ABNORMALITYPutri Eyanoer, MD.,Ms.Epi,Ph.D.

NUMERICAL NFORMATION ALLOWS BETTER CONFIRMATION

QUANTITATIVE

PREDICTION EXACT PROBABILITIES

Symptomatic coronary diseaseoccur in 1 in 100 middle aged menper year Cigarettes smoking doubles onesrisk of dying at all ages Extrogenos estrogens reduce therisk of fractures from osteoporosisby half

SCALE CHARACTERISTIC EXAMPLES

CATEGORICAL

Nominal Occur in categories without any inherent order

Race, religion, occupation

Ordinal Posses some inherent ordering/rank

Level of education, salary

NUMERICAL

Interval Posses inherent ordering and the interval between successive values is equal

Temperature

Ratio Similar to that of interval BUT with existing absolute zero

Height, weight, age

VALIDITYRE

LIA

BILI

TYHIGH

HIGH

LOW

LOW

FREQ

UEN

CY

MEASUREMENT

VALIDITY the degree to which the data measure what they

were intended to measure the result of a measurement correspond to the true

state accuracy

RELIABILITY Reliability=the extent that repeated measurement of

a stable phenomenon by different people and instrument, at different time/place get similar results

VARIATIONS

MEASUREMENT

INSTRUMENT

OBSERVER

BIOLOGIC

WITHIN INDIVIDUALS

AMONG INDIVIDUALS

-50 40 30 20 10 0 10 20 30 40 50+

Monitored fetal heart rate 130-150

Monitored fetal heart rate < 130

Monitored fetal heart rate >150

UNDERESTIMATE OVERESTIMATE

Num

ber o

f Obs

erva

tions

400 -

300 -

200 -

100 -

0 -NOON 6 PM MIDNIGHT 6 AM

DAY 1

DAY 2

DAY 3

SOURCE OF VARIATIONS

CONDITION OF MEASUREMENTS DISTRIBUTIONS

MEASURE MENTS

1 patients, 1 observer, repeated observation at one point in time

1 patient, many observers, at one time

BIOLOGICand MEASURE MENT

1 patient, 1 observer at many times of the day

Many patients

DIASTOLIC BP (mmHg)

BLINDED :SINGLEDOUBLE TRIPLE

CALIBERATED INSTRUMENTS

ASSOCIATED WITH DISEASE

TREATABLE

ASSESING NORMALITY

Based in statistical theory and has no necessary relationship to natural distribution

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+s +2s +3s -s +2s+3s

68%95%99%

KURTOSIS

SKEWNESS

freq

uenc

y

70 100 130IQ Scores

Average IQ in the population is 100pts. The further from 100

you look, the fewer people you find

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Based in statistical theory and has no necessary relationship to natural distribution

Many statistical methods require that the numeric variables we are working with have an approximate normal distribution.

For example, t-tests, F-tests, and regression analyses all require in some sense that the numeric variables are approximately normally distributed.

Standardized normal distribution with empirical rule percentages.

Histogram and Boxplot Normal Quantile Plot

(also called Normal Probability Plot) Goodness of Fit Tests

Shapiro-Wilk Test (JMP)Kolmogorov-Smirnov Test (SPSS) Anderson-Darling Test (MINITAB)

The cholesterol levels of the patients appear to be approximately normal, although there is some evidence of right skewnessas the mean is larger than the median.

The red curve represents a normal distribution fit to these data and the bluecurve the density estimate for these data, these curves should agree if our data is normally distributed.

The systolic volumes of the male heart patients in this study suggest that they come from a right skewedpopulation distribution.

The red curve represents a normal distribution fit to these data and the blue is the estimated density from the data which does not agree with the imposed normal.

Outliers are not consistent with normality.

Ho: The distribution of systolic volume is normal

HA: The distribution of systolic volume

is NOT normalBecause p < .0001 we have strong evidence against normality for the systolic volume population distribution using the Shapiro-Wilk test.

Ho: The distribution of systolic volume is normal

HA: The distribution of systolic volume is NOT normal

We do not have evidence at the = .05 level against the normality of the population systolic volume distribution when using the Kolmogorov-Smirnov test from SPSS.

Ho: The distribution of cholesterol level is normal

HA: 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).

ABNORMALITYSlide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12ASSESING NORMALITY Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22