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Introduction
Creating New Knowledge
Scientific Cycle
Observe world
Scientific Cycle
Observe world
Isolate problem
Scientific Cycle
Observe world
Isolate problem
Propose theory
Scientific Cycle
Observe world
Isolate problem
Propose theory
Design study
Scientific Cycle
Observe world
Scientific Cycle
Isolate problem
Propose theory
Design study
Make predictions
Observe world
Scientific Cycle
Isolate problem
Propose theory
Design study
Collect data
Make predictions
Observe world
Scientific Cycle
Isolate problem
Propose theory
Design study
Collect data
Make predictions
Compare
Scientific Cycle
Observe world
Isolate problem
Propose theory
Design study
Make predictions
Compare
Collect data
Presentation
Scientific Cycle
Observe world
Isolate problem
Refine – revise/replace
Propose theory
Design study
Make predictions
Compare
Collect data
Presentation
Scientific Cycle
Observe world
Expand/restrict/modify scope
Isolate problem
Refine – revise/replace
Propose theory
Design study
Make predictions
Compare
Collect data
Presentation
Scientific Cycle
Observe world
Expand/restrict/modify scope
Isolate problem
Refine – revise/replace
Propose theory
Design study
Make predictions
Compare
Collect data
Presentation
Design
Experiments, surveys, interventions, observational studies
Data
Descriptive:
Tables, graphs
Inference:
Probabilistic models and inference
theory to draw conclusion such as
• Tests of theories/hypotheses
• Prediction of unobserved events
• Decisions
Design
Experiments, surveys, interventions, observational studies
Data
Descriptive:
Tables, graphs
Inference:
Probabilistic models and inference
theory to draw conclusion such as
• Tests of theories/hypotheses
• Prediction of unobserved events
• Decisions
Design
How to optimally collect the data in
order to later perform inference
Data
Descriptive:
Tables, graphs
Inference:
How to optimally use the data to
answer the question of interest
Design
How to optimally collect the data in
order to later perform inference
Data
Descriptive:
Tables, graphs
Inference:
How to optimally use the data to
answer the question of interest
Note! A poorly designed study
cannot be rescued by statisticians
Population
Sample survey
population
Data,
observations
Inferential statistics =
Draw conclusions about the
population from the sample survey.
Writing a science report.
Statistical perspective!
• Formulate a research problem.
• Define the population and plan a sample
survey.
• Find relevant variables to measure.
• Make descriptive statistics.
• Make inferential statistics.
• Write report.
Define the population and perform a
sample survey.
• Population: A group of individuals which we want
to investigate.
• Total survey: All the units in a population are
investigated.
• Sample survey: A subsample of the populations is
chosen and investigated.
• Random sampling: The sample units are chosen
by some random mechanism.
Where it can go wrong!
• A study is carried out to understand the
training habits of students at Umeå
university.
• The researcher hands out questionnaires at
the entrance of Iksu.
• Result: Students at Umeå University train a
lot more than expected.
• Where did it go wrong?
Where it can go wrong!
• A study is carried out to find out if students
at Umeå University prefer the campus pups
more than the inner city pubs.
• The researcher hands out questionnaires to
random persons in the queue at a campus
pub.
• Result: A majority of the students prefer
campus pubs.
• Where did it go wrong?
Why a sample survey rather than a
total survey?
Why a sample survey rather than a total survey?
• Cheaper
• Faster
• Cannot be used when the population is very big
or infinitely large
• Trials where the objects are used or destroyed
Why make a random sample?
• If the sample is random it is possible to use
probability theory to control the error that is arising
from the fact that we just study a sample and not
the entire population. This is impossible is the
sample is not random. Make a random sample.
• Give objective measures of the precision of the
results of the survey.
• Make objective comparisons between different
sampling plans prior to the survey.
• Calculate how large samples you need in order to
achieve a certain margin of error.
Find relevant variables to measure.
Variable: Property connected with the units in a
population.
Measurement: An allocation of numbers to the
subjects in a survey such that specific
relationships between the subjects, in
consideration to some specific property, can
be seen in the numbers.
Why do we measure?
• To describe, To compare, To evaluate.
Examples of things we want to measure:
• Length
• Stress
• Welfare
• Consumer satisfaction.
Data levels
Data levels are important because different level
of the data means different methods of
analyzing the data.
• Nominal Data
– Classification,
• Ordinal Data
– Classification and Order
• Interval Data
– Classification, Order, and Equivalent distance
• Ratio Data
– Classification, Order, Equivalent distance, and
Absolute zero
Which type of variable?
(Help me!)
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Age
Age group 25-34, 35-44, 45-54,...
