Outline: •DESCRIPTIVE STATISTICS •INTRODUCTION TO SPSS Descriptive statistics: example Patient ID Gender (1=Male, Age (years) Smoking status (1=none, DBP (diastolic 2=Female) 2=light, 3=heavy) Blood Pressure) 11 581 47 21 381 61 32 591 42 42 511 75 5 2 45 2 103 62 452 91 71 351 76 81 521 84 91 363 99 10 1 51 3 104 11 1 42 3 69 12 1 41 3 97 13 1 42 1 59 14 1 46 2 69 Organizing & Summarizing data Categorical variable Continuous variable Tables Graphs Measures of Measures of Central tendency Dispersion Numbers Histogram Mean Range Percentages Frequency Mode Variance polygon Median Standard deviation Organizing & Summarizing data Categorical variable Continuous variable Tables Graphs Measures of Measures of Central tendency Dispersion Numbers Histogram Mean Range Percentages Frequency Mode Variance polygon Median Standard deviation Tables Number (N) Percentage (%) Gender Males 30 30% Females 70 70% Marital Status Single 90 90% Married 5 5% Other 5 5% Organizing & Summarizing data Categorical variable Continuous variable Tables Graphs Measures of Measures of Central tendency Dispersion Numbers Histogram Mean Range Percentages Frequency Mode Variance polygon Median Standard deviation Histogram 1= Illiterate 2= Elementary 3= Secondary 4= University Frequency Polygon Organizing & Summarizing data Categorical variable Continuous variable Tables Graphs Measures of Measures of Central tendency Dispersion Numbers Histogram Mean Range Percentages Frequency Mode Variance polygon Median Standard deviation Mean Population (μ) ∑ xi Sample mean = x = n Properties of means: Uniqueness Simplicity Affected by extreme value Median The values which divide the set into 2 equal parts If n= odd: Median= middle value If n= even: Median= mean of middle 2 values Properties of medians: Uniqueness Simplicity Not affected by extreme values Mode Most frequently occurring value. Properties of medians: Not unique Simplicity Not affected by extreme values Organizing & Summarizing data Categorical variable Continuous variable Tables Graphs Measures of Measures of Central tendency Dispersion Numbers Histogram Mean Range Percentages Frequency Mode Variance polygon Median Standard deviation Range Difference between highest and lowest value. Range = Xh – Xl Variance Measures the dispersion relative to the scatter of the values around their mean. (x − x)2 Variance = ∑ i n −1 Standard deviation SD= square root of variance. (x − x)2 SD= ∑ i n −1 Measures of Dispersion: Example Set 1: 21 22 23 23 23 24 24 25 28 Mean = 213/9 = 23.6 Median = 23 SD= 2.0 Range= 7 Set 2: 15 18 21 21 23 25 25 32 33 Mean = 213/9 = 23.6 Median = 23 SD= 5.9 Range= 18 Normal/ Gaussian Distribution Normal/ Gaussian Distribution Properties of a Normal Distribution: A continuous, Bell shaped, symmetrical Distribution; Both tails extend to infinity. The mean, median, and mode are identical The shape is completely determined by the mean (μ,x) and standard deviation (σ,SD). Normal/ Gaussian Distribution Mean Mode Median Normal/ Gaussian Distribution Properties of a Normal Distribution (Cont’d): A normal distribution can have any μ and any σ: e.g.: μ=3 , σ = 2.62 The area under the curve represents 100% of all the observations. In any normal distribution: 68% of the observations fall within 1σ of the mean μ 95% of the observations fall within 2σ of the mean μ 99.7% of the observations fall within 3σ of the mean μ Normal distribution 2 SD 2 SD 1 SD 1 SD 3 SD 3 SD Normal Distribution Figure 1 Figure 2 Which distribution has a larger standard deviation? Which distribution has a larger variance? Normal Distribution T (True) or F (False): In any normal distribution, 95% of the observations fall within 2 standard deviations of the mean Normal Distribution T (True) or F (False): The Gaussian distribution is a bell shaped and has a symmetrical distribution Normal Distribution T (True) or F (False): In a normal distribution, the mean, median, and mode are identical Introduction to SPSS Create a database Analyze / Descriptive statistics Frequencies Descriptive Crosstabs Data / Select cases.