Proiect statistica - brainhead

Proiectul este bazat pe un set de data privind greutatea si marimea creierului la femei si barbati. Sa se stabileasca daca exista vreo legatura intre marimea si greutatea creierului unei femei si cea a unui barbat.

S-au impartit datele in coloane pentru femei si barbati pentru marime:

>boxplot(barbati,femei)

> par(mfrow=c(2,1))

> hist(barbati)

> hist(femei)

> qqnorm(barbati)

> qqnorm(femei)

> par(mfrow=c(1,1))

> qqnorm(barbati)

> qqline(barbati)

> par(mfrow=c(1,1))

> qqnorm(femei)

> qqline(femei)

> var(barbati)

[1] 725071.7

> var(femei)

[1] 509550.9

> var.test(barbati,femei)

F test to compare two variances

data: barbati and femei

F = 1.423, num df = 133, denom df = 126, p-value = 0.04631

alternative hypothesis: true ratio of variances is not equal to 1

95 percent confidence interval:

1.005825 2.009798

sample estimates:

ratio of variances

1.422962

Vom elimina datele aberante:

> barbatif=barbati[barbati<5000]

> barbatif=barbatif[barbatif>2000]

> var(barbatif)

[1] 106487.9

> femeif=femei[femei<5000]

> femeif=femeif[femeif>2000]

> var(femeif)

[1] 133887.4

> var.test(barbatif,femeif)

F test to compare two variances

data: barbatif and femeif

F = 0.7954, num df = 130, denom df = 124, p-value = 0.1976

alternative hypothesis: true ratio of variances is not equal to 1

95 percent confidence interval:

0.560346 1.127276

sample estimates:

ratio of variances

0.7953541

> t.test(barbatif,femeif)

Welch Two Sample t-test

data: barbatif and femeif

t = 4.5708, df = 247.604, p-value = 7.675e-06

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

112.9047 283.8845

sample estimates:

mean of x mean of y

3794.947 3596.552

> cor.test(set.data[,"greutate"],set.data[,"marime"])

Pearson's product-moment correlation

data: set.data[, "greutate"] and set.data[, "marime"]

t = 7.9442, df = 235, p-value = 8.082e-14

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

0.3534023 0.5550012

sample estimates:

cor

0.4601118

> cor.test(set.data[,"greutate"],set.data[,"marime"])

Pearson's product-moment correlation

data: set.data[, "greutate"] and set.data[, "marime"]

t = 7.9442, df = 235, p-value = 8.082e-14

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

0.3534023 0.5550012

sample estimates:

cor

0.4601118