Common Statistical Tests Descriptive statistics (common in all types of

studies – first step in reporting findings) Continuous variables: T-test, ANOVA,

Pearson correlation, linear regression (e.g., pain VAS, age, cholesterol)

Categorical, Nominal: Chi-square test, relative risks, proportions, Mantel-Haentzel, Spearman correlation, logistic regression (e.g., gender, death, categorical scales)

*Most assume random sampling or random group assignment – frequently violated.

Descriptive Statistics Measures of central tendency

Mean, median, mode Measures of variability

Standard deviation, standard error, confidence intervals, range of scores

Frequency distribution How many people in each level of the variable

Proportions Proportion (%) of sample at each level Often also referred to as frequency distribution

Central Tendency Mean

mathematical average Used when distribution is normal

Median 50th percentile – ½ scores below, ½ above Used when distribution is skewed

Mode Score with the highest frequency Seldom reported

Measures of Variability Standard deviation

Variability of scores around mean in your sample (spread of scores in your sample)

E.g., mean of 100, S.D. 10 means that 68% of scores are between 90 and 110, 95% of scores are within 2 standard deviations of mean

Standard error Measure of the inaccuracy of the sample mean

compared to the true population mean Often used incorrectly in presentation of results

Standard error smaller than standard deviation - makes data look less variable

Measures of Variability Range of scores

Range of scores observed Confidence intervals

Range of values we are fairly confident will include the true value we are interested in

Mean=100, 95% CI 85-105 – if we measured that value on 100 samples, 95% of those values would fall within the confidence intervals

چرا آزمون آماری؟خطای ناشی از نمونه گیریمفهوم H0 (یا عدم ارتباط) فرض برابری >= چقدر نتایج بدست آمده ناشی از شانس است؟

P Value ردH0 = 0.05به غلط =< خطای نوع اول قبولH0 = 0.2به غلط =< خطای نوع دوم

Frequency Distribution

0

5

10

15

20

25

30

35

40

45

Responders

20-29 years30-39 years40-49 years50-59 years60-69 years

آزمون های آماری

پی بردن به اختالف:1.مقایسه میانگین فشار خون

مقایسه توزیع جنسی در رشته های مختلف

پی بردن به ارتباط:1.تعیین ارتباط نوع شخصیت و رشته تحصیلی

IHDتعیین ارتباط عفونت کالمیدیا با

آزمون آماری جهت مقایسه

متغیر کیفی(درصد) متغیر کمی(میانگین)

سه گروه یا بیشتردو گروه

Paire

d t te

st

Ind

ep

en

den

t t test

زوجی مستقل

AN

OV

A

Rep

eate

d m

easu

res

زوجی مستقل

سه گروه یا بیشتردو گروه

یجذور کا

م

McN

em

ar

Chi S

qu

re

Coch

ran

زوجیمستقلزوجیمستقل

Statistical Analysis Student’s T-Test

Measures differences between group means

Requires continuous data, assumes normal distribution in each group, random sampling

Considers variability within groups T-test for independent samples, t-test

for dependent samples

Statistical Analysis Analysis of Variance

Similar in concept to t-test Used when more than two groups

E.g., experimental group, placebo group, alternative medication group

Requires continuous variables, normal distribution in each group, random sampling

Statistical Analysis Chi-Square

Differences between proportions, discrete data

2 X 2 table Considers variability within groups

Mantel-Haentzel Extension of Chi-square Way of calculating adjusted odds ratios for

stratified data

Chi Square

Depressed

NotDepresse

d

Total

Smoker 89 (33%)a

179 (67%)

b

268a + b

Non-smoker

131 (17%)

c

647 (83%)

d

778c + d

Total 220a + c

826b + d

1046T (total)

Chi Square

Depressed

NotDepressed

Total

Smoker a b a + b

Non-smoker

c d c + d

Total a + c b + d T = a + b + c + d

آزمون های آماری جهت پی بردن به ارتباط

Correlation Regression

Correlation Coefficients Possible values from –1 to +1 -1 = perfect negative correlation

As exposure increases, disease (health condition) decreases

0 = no relationship or no linear relationship

+1 = perfect positive correlation As exposure increases, disease

increases

Other Statistics Logistic Regression

Odds ratios (cohort, case-control, cross-sectional studies)

Odds that an exposed person develops the disease: odds than a non-exposed person develops the disease

Crude OR (just taking exposure and outcome into consideration)

Adjusted OR (odds taking all other factors/confounders into consideration)

Other Statistics Linear regression

When outcome is continuous A kind of correlation Can adjust for other factors/confounders in

the model Cox Proportional Hazards

When outcome is time to an event Time to death, recovery, onset of

symptoms Regression model