statistical analysis of data. what is a statistic???? population sample parameter: value that...
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Statistical Analysis of Data
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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!!!
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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
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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
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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
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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
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1. Frequency Distributions
How many brothers & sisters do you have?
# of bros & sis Frequency
7 ?6 ?5 ?4 ?3 ?2 ?1 ?0 ?
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Histogram of the categorical variables
2. Graphical Representations
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Polygon - Line Graph
2. Graphical Representations
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Summary Statisticsdescribe data in just 2 numbers
Measures of central tendency• typical average score
Measures of dispersion• typical average variation
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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
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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
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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.
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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
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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