Descriptive and Inferential Statistics - intro

Helpful in understanding the basics.
Credit - Multiple sources.

1. Descriptive & Inferential Descriptive & Inferential
StatisticsStatistics
Descriptive 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

2. Descriptive Descriptive
StatisticsStatistics
3 Types
1. Frequency Distributions 3. Summary Stats
2. Graphical Representations
# of Ss that fall
in a particular category
Describe data in just one
number
Graphs & Tables

3. Altman, D. G et al. BMJ 1995;310:298
Central Limit Theorem: the larger the sample size, the closer a
distribution
will approximate the normal distribution or
A distribution of scores taken at random from any distribution will tend
to
form a normal curve
jagged
smooth

4. 2.5% 2.5%
5% region of rejection of null hypothesis
Non directional
Two Tail
body temperature, shoe sizes, diameters of trees,
Wt, height etc…
IQ
68%
95%
13.5%
13.5%
Normal Distribution:
half the scores above
mean…half below
(symmetrical)

6. Summary Statistics
describe data in just 2 numbers
Measures of central tendency
• typical average score
Measures of variability
• typical average variation

7. 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

8. 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


9. Special Property of the Mean
Balance 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.

10. Summary Statistics
describe data in just 2 numbers
Measures of central tendency
• typical average score
Measures of variability
• typical average variation
1.range: distance from the
lowest to the highest (use 2
data points)
2. Variance: (use all data points)
3. Standard Deviation
4. Standard Error of the Mean

11. 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 variance
s
2
3. Standard Deviation= SD= s
2
4. Standard Error of the mean = SEM = SD/ n

12. Inferential Statistics
Population
Sample
Draw inferences about the
larger group
Sample
Sample
Sample

13. Sampling Error: variability among
samples due to chance vs population
Or true differences? Are just due to
sampling error?
Probability…..
Error…misleading…not a mistake

14. Probability
•Numerical indication of how likely it is that a
given event will occur (General
Definition)“hum…what’s the probability it will rain?”
•Statistical probability:
the odds that what we observed in the sample did
not occur because of error (random and/or
systematic)“hum…what’s the probability that my results
are not just due to chance”
•In other words, the probability associated with
a statistic is the level of confidence we have that
the sample group that we measured actually
represents the total population

15. Chain of Reasoning for
Inferential Statistics
Population
Sample
Inference
Selection
Measure
Probability
data
Are our inferences valid?…Best we can do is to calculate probability
about inferences

16. Inferential Statistics: uses sample data
to evaluate the credibility of a hypothesis
about a population
NULL Hypothesis:
NULL (nullus - latin): “not any”  no
differences between means
H
0
: 
1
= 
2
“H- Naught”
Always testing the null hypothesis

17. Inferential statistics: uses sample data to
evaluate the credibility of a hypothesis
about a population
Hypothesis: Scientific or alternative
hypothesis
Predicts that there are differences
between the groups
H
1 : 
1 = 
2

18. Hypothesis
A statement about what findings are expected
null hypothesis
"the two groups will not differ“
alternative hypothesis
"group A will do better than group B"
"group A and B will not perform the same"

19. Inferential Statistics
When making comparisons
btw 2 sample means there are 2
possibilities
Null hypothesis is true
Null hypothesis is false
Not reject the Null Hypothesis
Reject the Null hypothesis

20. Hypothesis Testing -Decision
Decision Right or Wrong?
But we can know the probability of being right
or wrong
Can specify and control the probability of
making TYPE I of TYPE II Error
Try to keep it small…

21. 2.5% 2.5%
5% region of rejection of null hypothesis
Non directional
Two Tail

22. 5%
5% region of rejection of null hypothesis
Directional
One Tail

23. Error in Testing

24. Take medical testing—a type 1 error (false positive) in this
field
 might lead to unnecessary treatment, while a type 2 error
(false negative) could result in a missed diagnosis.

25. Reducing Errors
•Increase Sample Size
•Use Multiple Tests
•Continuously monitor and feedback
•Conduct root cause analysis

26. Inferential statistics
Used for Testing for Mean Differences
T-test: when experiments include only 2 groups
a.Independent
b. Correlated
i. Within-subjects
ii. Matched
Based on the t statistic (critical values) based on
df & alpha level

27. Inferential statistics
Used for Testing for Mean Differences
Analysis of Variance (ANOVA): used when
comparing more than 2 groups
1. Between Subjects
2. Within Subjects – repeated measures
Based on the f statistic (critical values) based on
df & alpha level
More than one IV = factorial (iv=factors)
Only one IV=one-way anova

28. Inferential statistics
Meta-Analysis:
Allows for statistical averaging of results
From independent studies of the same
phenomenon