000000 0.001855288
## Mind 0.000000000 0.001855288
## Science 0.001855288 0.001855288
## Value 0.011131725 0.0055658630.6 Change over time in the two broad families
FormalModel <- glm(Formal ~ year, data= data)
summary(FormalModel)##
## Call:
## glm(formula = Formal ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.2274 -0.2216 -0.1987 -0.1872 0.8128
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.560329 5.416186 -1.027 0.305
## year 0.002867 0.002691 1.065 0.287
##
## (Dispersion parameter for gaussian family taken to be 0.1661282)
##
## Null deviance: 150.87 on 908 degrees of freedom
## Residual deviance: 150.68 on 907 degrees of freedom
## AIC: 951.98
##
## Number of Fisher Scoring iterations: 2exp(confint(FormalModel))## Waiting for profiling to be done...## 2.5 % 97.5 %
## (Intercept) 0.00000009438748 156.835912
## year 0.99759599228188 1.008173table(data$TimePeriod, data$Formal)##
## 0 1
## 2005-2009 301 69
## 2015-2019 417 1220.6.0.1 Logistic regression asking whether the proportion of papers that use logic is changing over time
##
## Call:
## glm(formula = Logic ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.1577 -0.1537 -0.1476 -0.1435 0.8565
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.194112 4.744615 0.462 0.644
## year -0.001016 0.002357 -0.431 0.667
##
## (Dispersion parameter for gaussian family taken to be 0.1274848)
##
## Null deviance: 115.65 on 908 degrees of freedom
## Residual deviance: 115.63 on 907 degrees of freedom
## AIC: 711.31
##
## Number of Fisher Scoring iterations: 2## Waiting for profiling to be done...## 2.5 % 97.5 %
## (Intercept) 0.0008208564 98065.06425
## year 0.9943805509 1.003610.6.0.2 Logistic regression asking whether the proportion of papers that use probability is changing over time
ProbModel <- glm(Probability ~ year, data= data)
summary(ProbModel)##
## Call:
## glm(formula = Probability ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.10100 -0.08974 -0.07848 -0.03343 0.97783
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11.267085 3.307159 -3.407 0.000686 ***
## year 0.005631 0.001643 3.427 0.000637 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.06193934)
##
## Null deviance: 56.906 on 908 degrees of freedom
## Residual deviance: 56.179 on 907 degrees of freedom
## AIC: 55.154
##
## Number of Fisher Scoring iterations: 2confint(ProbModel)## 2.5 % 97.5 %
## (Intercept) -17.748997420 -4.785172102
## year 0.002410505 0.008850601exp(confint(ProbModel))## 2.5 % 97.5 %
## (Intercept) 0.0000000195753 0.008352686
## year 1.0024134126886 1.0088898830.6.0.3 Is there still an increase over time in the probability family when we ignore the decision theory papers?
noDec <- filter(data, Decision != "Yes")
ProbModel <- glm(Probability ~ year, data= noDec)
summary(ProbModel)##
## Call:
## glm(formula = Probability ~ year, data = noDec)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.06339 -0.05737 -0.05134 -0.02726 0.97876
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.015201 2.779887 -2.164 0.0307 *
## year 0.003011 0.001381 2.180 0.0295 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.04288306)
##
## Null deviance: 38.198 on 887 degrees of freedom
## Residual deviance: 37.994 on 886 degrees of freedom
## AIC: -272.53
##
## Number of Fisher Scoring iterations: 2confint(ProbModel)## 2.5 % 97.5 %
## (Intercept) -11.4636794315 -0.566721589
## year 0.0003039303 0.005717454exp(confint(ProbModel))## 2.5 % 97.5 %
## (Intercept) 0.00001050479 0.5673825
## year 1.00030397651 1.00573380.6.0.4 McNemar’s exact test asking whether the proportion of logic papers is higher than the proportion of probability papers in each time period
