Introduction to statistics

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INTRODUCTION TO STATISTICS

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INTRODUCTIONTO

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

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INFERENTIAL STATISTICSThe 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 POPULATIONis the set of all the individuals of

interest in particular study

THE SAMPLEis 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 data2. 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 QUANTITATIVECategories

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 amountIt 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 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

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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 forgetWhat I see, I rememberWhat I do, I understand

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Introduction to statistics

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