Proportsioonide_vordlus
print(tekstid)## # A tibble: 300 x 10
## kood keeletase sonad spikkus lpikkus lemmad yld_kaanded yld_Par S_ains
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 A2I_… 1 39 4.87 4.33 31 4 0.128 0.256
## 2 A2I_… 1 72 4.19 6 43 7 0.0417 0.194
## 3 A2I_… 1 38 5.74 6.33 26 8 0.158 0.237
## 4 A2I_… 1 61 5.46 7.62 43 7 0.0656 0.262
## 5 A2I_… 1 75 4.77 6.25 45 10 0.08 0.24
## 6 A2II… 1 31 5.10 5.17 26 7 0.161 0.452
## 7 A2II… 1 47 4.64 7.83 41 6 0.0213 0.447
## 8 A2II… 1 40 4.78 6.67 32 5 0.1 0.35
## 9 A2II… 1 43 5 6.14 33 8 0.0465 0.326
## 10 A2II… 1 57 4.60 7.12 42 7 0.0526 0.351
## # … with 290 more rows, and 1 more variable: V_aux <dbl>Osakaalude asemel on vaja absoluutarve. Ainsuslike nimisõnade arvu leidmiseks korrutan nende osakaalu sõnade arvuga tekstis ja talletan korrutise uues tulbas.
tekstid <- tekstid %>% mutate(S_ains_arv = S_ains * sonad)Leian kõigi sõnade arvu ning ainsuslike nimisõnade arvu keeleoskustasemete kaupa.
tekstid %>% group_by(keeletase) %>% summarise(sonad_sum = sum(sonad))## # A tibble: 4 x 2
## keeletase sonad_sum
## <dbl> <dbl>
## 1 1 3767
## 2 2 8716
## 3 3 12500
## 4 4 16460tekstid %>% group_by(keeletase) %>% summarise(S_ains_sum = sum(S_ains_arv))## # A tibble: 4 x 2
## keeletase S_ains_sum
## <dbl> <dbl>
## 1 1 1015.
## 2 2 1961.
## 3 3 2448.
## 4 4 3715.Ainsuslike nimisõnade osakaal B1-tasemega õppijate kirjutistes jääb 95% tõenäosusega vahemikku 21,6% kuni 23,4%. Kui soovin üldistada 99% kindlusega, siis on vahemikuks 21,4% kuni 23,7%.
prop.test(1961, 8716)##
## 1-sample proportions test with continuity correction
##
## data: 1961 out of 8716, null probability 0.5
## X-squared = 2635.7, df = 1, p-value < 2.2e-16
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
## 0.2162878 0.2339332
## sample estimates:
## p
## 0.2249885prop.test(1961, 8716, conf.level=0.99)##
## 1-sample proportions test with continuity correction
##
## data: 1961 out of 8716, null probability 0.5
## X-squared = 2635.7, df = 1, p-value < 2.2e-16
## alternative hypothesis: true p is not equal to 0.5
## 99 percent confidence interval:
## 0.2136228 0.2367747
## sample estimates:
## p
## 0.2249885Ainsuslike nimisõnade osakaal B2-tasemega õppijate kirjutistes jääb 99% tõenäosusega vahemikku 18,7% kuni 20,5%.
prop.test(2448, 12500, conf.level=0.99)##
## 1-sample proportions test with continuity correction
##
## data: 2448 out of 12500, null probability 0.5
## X-squared = 4624.4, df = 1, p-value < 2.2e-16
## alternative hypothesis: true p is not equal to 0.5
## 99 percent confidence interval:
## 0.1868202 0.2051839
## sample estimates:
## p
## 0.19584Loon maatriksi B1- ja B2-taseme summadega ning võrdlen ainsuslike nimisõnade osakaalu kahel tasemel. 95% tõenäosusega esineb B1-tasemel 1,8% kuni 5% võrra rohkem ainsuslikke nimisõnu. Kui soovin olla üldistatavas vahemikus 99% kindel, siis on erinevus üldkogumis 1,3% kuni 5,5%.
matrix(nrow=2, ncol=2, c(1961, 8716, 2448, 12500))## [,1] [,2]
## [1,] 1961 2448
## [2,] 8716 12500prop.test(matrix(nrow=2, ncol=2, c(1961, 8716, 2448, 12500)))##
## 2-sample test for equality of proportions with continuity correction
##
## data: matrix(nrow = 2, ncol = 2, c(1961, 8716, 2448, 12500))
## X-squared = 17.171, df = 1, p-value = 3.416e-05
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## 0.01771997 0.05018010
## sample estimates:
## prop 1 prop 2
## 0.4447721 0.4108220prop.test(matrix(nrow=2, ncol=2, c(1961, 8716, 2448, 12500)), conf.level=0.99)##
## 2-sample test for equality of proportions with continuity correction
##
## data: matrix(nrow = 2, ncol = 2, c(1961, 8716, 2448, 12500))
## X-squared = 17.171, df = 1, p-value = 3.416e-05
## alternative hypothesis: two.sided
## 99 percent confidence interval:
## 0.01266315 0.05523692
## sample estimates:
## prop 1 prop 2
## 0.4447721 0.4108220Loon iga keeletaseme jaoks uue andmetabeli kahe summamuutujaga ning kasutan maatriksites tabelitest võetud muutujate nimesid.
