STATISTICAL CONCEPT (PART 2)

MENGANALISIS DATAPER VARIABEL (UNIVARIATE)

Omega-Hat StatServAli Hasmy

(Director)

CENTRAL TENDENCY

MEASURES OF CENTRAL TENDENCY IN STATISTICAL ANALYSIS MOST KNOWN AS

“AVERAGES”

CENTRAL TENDENCY

AVERAGE TYPESMEANSMEDIANSMODES

AVERAGE TYPES

KIND OF MEANS Arithmetic Mean Weighted Mean Winsorized Mean Trimmed Mean Mid Mean Harmonic Mean Quadratic Mean Geometric mean

KIND OF MEANS

KIND OF MEDIANS Median (Q2) Midrange Midhinge Trimean Crude Median Refined Median

KIND OF MEDIAN

KIND OF MODES Mode Minor Mode Major Mode Crude Mode Refined Mode

KIND OF MODES

AVERAGES IN NATUREAVERAGES IN NATURE

CENTRAL TENDENCY MEASURES

MEANS MEDIANS MODES

LEVEL OF MEASUREMEN

T

NOMINAL √

ORDINAL √ √

INTERVAL √ √ √

RATIO √ √ √

AVERAGES IS THE

SPECIAL CASES FROM

MEASURES OF

LOCATION/ POSITION

ADDITIONAL KINDS OF LOCATION MEASURES

ARE QUARTILE (HINGE), DECILE,

PERCENTILE AND OTHER QUANTILES

KIND OF STATISTICSKIND OF STATISTICS

MEAN

MEDIAN

FREQUENCY/ RANK

PARAMETRIC STATISTICS based on

ROBUST STATISTICS based on

FREE DISTRIBUTION STATISTICS

based on

INTERVAL/ RATIO DATA

NOMINAL /ORDINAL

DATA

ORDINAL DATA

MENCANTUMKAN UKURAN PEMUSATAN DATA TANPA UKURAN VARIASINYA DAPAT DIKATEGORIKAN SEBAGAI “BERBOHONG SECARA STATISTIKA” !

VARIATIONS

MEASURES OF VARIATION IN

STATISTICAL ANALYSIS ALSO KNOWN AS

“DISPERSION MEASURES”

VARIATIONS

VARIATION TYPES BASED ON DEVIATION

MEASURES BASED ON RANGES

(SPREADS) BASED ON FREQUENCIES

VARIATION TYPES

DEVIATIONS Arithmetic Mean Deviation Arithmetic Mean Absolute Deviation

(another kind is: Median Absolute Deviation)

Variance (another kind is: Winsorized Variance & Biweight Midvariance)

Standard Deviation Coefficient of Relative Variation (CRV)

DEVIATIONS

RANGES

Range Interquartile Range (H-

Spread) Semi-interquartile Range

RANGES

BASED ON FREQUENCIES

Relative Frequency of Modal Value or Class

Index of Qualitative Variation (IQV)

BASED ON FREQUENCIES

VARIATIONS IN NATUREVARIATIONS IN NATURE

VARIATION MEASURES

DEVIATIONS

RANGESBASED

ON FREQ.

LEVEL OF MEASUREMEN

T

NOMINAL √

ORDINAL √ √

INTERVAL √ √ √

RATIO √ √ √

UNIVARIATE ANALYSISUNIVARIATE ANALYSIS

• Interval/Ratio Data• Random Sample• Symmetric

distribution

DESCRIPTIVE

• Interval/Ratio Data• Random Sample• Normal Distribution

INFERENCE

MEAN

- Point Est. (MEAN)

- Interval Est. (MEAN ± 2 SEM)

CI = 95%

TIDAK SELALUberarti bahwa

peluang nilai parameter akan berada dalam rentang tersebut sebesar 95%

juga

TERGANTUNG APAKAH MEAN DAPAT MEWAKILI MU ATAU TIDAK

Mean ± 2 SE

TIDAK SELALUberarti sama dengan

Confidence Interval 95%

Tergantung dari besarnya sampel

(seharusnya > 30)

UNIVARIATE ANALYSISUNIVARIATE ANALYSIS

• Ordinal/Interval/Ratio Data

• Random Sample• Free distribution

DESCRIPTIVE

• Ordinal/Interval Ratio Data

• Random Sample• Free Distribution

INFERENCE

MEDIAN

- M, W,AND SKIPPED ESTIMATORS

- R AND HODGES-LEHMANN ESTIMATOR

VARIABLE INVOLVES Categorical Variable Discrete Variable Nominal Variable Dichotomous/Binary Variable True Dichotomous Variable Artificial Dichotomous Variable Trichotomous Variable Polytomous Variable Ordinal Variable Numerical Variable Rank-Ordered Variable Continuous Variable Interval Variable Ratio Variable

TERIMA KASIHTERIMA KASIH