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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 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.

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?

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

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.

Two General Purpose of Statistics (Gravetter,

2007)

- 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 - 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

DESCRIPTIVE STATISTICS

- The purpose of descriptive statistics is to

organize and to summarize observations so that

they are easier to comprehend

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

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

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

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

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

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

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

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

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

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.

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

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.

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.

MEASUREMENTS and SCALES (Stevens, 1946)

Ratio

Interval

Ordinal

Nominal

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.

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.

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

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

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.

RATIO Scale

- One thing is certain Scales the kinds just

mentioned HAVE ZERO POINT.

Confucius, 451 B.C

- What I hear, I forget
- What I see, I remember
- What I do, I understand