summad_A2 <- tekstid %>% filter(keeletase==1) %>% summarise(
sonad_sum = sum(sonad),
S_ains_sum = sum(S_ains_arv)
)
summad_B1 <- tekstid %>% filter(keeletase==2) %>% summarise(
sonad_sum = sum(sonad),
S_ains_sum = sum(S_ains_arv)
)
summad_B2 <- tekstid %>% filter(keeletase==3) %>% summarise(
sonad_sum = sum(sonad),
S_ains_sum = sum(S_ains_arv)
)
summad_C1 <- tekstid %>% filter(keeletase==4) %>% summarise(
sonad_sum = sum(sonad),
S_ains_sum = sum(S_ains_arv)
)A2- ja B1-taseme võrdlus toob esile, et 95% tõenäosusega esineb A2-tasemel 2% kuni 5,8% võrra rohkem ainsuslikke nimisõnu. 99% usaldusnivoo juures jääb üldistatav erinevus vahemikku 1,4% kuni 6,4%.
matrix(nrow=2, ncol=2, c(summad_A2$S_ains_sum, summad_A2$sonad_sum,
summad_B1$S_ains_sum, summad_B1$sonad_sum))## [,1] [,2]
## [1,] 1015.001 1961.002
## [2,] 3767.000 8716.000prop.test(matrix(nrow=2, ncol=2, c(summad_A2$S_ains_sum, summad_A2$sonad_sum,
summad_B1$S_ains_sum, summad_B1$sonad_sum)))##
## 2-sample test for equality of proportions with continuity correction
##
## data: matrix(nrow = 2, ncol = 2, c(summad_A2$S_ains_sum, summad_A2$sonad_sum, summad_B1$S_ains_sum, summad_B1$sonad_sum))
## X-squared = 17.182, df = 1, p-value = 3.397e-05
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## 0.02024374 0.05833939
## sample estimates:
## prop 1 prop 2
## 0.3410620 0.3017704prop.test(matrix(nrow=2, ncol=2, c(summad_A2$S_ains_sum, summad_A2$sonad_sum,
summad_B1$S_ains_sum, summad_B1$sonad_sum)), conf.level=0.99)##
## 2-sample test for equality of proportions with continuity correction
##
## data: matrix(nrow = 2, ncol = 2, c(summad_A2$S_ains_sum, summad_A2$sonad_sum, summad_B1$S_ains_sum, summad_B1$sonad_sum))
## X-squared = 17.182, df = 1, p-value = 3.397e-05
## alternative hypothesis: two.sided
## 99 percent confidence interval:
## 0.01432386 0.06425928
## sample estimates:
## prop 1 prop 2
## 0.3410620 0.3017704B2- ja C1-taseme võrdluses selgub, et 95% tõenäosusega on C1-tasemel ainsuslikke nimisõnu 2,1% kuni 4,8% võrra vähem.
matrix(nrow=2, ncol=2, c(summad_B2$S_ains_sum, summad_B2$sonad_sum,
summad_C1$S_ains_sum, summad_C1$sonad_sum))## [,1] [,2]
## [1,] 2447.999 3715
## [2,] 12500.000 16460prop.test(matrix(nrow=2, ncol=2, c(summad_B2$S_ains_sum, summad_B2$sonad_sum,
summad_C1$S_ains_sum, summad_C1$sonad_sum)))##
## 2-sample test for equality of proportions with continuity correction
##
## data: matrix(nrow = 2, ncol = 2, c(summad_B2$S_ains_sum, summad_B2$sonad_sum, summad_C1$S_ains_sum, summad_C1$sonad_sum))
## X-squared = 24.487, df = 1, p-value = 7.48e-07
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## -0.04800183 -0.02083963
## sample estimates:
## prop 1 prop 2
## 0.3972091 0.4316298Salvestan osastavas käändes sõnade arvu eraldi tulbana ning arvutan summad keeleoskustasemeti.
tekstid <- tekstid %>% mutate(yld_Par_arv = yld_Par * sonad)
tekstid %>% group_by(keeletase) %>% summarise(yld_Par_sum = sum(yld_Par_arv))## # A tibble: 4 x 2
## keeletase yld_Par_sum
## <dbl> <dbl>
## 1 1 216.
## 2 2 544.
## 3 3 933.
## 4 4 1305.Võrdlen kõrvutiasetsevaid keeleoskustasemeid. Erinevus on statistiliselt oluline vaid B1- ja B2-taseme vahel (p = 0,001).
