Transcript What is Statistics?

Introducing the Study of Statistics
Henan University of Technology – November 2013
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.1
What is Statistics? Seven 7 Steps
1. Population
2. Sample
3. Variable
4. Distribution
5. Probability
6. Tables
7. Inferences
Try to learn what each of
these 7 Steps really means
and you will be well on
your way to be the master
of statistics.
Descriptive Statistics covers
the first 6 Steps but its
important to understand
why we study statistics
which is Step 7.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.2
Seven 7 Steps
•
7 steps - so if you don’t follow these steps
which step is the problem? This course
concerns Steps 1 to 6 but for the uses of
statistics we refer to Step 7 as well.
•
Note down the problem area for you (if any)
and seek help about it. Resources include:
lecturer, tutors, internet, textbooks, website
and powerpoints. All of these resources are
available to you to help you learn.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.3
What is a Distribution?
•
A distribution is an arrangement of values of a
variable showing their observed or theoretical
frequency of occurrence.
•
Distributions may be based on Discrete data or
Continuous data. What is the difference?
•
Throws of a dice = Discrete data
•
Share market movements = Continuous data
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.4
Distributions of Each Type
Discrete
Continuous
Binomial
Normal
Poisson
Uniform
Exponential
Students’ t
Chi Squared
F
We will be looking at these distributions during the course
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.5
Distributions and Variables
A distribution is an arrangement of values of a
variable showing their observed or theoretical
frequency of occurrence.
A variable is a characteristic of a population. Throw
two dice you get 36 possible pairs i.e. a population
of 36.
A characteristic = example the sum of two dice.
A random variable is a rule that assigns a number to
each outcome example the sum of the two dice = 11
possible outcomes. (2 to 12)
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.6
Distributions and Variables
How many possible outcomes for the difference
between two dice?
Only 6 possible outcomes – because it’s a different
characteristic or rule, its still a random variable
of the population of 36 possible pairs.
This is the reason we have so many distributions:
Because we want to look at different rules within the
data to get the information we need.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.7
What is Statistics? Seven 7 Steps
1. Population
2. Sample
A population is the group of all of
the items of interest. For example,
all of the fish in a lake. Or, all of
the people in China. Or all of the
Panda in China.
3. Variable
It can be a group of things.
Possible number of combinations
4. Distribution when you throw two dice. Share
market changes in Shanghai stock
5. Probability market. Interest rates paid by
Chinese banks.
6. Tables
7. Inferences
A parameter is a measurement
of the population – e.g. mean,
population standard deviation.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.8
What is Statistics? Seven 7 Steps
1. Population
2. Sample
3. Variable
4. Distribution
5. Probability
6. Tables
7. Inferences
A sample is a set of data
drawn from the population.
For example, catching some
fish in a lake. A survey of
some Chinese people.
Studying some Panda.
Shanghai stock market
changes between 1990 and
2005.
Populations can be very, very
large so its easier to study
samples and use that evidence
to support or oppose a point
of view.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.9
What is Statistics? Seven 7 Steps
1. Population
2. Sample
3. Variable
4. Distribution
5. Probability
6. Tables
7. Inferences
A variable is a characteristic of a
population. For example, fish in a
lake over the length of 20
centimetres. Panda over the
weight of 30 kilogrammes.
A variable is a characteristic of a
population but a parameter is a
measurement of a population.
For example, the mean outcome
of one dice throw is 3.5. but one
throw is a variable with 6
possible outcomes.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.10
What is Statistics? Seven 7 Steps
1. Population
2. Sample
3. Variable
4. Distribution
5. Probability
6. Tables
7. Inferences
A distribution is an arrangement
of values of a variable showing
their observed or theoretical
frequency of occurrence.
Throw a single dice 24 times
and observe how often the
number 6 appears. Try again
with number 1 this time. These
are two distributions.
The theoretical distribution is
one 6 every 6 throws and one 1
every 6 throws.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.11
What is Statistics? Seven 7 Steps
1. Population
2. Sample
3. Variable
4. Distribution
5. Probability
6. Tables
7. Inferences
Probability is likelihood – the
chance of an event occurring. The
event needs to be clearly defined
and understood.
An event is often a collection of
more simple events.
The probability of an event is the
sum of the probabilities of the
simple events. The probability of
throwing a dice and getting a
value equal to or less than 3 is
1/2 or 1/6 plus 1/6 plus 1/6.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.12
What is Statistics? Seven 7 Steps
1.
2.
3.
4.
Tables list out the probabilities of
Population actual events with varying
degrees of significance. The lower
the degrees of significance the
Sample
higher degree of confidence we
can have in our proposed value –
Variable
using the table’s value to compare
Distribution with our proposed value.
5. Probability
6. Tables
7. Inferences
Tables vary according to the
probability distribution being
used. And some tables list critical
values ( for selected levels of
significance) rather than produce
a full set of numbers.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.13
What is Statistics? Seven 7 Steps
1. Population
2. Sample
3. Variable
Inferential statistics developes
methods to draw conclusions
about characteristics of a
population – based on sample
data.
It is logical to move from
descriptive to inferential statistics.
4. Distribution Statistics aims to get new
understanding – to get useful
5. Probability information from lots of data.
6. Tables
7. Inferences
Similar problems are likely to
have similar solutions. But we
need to build confidence before
making such judgements.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.14
Statistic
Finally the word ‘statistic’:
• Recall we use the word ‘parameter’ to refer
to a measurement of a population
• ‘Population’ covers all of the items of
interest while ‘sample’ covers only a
proportion of the population
• We use the word ‘statistic’ to refer to a
measurement of a sample
• A sample statistic is a guide to the value of
a population parameter
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.15
Statistic
Finally the word ‘statistic’:
• Recall we use the word ‘parameter’ to refer
to a measurement of a population
• ‘Population’ covers all of the items of
interest while ‘sample’ covers only a
proportion of the population
• We use the word ‘statistic’ to refer to a
measurement of a sample
• A sample statistic is a guide to the value of
a population parameter
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1.16