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