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INTRODUCTION TO STATISTICS

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INTRODUCTION TO STATISTICS INTRODUCTION (1) In early 1987, the US Food and Drug Administration (FDA) was faced a unprecedented situation. Thousands of people were ... – PowerPoint PPT presentation

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Title: INTRODUCTION TO STATISTICS


1
INTRODUCTION TO STATISTICS
2
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.

3
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?

4
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

5
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.

6
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

7
DESCRIPTIVE STATISTICS
  • The purpose of descriptive statistics is to
    organize and to summarize observations so that
    they are easier to comprehend

8
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

9
SOME TIPS ON STUDYING STATISTICS
  • Is statistics a hard subject?
  • IT IS and IT ISNT
  • 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

10
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

11
POPULATIONS and SAMPLES
THE POPULATION is the set of all the individuals
of interest in particular study
The sample is selected from the population
The result from the sample are generalized from
the population
THE SAMPLE is a set of individuals selected from
a population, usually intended to represent the
population in a research study
12
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

13
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

14
TWO KINDS OF NUMERICAL DATA
  • Generally fall into two major categories
  • Counted ? frequencies ? enumeration data
  • Measured ? metric or scale values ? measurement
    or metric data

Statistical procedures deal with both kinds of
data
15
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

16
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

17
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.

18
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

19
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.

20
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.

21
MEASUREMENTS and SCALES (Stevens, 1946)
Ratio
Interval
Ordinal
Nominal
22
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.

23
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.

24
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

25
INTERVAL Scale
  • The top of this illustration shows three
    temperatures in degree Celsius 00, 500, 1000. It
    is tempting to think of 1000C 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 1000C is twice as hot as one of
    500C or that a rise from 400C to 480C is a 20
    increase

26
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.

27
RATIO Scale
  • One thing is certain Scales the kinds just
    mentioned HAVE ZERO POINT.

28
Confucius, 451 B.C
  • What I hear, I forget
  • What I see, I remember
  • What I do, I understand
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