Statistical Analysis of Data
What is a Statistic???? What is a Statistic????
Population
Sample
SampleSample
Sample
Parameter: value that describes a population
Statistic: a value that describes a sample PSYCH always using samples!!!
Descriptive & Inferential Descriptive & Inferential StatisticsStatisticsDescriptive StatisticsDescriptive Statistics
• OrganizeOrganize
• SummarizeSummarize
• SimplifySimplify
• Presentation of dataPresentation of data
Inferential StatisticsInferential Statistics •Generalize from Generalize from samples to popssamples to pops•Hypothesis testingHypothesis testing•Relationships Relationships among variables among variables
Describing data Make predictionsMake predictions
Descriptive Descriptive StatisticsStatistics
3 Types
1. Frequency Distributions 3. Summary Stats
2. Graphical Representations
# of Ss that fallin a particular category
Describe data in just one number
Graphs & Tables
1. Frequency Distributions
# of Ss that fallin a particular category
How many males and how many females are in our class?
Frequency(%)
? ?
?/tot x 100 ?/tot x 100
-----% ------%
total
scale of measurement?
nominal
1. Frequency Distributions
# of Ss that fallin a particular category
Categorize on the basis of more that one variable at same timeCROSS-TABULATION
Democrats
Republican
total
24 1 25
19 6 25
Total 43 7 50
1. Frequency Distributions
How many brothers & sisters do you have?
# of bros & sis Frequency
7 ?6 ?5 ?4 ?3 ?2 ?1 ?0 ?
Histogram of the categorical variables
2. Graphical Representations
Polygon - Line Graph
2. Graphical Representations
Summary Statisticsdescribe data in just 2 numbers
Measures of central tendency• typical average score
Measures of dispersion• typical average variation
Measures of Central Tendency
• Quantitative data:– Mode – the most frequently occurring
observation– Median – the middle value in the data (50
50 ) – Mean – arithmetic average
• Qualitative data:– Mode – always appropriate– Mean – never appropriate
Mean
• The most common and most useful average
• Mean = sum of all observations number of all observations
• Observations can be added in any order.
• Sample vs population
• Sample mean = X
• Population mean =• Summation sign = • Sample size = n• Population size = N
Notation
Special Property of the MeanBalance Point
• The sum of all observations expressed as positive and negative deviations from the mean always equals zero!!!!– The mean is the single point of equilibrium
(balance) in a data set
• The mean is affected by all values in the data set– If you change a single value, the mean
changes.
Summary Statisticsdescribe data in just 2 numbers
Measures of central tendency• typical average score
Measures of dispersion• typical average variation 1. range: distance from the
lowest to the highest (use 2 data points)
2. Variance: (use all data points)3. Standard Deviation4. Standard Error of the Mean
Measures of Variability
2. Variance: (use all data points):
average of the distance that each score is from the mean (Squared deviation from the mean)
otation for variances2
3. Standard Deviation= SD= s2
4. Standard Error of the mean = SEM = SD/ n
