Omega-Hat StatServ Ali Hasmy (Director) MEASURES OF CENTRAL TENDENCY IN STATISTICAL ANALYSIS MOST...
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Transcript of Omega-Hat StatServ Ali Hasmy (Director) MEASURES OF CENTRAL TENDENCY IN STATISTICAL ANALYSIS MOST...
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
KIND OF MEANS Arithmetic Mean Weighted Mean Winsorized Mean Trimmed Mean Mid Mean Harmonic Mean Quadratic Mean Geometric mean
KIND OF MEANS
AVERAGES IN NATUREAVERAGES IN NATURE
CENTRAL TENDENCY MEASURES
MEANS MEDIANS MODES
LEVEL OF MEASUREMEN
T
NOMINAL √
ORDINAL √ √
INTERVAL √ √ √
RATIO √ √ √
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
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