## Logic
## Probability Absent Present
## Absent 304 55
## Present 9 2##
## Exact McNemar test (with central confidence intervals)
##
## data: OldFreqs
## b = 55, c = 9, p-value = 0.000000003542
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 2.996214 14.066124
## sample estimates:
## odds ratio
## 6.111111## Logic
## Probability Absent Present
## Absent 421 68
## Present 39 11##
## Exact McNemar test (with central confidence intervals)
##
## data: NowFreqs
## b = 68, c = 39, p-value = 0.006518
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 1.159364 2.655239
## sample estimates:
## odds ratio
## 1.743590.6.0.5 Is there still an increase over time in the probability family when we ignore the advanced papers?
withoutAdvanced <- data %>%
filter(LogLevel != 3)
ProbModel <- glm(Probability ~ year, data= withoutAdvanced)
summary(ProbModel)##
## Call:
## glm(formula = Probability ~ year, data = withoutAdvanced)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.09763 -0.08699 -0.07635 -0.03378 0.97686
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -10.645350 3.306997 -3.219 0.00133 **
## year 0.005321 0.001643 3.239 0.00125 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.06040846)
##
## Null deviance: 54.216 on 888 degrees of freedom
## Residual deviance: 53.582 on 887 degrees of freedom
## AIC: 31.78
##
## Number of Fisher Scoring iterations: 2confint(ProbModel)## 2.5 % 97.5 %
## (Intercept) -17.126945635 -4.163754681
## year 0.002100944 0.008540942exp(confint(ProbModel))## 2.5 % 97.5 %
## (Intercept) 0.00000003646381 0.01554907
## year 1.00210315288999 1.00857752withoutAdvanced <- data %>%
filter(ProbLevel != 3)
ProbModel <- glm(Probability ~ year, data= withoutAdvanced)
summary(ProbModel)##
## Call:
## glm(formula = Probability ~ year, data = withoutAdvanced)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.07791 -0.06988 -0.06186 -0.02975 0.97827
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.023895 2.999292 -2.675 0.00760 **
## year 0.004013 0.001490 2.693 0.00721 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.05040602)
##
## Null deviance: 45.429 on 895 degrees of freedom
## Residual deviance: 45.063 on 894 degrees of freedom
## AIC: -130.19
##
## Number of Fisher Scoring iterations: 2confint(ProbModel)## 2.5 % 97.5 %
## (Intercept) -13.902400214 -2.145389778
## year 0.001092424 0.006933136exp(confint(ProbModel))## 2.5 % 97.5 %
## (Intercept) 0.0000009167783 0.1170224
## year 1.0010930213055 1.00695720.7 Change over time in the individual methods
0.7.0.1 Non-Modal Logic
##
## Call:
## glm(formula = Nonmodal ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.08110 -0.08011 -0.07911 -0.07514 0.92586
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.922428 3.569592 -0.258 0.796
## year 0.000497 0.001773 0.280 0.779
##
## (Dispersion parameter for gaussian family taken to be 0.07215951)
##
## Null deviance: 65.454 on 908 degrees of freedom
## Residual deviance: 65.449 on 907 degrees of freedom
## AIC: 193.98
##
## Number of Fisher Scoring iterations: 2Odds ratio and confidence interval
## [1] 1.000497## 2.5 % 97.5 %
## (Intercept) 0.0003638751 434.347253
## year 0.9970259050 1.0039810.7.0.2 Modal Logic
##
## Call:
## glm(formula = Modal ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.07404 -0.06726 -0.05708 -0.05369 0.94970
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.473791 3.169707 1.096 0.273
## year -0.001696 0.001575 -1.077 0.282
##
## (Dispersion parameter for gaussian family taken to be 0.05689767)
##
## Null deviance: 51.672 on 908 degrees of freedom
## Residual deviance: 51.606 on 907 degrees of freedom
## AIC: -22.021
##
## Number of Fisher Scoring iterations: 2Odds ratio and confidence interval
## [1] 0.9983058## 2.5 % 97.5 %
## (Intercept) 0.06465309 16095.611914
## year 0.99522956 1.0013920.7.0.3 Set theory
##
## Call:
## glm(formula = Set ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.03457 -0.03295 -0.03133 -0.02487 0.97674
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.5961673 2.2577626 -0.707 0.480
## year 0.0008077 0.0011216 0.720 0.472
##
## (Dispersion parameter for gaussian family taken to be 0.02886775)
##
## Null deviance: 26.198 on 908 degrees of freedom
## Residual deviance: 26.183 on 907 degrees of freedom
## AIC: -638.8
##
## Number of Fisher Scoring iterations: 2Odds ratio and confidence interval
## [1] 1.000808## 2.5 % 97.5 %
## (Intercept) 0.002426511 16.927951
## year 0.998610367 1.0030110.7.0.4 Probability theory
##
## Call:
## glm(formula = Prob ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.04360 -0.03971 -0.03583 -0.02029 0.98360
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.878176 2.334296 -1.661 0.0970 .
