Introduction to Statistics

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INTRODUCTION
TO
STATISTICS

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INTRODUCTION (1)
 In early 1987, the US Food and Drug Administration
(FDA) was faced a unprecedented situation.
Thousands of people were dying of acquired
immunodeficiency syndrome (AIDS).
 Not only was there no known, but there was not even
a drug available to slow the developmental of the
disease.
 Early clinical trials of an experimental antiviral drug
known then as azidothymidine (AZT) were
promising
 Only 1 of 145 AIDS patients on AZT had died,
compared to 19 of 137 patients in a control groups
given a placebo.

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INTRODUCTION (2)
 There were medical questions remaining to be
answered. What was the optimal dose? For
how long would the drug continue to thwart
the virus?
 There was also an important statistical
question, one that had to be answered before
the medical and ethical questions could be
addressed. Was the fewer number of deaths
among AIDS patients using AZT the result of
the drug, or was it due just to chance?

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INTRODUCTION (3)
 Statistical test showed that the differences
between the two groups was so great that the
probability of their having occurred by chance
was less than one in a thousand (Fischl et al.,
1987).
 Armed with these statistics, the FDA gave
final approval of the use of AZT in March of
1987, after only 21 months of testing

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What is STATISTICS?
 A set of mathematical procedure for organizing,
summarizing, and interpreting information
(Gravetter, 2004)
 A branch of mathematics which specializes in
enumeration data and their relation to metric data
(Guilford, 1978)
 Any numerical summary measure based on data
from a sample; contrasts with a parameter which
is based on data from a population (Fortune,
1999)
 etc.

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Two General Purpose of Statistics
(Gravetter, 2007)
1. Statistic are used to organize and summarize
the information so that the researcher can see
what happened in the research study and can
communicate the result to others
2. Statistics help the researcher to answer the
general question that initiated the research by
determining exactly what conclusions are
justified base on the result that were obtained

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DESCRIPTIVE STATISTICS
The purpose of descriptive statistics is to
organize and to summarize observations so that
they are easier to comprehend

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INFERENTIAL STATISTICS
The purpose of inferential statistics is to draw an
inference about condition that exist in the
population (the complete set of observation)
from study of a sample (a subset) drawn from
population

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SOME TIPS ON STUDYING STATISTICS
 Is statistics a hard subject?
IT IS and IT ISN’T
 In general, learning how-to-do-it requires
attention, care, and arithmetic accuracy, but it
is not particularly difficult.
LEARNING THE ‘WHY’ OF THINGS MAY
BE HARDER

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SOME TIPS ON STUDYING STATISTICS
 Some parts will go faster, but others will
require concentration and several readings
 Work enough of questions and problems to
feel comfortable
 What you learn in earlier stages becomes the
foundation for what follows
 Try always to relate the statistical tools to real
problems

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POPULATIONS and SAMPLES
THE POPULATION
is the set of all the individuals of
interest in particular study
THE SAMPLE
is a set of individuals selected from a population, usually
intended to represent the population in a research study
The sample is selected
from the population
The result from the
sample are generalized
to the population

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PARAMETER and STATISTIC
 A parameter is a value, usually a numerical
value, that describes a population.
A parameter may be obtained from a single
measurement, or it may be derived from a set
of measurements from the population
 A statistic is a value, usually a numerical
value, that describes a sample.
A statistic may be obtained from a single
measurement, or it may be derived from a set
of measurement from sample

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SAMPLING ERROR
 It usually not possible to measure everyone in the
population
 A sample is selected to represent the population. By
analyzing the result from the sample, we hope to
make general statement about the population
 Although samples are generally representative of
their population, a sample is not expected to give a
perfectly accurate picture of the whole population
 There usually is some discrepancy between sample
statistic and the corresponding population parameter
called sampling error

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TWO KINDS OF NUMERICAL DATA
Generally fall into two major categories:
1. Counted  frequencies  enumeration data
2. Measured  metric or scale values 
measurement or metric data
Statistical procedures deal with both kinds of data

