Normality tests P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S - - PowerPoint PPT Presentation

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Normality tests P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S - - PowerPoint PPT Presentation

Oct 05, 2022 561 likes •1.46k views

Normality tests P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R Zuzanna Chmielewska Actuary PRACTICING STATISTICS INTERVIEW QUESTIONS IN R Testing normality Statistical tests Shapiro-Wilk test Kolmogorov-Smirnov test Visual

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Normality tests

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

Zuzanna Chmielewska

Actuary

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Testing normality

Statistical tests Shapiro-Wilk test Kolmogorov-Smirnov test Visual measure Q-Q plot

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Shapiro-Wilk test

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Shapiro-Wilk test

Razali, Nornadiah; Wah, Yap Bee (2011). "Power comparisons of Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Anderson–Darling tests"

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

P-value

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Shapiro-Wilk test

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Kolmogorov-Smirnov test

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Kolmogorov-Smirnov test

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Kolmogorov-Smirnov test

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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Transforming data for normality

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Transforming data for normality

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Checking normality in R

Method Function Shapiro-Wilk test

shapiro.test(x)

Kolmogorov-Smirnov test

ks.test(x, y = "pnorm")

Q-Q plot

qqnorm(x); qqline(x)

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Summary

normality tests Shapiro-Wilk test Kolmogorov-Smirnov test p-value Q-Q plot data transformation checking normality in R

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Let's practice!

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

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Inference for a mean

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

Zuzanna Chmielewska

Actuary

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Inference for a mean

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Inference for a mean

condence interval

  • ne-sample mean
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Assumptions

The t-test's assumptions: normally distributed underlying data (recall CLT!) random sample independent observations

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Condence interval

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Condence interval

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Condence interval

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Condence interval

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95% condence interval

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

95% condence interval

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

95% condence interval

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

95% condence interval

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One-sample t-test

H : μ = μ H : μ ≠ μ

where:

μ - the population's mean μ - the hypothesized mean

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t-test in R

t.test(x)

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

t-test in R

t.test(x)

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t-test in R

t.test(x)

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t-test in R

t.test(x, mu = 2)

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t-test in R

t.test(x, mu = 2, conf.level = 0.9)

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Summary

t-test's assumptions condence interval

  • ne-sample t-test

t.test() in R

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Let's practice!

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

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Comparing two means

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

Zuzanna Chmielewska

Actuary

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Comparing two means

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Hypotheses

Two-tailed test:

H : μ = μ H : μ ≠ μ

where:

μ - the rst population's mean μ - the second population's mean

1 2 1 1 2 1 2

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Assumptions

The two-sample t-test's assumptions: normally distributed underlying data random samples independent observations homogeneity of variances

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Assumptions

The two-sample t-test's assumptions: normally distributed underlying data random sample independent observations homogeneity of variances - e.g. bartlett.test()

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Teaching methods

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Teaching methods

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Teaching methods

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Teaching methods

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Teaching methods

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Teaching methods

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Teaching methods

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Teaching methods

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Teaching methods

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Teaching methods

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

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t-test in R

Two-sample t-test

t.test(value ~ group, data = df, var.equal = TRUE)

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t-test in R

Two-sample t-test

t.test(value ~ group, data = df, var.equal = TRUE)

Paired t-test

t.test(value ~ group, data = df, paired = TRUE)

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Summary

two-sample t-test hypotheses assumptions paired t-test

t.test() in R

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Let's practice!

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

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ANOVA

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R

Zuzanna Chmielewska

Actuary

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Hypotheses

H : μ = μ = ... = μ H : ∃ μ ≠ μ

1 2 n 1 (i,j) i j

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Hypotheses

H : μ = μ = μ

1 2 3

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Hypotheses

Two-sample t-test:

H : μ = μ

1 2

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Hypotheses

H : μ = μ = ... = μ

1 2 n

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Why not multiple t-tests?

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Why not multiple t-tests?

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Why not multiple t-tests?

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Why not multiple t-tests?

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Why not multiple t-tests?

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Assumptions

independence of cases normal distributions homogeneity of variances

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ANOVA in R

  • neway.test(value ~ group, data, var.equal = TRUE)
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Box plot

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Box plot

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Box plot

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Box plot

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Box plot

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PRACTICING STATISTICS INTERVIEW QUESTIONS IN R

Box plot

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Box plot

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Summary

hypotheses of ANOVA type I and II errors assumptions of ANOVA

  • neway.test() in R

box plot

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Let's practice!

P RACTICIN G S TATIS TICS IN TERVIEW QUES TION S IN R