ANALISIS DATA EXPLORASI MINGGU KE 2 BOX PLOT dan STEAM LEAF

ANALISIS DATA EXPLORASI MINGGU KE 3

UJI GOODNESS UNTUK DISTRIBUSI NORMAL2PENILAIAN ATAS DISTRIBUSI NORMAL DAN TRANFRMASI DATABanyak metode/analisis statistika dalam penggunaannya mengharuskan persyaratan bahwa variabel/ data yang dipakai memiliki distribusi (normal, poisson, dll).Misalnya, penggunaan t-tes, F-tes, dan analisis regresi.

Standardized normal distribution with empirical rule percentages.3PENILAIAN DISTRIBUSI NORMALMetode eksplorasi data: Histogram and BoxplotNormal Quantile Plot (juga disebut dengan Normal Probability Plot)

Goodness of Fit Tests, seperti Anderson-Darling Test (MINITAB)Kolmogorov-Smirnov Test (SPSS)Lillefors Test Shapiro-Wilk TestPermasalahan : tidak semuanya sama/ sesuai4MENGUJI DISTRIBUSI NORMALPengujian dengan statistika deskriptif secara konfensional : histogram dengsn kurva normal, normal scores plot (normal probability plot).

Jika data "normal, maka sumbu non-linear vertikal di plot probabilitas harus menghasilkan pendekatan suatu plot pencar yang linier mewakili data mentah.

5MENGUJI DISTRIBUSI NORMAL

6MENGUJI DISTRIBUSI NORMAL Bila data diplot vs diharapkan z-skor plot probabilitas normal menunjukkan skewness kanan oleh kurva lentur ke bawah.

Bila data diplot vs diharapkan z-skor plot probabilitas normal menunjukkan skewness kiri oleh kurva lentur atas.

7MENGUJI DISTRIBUSI NORMAL

8Assessing Normality and Data Transformations

Histograms and BoxplotsKurva merah merupakan distribusi yang sesuai ( fit) data distribusi normal, dan kurva biru estimasi fungsi densitas, kurva ini berdistribusi normal jika data terdistribusi secara normal

Histograms and BoxplotsKurva merah merupakan distribusi fit normal data dan biru adalah perkiraan kepadatan dari data yang tidak setuju

Outliers are not consistent with normality.Normal Quantile Plot

THE IDEAL PLOT:Here is an example where the data is perfectly normal. The plot on right is a normal quantile plot with the data on the vertical axis and the expected z-scores if our data was normal on the horizontal axis. When our data is approximately normal the spacing of the two will agree resulting in a plot with observations lying on the reference line in the normal quantile plot. The points should lie within the dashed lines.Normal Quantile Plot

THE IDEAL PLOT:Here is an example where the data is perfectly normal. The plot on right is a normal quantile plot with the data on the vertical axis and the expected z-scores if our data was normal on the horizontal axis. When our data is approximately normal the spacing of the two will agree resulting in a plot with observations lying on the reference line in the normal quantile plot. The points should lie within the dashed lines.Normal Quantile Plot (right skewness)The systolic volumes of the male heart patients are clearly right skewed.

When the data is plotted vs. the expected z-scores the normal quantile plot shows right skewness by a upward bending curve.

Normal Quantile Plot(left skewness)The distribution of birthweights from this study of very low birthweight infants is skewed left. When the data is plotted vs. the expected z-scores the normal quantile plot shows left skewness by a downward bending curve.

Normal Quantile Plot(leptokurtosis)

Tests of NormalityThere are several different tests that can be used to test the following hypotheses:Ho: The distribution is normalHA: The distribution is NOT normalCommon tests of normality include:Shapiro-WilkKolmogorov-SmirnovAnderson-DarlingLilleforsProblem: THEY DONT ALWAYS AGREE!!Tests of NormalityHo: The distribution of systolic volume is normalHA: The distribution of systolic volume is NOT normal

Because p < .0001 we have strong evidence against normality for the systolic volume population distribution using the Shapiro-Wilk test.Tests of NormalityHo: The distribution of systolic volume is normalHA: The distribution of systolic volume is NOT normal

We do not have evidence at the a = .05 level against the normality of the population systolic volume distribution when using the Kolmogorov-Smirnov test from SPSS.Tests of NormalityHo: The distribution of cholesterol level is normalHA: The distribution of cholesterol level is NOT normal

We have no evidence against the normality of the population distribution of cholesterol levels for male heart patients (p = .2184).