Sex (male/female)
Education (primary, secondary, university)
Smoker (yes/no)
BMI (23.45, 28.12,…)
Car model (Volvo, Saab, Fiat)
Temperature (12C, -4C, 14C,…)
Descriptive statistics
• Measures of location
– mean
– median
• Measure of spread
–
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–
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range (min-max)
variance
standard deviation, SD
standard error of the mean, SEM
percentiles/quantiles (p25, p75, q1, q3,...)
• Frequency tables
• Graphs
– barchart/histogram
– boxplot
– scatterplot
Center and spread
Answering a research questions
is often to compare measures.
Workload and exam result
investigation.
Is there a difference in the study results
between males and females?
If so, what does the difference depend on?
A sample of graphs and plots.
Exam results (scale)
Workload (scale)
Histogram of Exam Score (scale)
Bar chart Grades (ordinal/ nominal)
Pie Chart of Grade
(ordinal/ nominal)
Boxplot of Exam Score, gender
(scale vs nominal)
Bar chart of Grade , gender
(nominal vs nominal)
Boxplot of Total Study Time, gender
(scale vs nominal)
Scatter plot (scale vs scale)
Is there a relation?
Inferential statistics
Is there a difference in how well females and
males perform on the exam if we take the
time the students study time into account?
Inferential statistics is a collection of
methods used to draw conclusions or
inference about the characteristics of
populations based on sample data.
• (Conclusion after analysis, no gender difference.)
Inferential statistics (The idea)
Hypothesis testing
In research we want to get answers to posed questions
(hypothesis).
• Are all coffee flavors equally popular?
• Is the use of bike helmets effective in protecting
people in bicycle accidents from head injuries?
• Is there a connection between gender and alcohol
consumption among the students at Umeå
university?
HYPOTHETIC-DEDUCTIVE METHOD
1
Hypothesis
Statement
Deduction – logically
valid argument
(Predictive inference)
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3
Induction
(Inductive inference)
1Tries to predict what will happen if the hypothesis holds.
2 ”Dialogue with reality”
Observation
Logical valid hypothesis (example)
Valid
Hypothesis: The animal is a
horse.
Statement: If the animal is a
horse it will have four legs.
Observation: The animal has not
four legs.
Conclusion: The animal is not a
horse.
Invalid
Hypothesis: The animal is a horse.
Statement: If the animal is a horse it
will have four legs.
Observation: The animal has four
legs.
Conclusion: It is a horse.
Non valid conclusion. It can be a pig
or some other animal.
Logical valid hypothesis (example)
Valid
Invalid
Hypothesis: It is raining.
Hypothesis: It is raining.
Statement: If it is raining the
ground will be wet.
Statement: If it it is raining the
ground will be wet.
Observation: The ground is not
wet.
Observation: The ground is wet.
Conclusion: It does not rain.
Conclusion: It rains.
Non valid conclusion. The ground can
be wet due to several reasons.
Contradiction proofs
Within statistical hypothesis testing (inference theory) we are
not looking for ”impossible” events” in order to reject posed
hypotheses.
(e.g. it is impossible that the ground is dry if it rains. If the
ground is dry hypothesis ”it rains” is rejected)
Instead we are looking for contradictions in terms of
”improbable events”.
Improbable event
Assume that we suspect that the usage of bicycle helmets is an effective way
to protect people in bicycle accidents from skull damage.
Null hypothesis: The percentage of persons with skull damage after a bicycle
accident is the same whether or not they use bicycle helmets.
Statement: If the percentage of persons with skull damage after a bicycle
accident is the same whether or not they use bicycle helmets, in a sample
survey there should only be a small difference in the percentage of people
with skull damage in the two groups.
If the hypothesis holds, it is an improbable event in a sample survey, to
observe a large percentage difference between these kinds of groups.
Test statistic
Within statistical inference theory the statements are
summarized in a test statistic.
From our hypothesis and from the probability theory we
can derive the distribution of the test statistic if the
null hypothesis is true.
Next, we draw a sample and calculate a value of the
observed test statistic and compare it with the derived
distribution to understand if we have an improbable
event.
If we get an improbable event the null hypothesis is
rejected.
P-value
The P-value describes how improbable the event is.
If the p-value is small, we either have something which is
improbable or the null hypothesis does not hold.
If the p-value is small (< 0.05 or <0.01) the null
hypothesis should be rejected.
Mosquito cream example:
We have tested anti mosquito creams on 10 students. Each
student did get the cream A on a random chosen arm and
cream B on the other arm. The students were then forced
to walk in the Amazon jungle. After some hours the
number of mosquito bites was counted on each arm.
Suppose 7 out of the 10 students did have less mosquito bites
on the arm with cream A. Is this enough evidence to say
that there is a difference in effectiveness between the
creams?
Help me with the null hypothesis.
Example:
• Null hypothesis: The anti mosquito creams A and B are
equally effective.
