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 50 th 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 – 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 گیری مفهوم H 0 => فرض برابری (یا عدم ارتباط) چقدر نتایج بدست آمده ناشی از شانس است؟ P Value رد H 0 به غلط => خطای نوع اول = 0.05 قبول H 0 به غلط => خطای نوع دوم = 0.2

Frequency Distribution

آزمون های آماری 1. پی بردن به اختلاف: مقایسه میانگین فشار خون مقایسه توزیع جنسی در رشته های مختلف 1. پی بردن به ارتباط: تعیین ارتباط نوع شخصیت و رشته تحصیلی تعیین ارتباط عفونت کلامیدیا با IHD

آزمون آماری جهت مقایسه متغیر کیفی(درصد) متغیر کمی(میانگین) دو گروهسه گروه یا بیشتر Paired t test Independent t test زوجیمستقل ANOVA Repeated measures زوجیمستقل دو گروهسه گروه یا بیشتر مجذور کای McNemar Chi Squre Cochran مستقلزوجیمستقلزوجی

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 DepressedNot Depressed Total Smoker89 (33%) a 179 (67%) b 268 a + b Non- smoker 131 (17%) c 647 (83%) d 778 c + d Total220 a + c 826 b + d 1046 T (total)

Chi Square DepressedNot Depressed Total Smokeraba + b Non- smoker cdc + d Totala + cb + dT = a + b + c + d

آزمون های آماری جهت پی بردن به ارتباط Correlation Regression

Correlation Coefficients Possible values from –1 to = 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