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DATUM and DATA
 The measurement or observation obtain for
each individual is called a datum or, more
commonly a score or raw score
 The complete set of score or measurement is
called the data set or simply the data
 After data are obtained, statistical methods are
used to organize and interpret the data

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VARIABLE
 A variable is a characteristic or condition that
changes or has different values for different
individual
 A constant is a characteristic or condition that
does not vary but is the same for every
individual
 A research study comparing vocabulary skills
for 12-year-old boys

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QUALITATIVE and QUANTITATIVE
Categories
 Qualitative: the classes of objects are different
in kind.
There is no reason for saying that one is greater
or less, higher or lower, better or worse than
another.
 Quantitative: the groups can be ordered
according to quantity or amount
It may be the cases vary continuously along a
continuum which we recognized.

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DISCRETE and CONTINUOUS Variables
 A discrete variable. No values can exist
between two neighboring categories.
 A continuous variable is divisible into an
infinite number or fractional parts
○ It should be very rare to obtain identical
measurements for two different individual
○ Each measurement category is actually an interval
that must be define by boundaries called real
limits

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CONTINUOUS Variables
 Most interval-scale measurement are taken to
the nearest unit (foot, inch, cm, mm)
depending upon the fineness of the measuring
instrument and the accuracy we demand for
the purposes at hand.
 And so it is with most psychological and
educational measurement. A score of 48 means
from 47.5 to 48.5
 We assume that a score is never a point on the
scale, but occupies an interval from a half unit
below to a half unit above the given number.

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FREQUENCIES, PERCENTAGES,
PROPORTIONS, and RATIOS
 Frequency defined as the number of objects or event
in category.
 Percentages (P) defined as the number of objects or
event in category divided by 100.
 Proportions (p). Whereas with percentage the base
100, with proportions the base or total is 1.0
 Ratio is a fraction. The ratio of a to b is the fraction
a/b.
A proportion is a special ratio, the ratio of a part to a
total.

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MEASUREMENTS and SCALES (Stevens, 1946)
Nominal
Ordinal
Interval
Ratio

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NOMINAL Scale
 Some variables are qualitative in their nature rather
than quantitative. For example, the two categories
of biological sex are male and female. Eye color,
types of hair, and party of political affiliation are
other examples of qualitative or categorical
variables.
 The most limited type of measurement is the
distinction of classes or categories (classification).
 Each group can be assigned a number to act as
distinguishing label, thus taking advantage of the
property of identity.
 Statistically, we may count the number of cases in
each class, which give us frequencies.

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ORDINAL Scale
 Corresponds to was earlier called
“quantitative classification”. The classes are
ordered on some continuum, and it can be
said that one class is higher than another on
some defined variable.
 All we have is information about serial
arrangement.
 We are not liberty to operate with these
numbers by way of addition or subtraction,
and so on.

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INTERVAL Scale
 This scale has all the properties of ordinal
scale, but with further refinement that a given
interval (distance) between scores has the
same meaning anywhere on the scale. Equality
of unit is the requirement for an interval
scales.
 Examples of this type of scale are degrees of
temperature. A 100
in a reading on the Celsius
scale represents the same changes in heat
when going from 150
to 250
as when going from
400
to 500

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INTERVAL Scale
 The top of this illustration shows three
temperatures in degree Celsius: 00
, 500
, 1000
. It
is tempting to think of 1000
C as twice as hot as
500
.
 The value of zero on interval scale is simply an
arbitrary reference point (the freezing point of
water) and does not imply an absence of heat.
 Therefore, it is not meaningful to assert that a
temperature of 1000
C is twice as hot as one of
500
C or that a rise from 400
C to 480
C is a 20%
increase

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INTERVAL Scale
 Some scales in behavioral science are
measurement of physical variables, such as
temperature, time, or pressure.
 However, one must ask whether the
variation in the psychological phenomenon
is being measured indirectly is being scaled
with equal units.
 Most measurements in the behavioral
sciences cannot posses the advantages of
physical scales.

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RATIO Scale
 One thing is certain: Scales …the kinds just
mentioned HAVE ZERO POINT.

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Confucius, 451 B.C
What I hear, I forget
What I see, I remember
What I do, I understand