Transcript What is Meant by Statistics?

Statistical analysis
Prepared and gathered by
Alireza Yousefy(Ph.D)
What is Meant by Statistics?
Statistics is the science of
collecting, organizing, presenting,
analyzing, and interpreting
numerical data to assist in making
more effective decisions
Types of Statistics
Descriptive Statistics: Methods of
organizing, summarizing, and
presenting data in an informative
way.
Types of Statistics
Inferential Statistics: A
decision, estimate, prediction,
or generalization about a
population, based on a
sample.
Scales of measurement
•
•
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Nominal
Ordinal
Interval
Ratio
Nominal scale
• Numbers represent labels, identify
categories
• Not really a scale at all
• Example: number codes for religious
affiliation: 1=protestant, 2=catholic,
3=Islamic etc.
Levels of Measurement
Nominal scale
• Nominal measurement consists of assigning
items to groups or categories.
• No quantitative information is conveyed and no
ordering of the items is implied.
• Nominal scales are therefore qualitative rather
than quantitative.
• Examples: Religious preference, race, and
gender are all examples of nominal scales
• Statistics: Sum, Frequency Distributions
Ordinal scale
• On a continuum
• Numbers only tell you the order in which
observations fall -- ranks
• Know nothing about the size of the
interval between numbers
• Examples: class rank, rank on a “best
movies” scale
Ordinal Scale
• Measurements with ordinal scales are ordered:
higher numbers represent higher values.
• However, the intervals between the numbers are
not necessarily equal.
• There is no "true" zero point for ordinal scales
since the zero point is chosen arbitrarily.
• For example, on a five-point Likert scale, the difference
between 2 and 3 may not represent the same difference
as the difference between 4 and 5.
• Also, lowest point was arbitrarily chosen to be 1. It could
just as well have been 0 or -5.
Interval scales
• Continuous scale in which equal
intervals between values represent
equivalent “amounts”
• However, ratios of values are not valid
and there is no true zero point
• Many scales in psychology are treated as
interval scales
• Examples of interval scales: IQ number,
Exam number …
Ratio scales
• All the properties of interval scales
• In addition, ratios make sense, e.g., 2 Kg is
twice the weight of 1Kg
• True zero point, e.g., zero weight, zero
money
• Tend to be concrete, tangible things, e.g.,
number of events, money, weight
Interval & Ratio Scales
• On interval measurement scales, one unit on the
scale represents the same magnitude on the trait
or characteristic being measure across the whole
range of the scale.
• For example, on an interval/ratio scale of
anxiety, a difference between 10 and 11 would
represent the same difference in anxiety as
between 50 and 51.
Assumption: 90% of analyses will use
following procedures
1) Cross tab with 2
2) t-test -- actually optional, since
ANOVA can accomplish same things,
but useful to know about
3) Analysis of Variance (ANOVA)
4) Simple Correlation/Regression
5) Multiple Regression
Some additional analyses could be useful:
we could learn them depending on time
• 2 Goodness of Fit Tests
• Spearman correlation
• Factor analysis/principal component
analysis
• Nonparametric analogues of common
parametric tests
Steps in planning analysis
1) Examine your data
– Exploratory data analysis
2) Choose analysis based on characteristics
of the data and your research questions -see following slides
Questions to answer to plan your
analysis
1) Type of data: Categorical or
measurement?
2) Type of research question: Focus on
differences or relationship
3) # of Groups or Variables
4) Independence (if relevant): Are your
measurements independent or dependent?
Are frequency of each levels of
One categorical variable fit
With expected frequency?
Type of
question
Qualitative
categorical
Goodness of fit2
Contingency table 2
Are two categorical
Variables relevant?
Pearson
correlation
continuous
1
measurement
rank
Type of data
Number of
prediction
Relationship
2or more
Quantitative
measurement
Spearman R
Type of
question
Multiple
regression
IndependentT
Mann Whitney U
I-Dep
2
Paired T
willcoxon
Difference
Number of
groups
1 way Anova
1
I-DEP
Number of
Ind variables
Repeated
Measures
More than 2
DEP
Friedman
Kruskal-Wallis
2 or more
Factorial
Anova
A STATISTICALLY SIGNIFICANT DIFFERENCE MEANS1
1. large -- NO, not necessarily. Even a small mean difference between
two groups could be statistically significant if the sample size is large
enough.
2. of practical significance -- NO. Statistical significance has to
do with mathematical probability. It has nothing to do with whether a
research result is meaningful or useful.
3. not likely to be due to sampling error -- YES. What you are
saying is that the difference is larger than the expected amount of
sampling error.
4. likely to be due to the treatment -- YES. There are two main
reasons for differences between "equivalent groups" -- one is sampling
error and the other is the treatment that was received by one group but
not the other. In this case, the difference is larger than what we would
expect from sampling error.
A STATISTICALLY SIGNIFICANT
DIFFERENCE MEANS-2
5. generalizable -- YES. Probability says that the difference
should be replicable in another sample taken from the same
population.
6. true -- If true means correct, absolute, 100%, then NO. We
cannot be absolutely certain that a difference exists in the
population - ever. A statistically significant difference simply
means that probability is on our side, based on evidence taken
from a sample.
7. too large to have occurred by chance -- YES
.
"Chance" refers to sampling error.
We can estimate the level of chance and see (after the
treatment) if the difference is even larger than that. If it is, then
we attribute the difference to the effects of the treatment.