prop.test(matrix(nrow=2, ncol=2, c(216, 3767, 544, 8716)))##
## 2-sample test for equality of proportions with continuity correction
##
## data: matrix(nrow = 2, ncol = 2, c(216, 3767, 544, 8716))
## X-squared = 0.96853, df = 1, p-value = 0.325
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## -0.05132010 0.01620033
## sample estimates:
## prop 1 prop 2
## 0.2842105 0.3017704prop.test(matrix(nrow=2, ncol=2, c(544, 8716, 933, 12500)))##
## 2-sample test for equality of proportions with continuity correction
##
## data: matrix(nrow = 2, ncol = 2, c(544, 8716, 933, 12500))
## X-squared = 10.155, df = 1, p-value = 0.001439
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## -0.06834421 -0.01667153
## sample estimates:
## prop 1 prop 2
## 0.3683142 0.4108220prop.test(matrix(nrow=2, ncol=2, c(933, 12500, 1305, 16460)))##
## 2-sample test for equality of proportions with continuity correction
##
## data: matrix(nrow = 2, ncol = 2, c(933, 12500, 1305, 16460))
## X-squared = 1.7813, df = 1, p-value = 0.182
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## -0.036188992 0.006709485
## sample estimates:
## prop 1 prop 2
## 0.4168901 0.4316298Võtan 20 korral valimist välja 50 juhuslikku B2-taseme teksti (kokku on 80 teksti) ning leian neis kõigi sõnade arvu ja osastavas käändes sõnade arvu. Võrdlen usaldusintervalli alam- ja ülempiire. Mõnel katsel tulemuseks saadud ülempiir on väiksem kui teisel katsel saadud alampiir.
yldarv <- 50 #juhuvalimi suurus
katseid <- 20
Par_kokku <- {}
sonad_kokku <- {}
for (i in 1:katseid){
juhuvalim <- tekstid %>% sample_n(yldarv) %>% filter(keeletase==3) %>% summarise(
yld_Par_sum = sum(yld_Par_arv),
sonad_sum = sum(sonad))
Par_kokku[[i]] <- juhuvalim$yld_Par_sum
sonad_kokku[[i]] <- juhuvalim$sonad_sum
}
#Loon tühja maatriksi, millel 20 rida ja 2 tulpa.
testivastused <- matrix(nrow=katseid, ncol=4)
#Talletan usaldusintervalli alam- ja ülempiiri maatriksi ridadena.
for (i in 1:katseid){
pt <- prop.test(Par_kokku[[i]], sonad_kokku[[i]])
testivastused[i, ] <- c(x1=pt$conf.int[1], y1=0, x2=pt$conf.int[2], y2=0)
}
print(testivastused)## [,1] [,2] [,3] [,4]
## [1,] 0.06401787 0 0.08684182 0
## [2,] 0.06502180 0 0.08500585 0
## [3,] 0.06795285 0 0.09000009 0
## [4,] 0.06874799 0 0.09899794 0
## [5,] 0.05504413 0 0.07689987 0
## [6,] 0.05866959 0 0.08348899 0
## [7,] 0.06629730 0 0.09275833 0
## [8,] 0.07211304 0 0.09362970 0
## [9,] 0.06704538 0 0.09320061 0
## [10,] 0.06479665 0 0.08968499 0
## [11,] 0.07252662 0 0.09508376 0
## [12,] 0.07203139 0 0.09375901 0
## [13,] 0.06682836 0 0.08946138 0
## [14,] 0.05309893 0 0.07421229 0
## [15,] 0.05356014 0 0.07466262 0
## [16,] 0.04488144 0 0.07030436 0
## [17,] 0.06583388 0 0.08869041 0
## [18,] 0.06388783 0 0.08521331 0
## [19,] 0.05845582 0 0.08410161 0
## [20,] 0.07134266 0 0.08922759 0ggplot() + xlim(0.04, 0.1) +
geom_curve(aes(x=V1, y=V2, xend=V3, yend=V4),
data=as_tibble(testivastused))## Warning: `as_tibble.matrix()` requires a matrix with column names or a `.name_repair` argument. Using compatibility `.name_repair`.
## This warning is displayed once per session.
Kuna osastavas käändes sõnade osakaal on tasemeti pigem sarnane, siis leian osastavas sõnade üldarvu ja kõigi sõnade üldarvu valimis. Selliste sõnade osakaalu saab 95% tõenäosusega üldistada 0,5% täpsusega: 7,0% - 7,5%.
tekstid %>% summarise(yld_Par_sum = sum(yld_Par_arv))## # A tibble: 1 x 1
## yld_Par_sum
## <dbl>
## 1 2998.tekstid %>% summarise(sonad_sum = sum(sonad))## # A tibble: 1 x 1
## sonad_sum
## <dbl>
## 1 41443prop.test(2998, 41443)##
## 1-sample proportions test with continuity correction
##
## data: 2998 out of 41443, null probability 0.5
## X-squared = 30317, df = 1, p-value < 2.2e-16
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
## 0.06987383 0.07488648
## sample estimates:
## p
## 0.07234032