## year 0.001942 0.001160 1.675 0.0943 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.03085802)
##
## Null deviance: 28.075 on 908 degrees of freedom
## Residual deviance: 27.988 on 907 degrees of freedom
## AIC: -578.2
##
## Number of Fisher Scoring iterations: 2Odds ratio and confidence interval
## [1] 1.001944## 2.5 % 97.5 %
## (Intercept) 0.0002131934 2.007639
## year 0.9996696777 1.0042240.7.0.5 Game theory and decision theory
##
## Call:
## glm(formula = Decision ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.04000 -0.03439 -0.02877 -0.00632 0.99930
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.6274915 1.9896648 -2.828 0.00478 **
## year 0.0028071 0.0009884 2.840 0.00461 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.022419)
##
## Null deviance: 20.515 on 908 degrees of freedom
## Residual deviance: 20.334 on 907 degrees of freedom
## AIC: -868.61
##
## Number of Fisher Scoring iterations: 2Odds ratio and confidence interval
## [1] 1.002811## 2.5 % 97.5 %
## (Intercept) 0.00007284601 0.1776713
## year 1.00087020054 1.00475560.7.0.6 Statistics
##
## Call:
## glm(formula = Statistics ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.01409 -0.01233 -0.01058 -0.00355 0.99470
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.7595067 1.2411039 -1.418 0.157
## year 0.0008785 0.0006165 1.425 0.155
##
## (Dispersion parameter for gaussian family taken to be 0.008723136)
##
## Null deviance: 7.9296 on 908 degrees of freedom
## Residual deviance: 7.9119 on 907 degrees of freedom
## AIC: -1726.6
##
## Number of Fisher Scoring iterations: 2Odds ratio and confidence interval
## [1] 1.000879## 2.5 % 97.5 %
## (Intercept) 0.01511564 1.960133
## year 0.99967009 1.0020890.7.0.7 Causal modeling
##
## Call:
## glm(formula = Causal ~ year, data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.01141 -0.01018 -0.00895 -0.00402 0.99598
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.2325464 1.1621602 -1.061 0.289
## year 0.0006161 0.0005773 1.067 0.286
##
## (Dispersion parameter for gaussian family taken to be 0.007648714)
##
## Null deviance: 6.9461 on 908 degrees of freedom
## Residual deviance: 6.9374 on 907 degrees of freedom
## AIC: -1846.1
##
## Number of Fisher Scoring iterations: 2Odds ratio and confidence interval
## [1] 1.000616## 2.5 % 97.5 %
## (Intercept) 0.02988679 2.844098
## year 0.99948471 1.0017490.8 Interrater reliabilities
0.8.0.1 Families
agreement(data$Logic_1, data$Logic_2)## agreement kappa
## 1 0.9192825 0.8063302agreement(data$Probability_1, data$Probability_2)## agreement kappa
## 1 0.9327354 0.83929860.8.0.2 Specific methods
agreement(data$c_1, data$c_2)## agreement kappa
## 1 0.9820628 0.6574501agreement(data$p_1, data$p_2)## agreement kappa
## 1 0.9282511 0.7081629agreement(data$d_1, data$d_2)## agreement kappa
## 1 0.9461883 0.7093831agreement(data$t_1, data$t_2)## Warning in cohen.kappa1(x, w = w, n.obs = n.obs, alpha = alpha, levels =
## levels): upper or lower confidence interval exceed abs(1) and set to +/- 1.## agreement kappa
## 1 0.9955157 0.9310238agreement(data$l_1, data$l_2)## agreement kappa
## 1 0.7713004 0.5163101agreement(data$m_1, data$m_2)## agreement kappa
## 1 0.8430493 0.5856999agreement(data$s_1, data$s_2)## agreement kappa
## 1 0.8430493 0.33670430.8.0.3 Subdisciplines
agreement(data$act_1, data$act_2)## agreement kappa
## 1 0.9506726 0.5360318agreement(data$dec_1, data$dec_2)## agreement kappa
## 1 0.9641256 0.6737381agreement(data$epi_1, data$epi_2)## agreement kappa
## 1 0.9013453 0.7219136agreement(data$lan_1, data$lan_2)## agreement kappa
## 1 0.9058296 0.6706519agreement(data$log_1, data$log_2)## agreement kappa
## 1 0.9058296 0.5352784agreement(data$met_1, data$met_2)## agreement kappa
## 1 0.9147982 0.7929029agreement(data$min_1, data$min_2)## agreement kappa
## 1 0.9596413 0.5874615agreement(data$sci_1, data$sci_2)## agreement kappa
## 1 0.9461883 0.618912agreement(data$val_1, data$val_2)## agreement kappa
## 1 0.9461883 0.73958740.8.0.4 Levels
cor.test(data$level_1, data$level_2, method = "spearman")## Warning in cor.test.default(data$level_1, data$level_2, method = "spearman"):
## Cannot compute exact p-value with ties##
## Spearman's rank correlation rho
##
## data: data$level_1 and data$level_2
## S = 585529, p-value < 0.00000000000000022
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## 0.6831935data <- data %>%
mutate(
Formal1 = case_when(
level_1 == 0 ~ 0,
TRUE ~ 1),
Formal2 = case_when(
level_2 == 0 ~ 0,
TRUE ~ 1)
)
table(data$Formal1, data$Formal2)##
## 0 1
## 0 17 17
## 1 17 172agreement(data$Formal1, data$Formal2)## agreement kappa
## 1 0.8475336 0.4100529Formal <- data %>%
filter(level_resolved != 0)
cor.test(Formal$level_1, Formal$level_2, method = "spearman")## Warning in cor.test.default(Formal$level_1, Formal$level_2, method =
## "spearman"): Cannot compute exact p-value with ties##
## Spearman's rank correlation rho
##
## data: Formal$level_1 and Formal$level_2
## S = 492706, p-value < 0.00000000000000022
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## 0.5757215