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