• Alternative hypothesis: The anti mosquito creams are
not equally effective
• Statement: If the Null hypothesis holds then we expect
that about half of the people in our sample get more
mosquito bites with cream A.
• Math Calculations gives that if the null hypothesis is
true then the number of people in our sample that get
more mosquito bites on arm with cream A is binominal
distributed.
If Null hypothesis is true.
Is 7 out of 10 a Improbable event?
The probability of getting 7 or more
and 3 or less is about 34%.
Conclusion
• The P-value is 34%. This means that it is not
uncommon to get the data we got in our
sample or anything more extreme if the null
hypothesis is true.
• We can not reject the Null hypotheses.
• We don’t have empirical support to claim that
there is a difference between the mosquito
creams.
Reasons for non-significant results
• There is no difference
• There is a difference, but we have too few
observations to detect it
• Important. The fact that we can’t reject the
null hypothesis does not mean that the null
hypothesis is true.
How to find the right test
The Principe behind all statistical tests are the
same. It’s just about finding the right test. You
can do this by looking at the chart.
(Hand out the chart)
1) Find the objective in the study.
2) Identify the level of the variables.
3) Use chart to find right test.
The steps of a statistical investigation
• Aim
• Formulation of the problem, (Boundaries and
more…)
• Planning (What to collect and how it relates to
the research question…)
• Data collection (Make a random sample…)
• Analysis (Descriptive and Inferential statistics…)
• Report
Some useful stuff if there
is more time
Questionnarie
• Construct the questionnaire so that the
respondents can easily
- understand the instructions
- understand the questions
- answer the questions
Keep the questionnarie as short as possible!
Test the questionnaire
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Pilot study
Try different orders of the questions.
Test the coding of the answers.
Does the questionnarie give the answers to
the questions you have?
• Should the response alternatives in the
answers be modified?
• Should the questions be reformulated?
Avoid leading questions
• Do you think it is reasonable to have stricter
punishments in order to reduce crime in our
society?
• Do you prefer to go to the theatre rather than
a movie if you want a cultural experience?
Avoid negativly formulated questions
• Should one not allow trucks to drive through
the city center?
• Better: Should one allow trucks to drive
through the city center?
Avoid hypothetical questions
• Would you choose to buy a locally produced
CD player if its price was 20% higher than that
of CD player produced in Japan?
One thing at the time!
• Do you consider the staff at the bank to be
friendly and competent?
• Better: Do you consider the staff at
the bank to be friendly?
Do you consider the staff at
the bank to be competent?
Fixed alternatives
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Easy to code and to work with.
Easy to answer.
Should be mutually exclusive.
Should be exhaustive.
Open questions
• Can be difficult to process and to code.
• The only alternative when the possible answers are
unknown or impossible to classify.
• Can be used in combination with fixed alternatives.
(ex: ‫ ם‬other ______ , ‫ ם‬why ? _____ )
• Best at the end of the questionnaire.
Think before you act
• Important issues at the planning stage:
(That is before you start collecting data!)
– What data to collect, how is the data helping you to solve
your problem.
– How to analyze the data.
– How does the way of collecting data influence the analysis.
• Total investigation or survey
• Sampling design of a survey
• Choice of method and measuring tool
– How to handle missing values
– How to present the results
Different kind of sampling
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Accidental (Convenient) sampling
Voluntary answers
Voluntary subjects
Other nonrandom sampling techniques…
Random sampling
Random sampling
• The sample units are chosen by some random
mechanism
• The probability of inclusion is known for each
unit
Different types of random sampling
• Simple random sampling
• Stratified sampling
• Cluster sampling
Simple random sampling
• Each subject from the population is chosen
randomly and entirely by chance, such that
each subject has the same probability of being
chosen at any stage during the sampling
process.
• In simple random sampling of n subjects all
possible combinations of n subjects have the
same chance to be selected
Stratified random sampling
The population is separated into non-overlapping
groups, strata, and then a simple random
sample is selected from each stratum.
The reasons for using stratified sampling are:
Stratified random sampling can increase the
quantity of information for a given cost
Stratified sampling allows for separate estimates
of population parameters within each stratum
Stratification may produce a smaller
bound on the error of estimation than
what you get in a simple random
sampling. This is especially true when
the strata are homogeneous.
The cost of administration may be
minimised by carefully planned
stratified sampling in compact and
well-defined geographical areas.
Cluster random sampling
The populationen is divided into groups (clusters) of subjects. An
number of such clusters are randomly chosen. All individuals
in the chosen clusters are selected.
The reasons for using cluster sampling are:
A good frame, (listing the individuals of the population) is either
not available or is very costly to obtain, while a listing of the
clusters is easily obtained.
The cost of obtaining observations increases as the distance
separating the individuals increases.
Sources of Errors
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Sampling error – unless we make a census…
Nonresponse
Frame error – Over-/Undercoverage
Measurement error
Data processing error