Slides of Discovering Statistics using SPSS by Muhammad Yousaf Abid. Iqra University Islamabad.

7/31/2019 Slides of Discovering Statistics using SPSS by Muhammad Yousaf Abid. Iqra University Islamabad.

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Chapter 1

Everything you ever wanted to know

about Statistics


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What will this chapter tell us?

This chapter will tell you the overview of some

important statistical concepts.


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BUILDING STATISTICAL MODELS

Real world phenomenon; it is the actual

phenomenon that really exists in a world.

The researcher wants to build a model which

most closely resembles the real world

phenomenon.


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How to Build Statistical Model?

Collecting data from the real world

Analyse the data to draw conclusions

Building statistical model based on conclusion.


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Why do we build statistical model?

Analogy: inference that if two or more things agree with one another in some respect theywill probably agree in others.

We build statistical model of real world

processes in an attempt to predict how these

processes operate under certain conditions.


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Explanation: Imagine a engineer who wishes to

build a bridge across a river.

a) The engineer collects data from the real

world i.e. looks at bridges in the real world. E.g.

bridge structure, usage, material's it made of.

b) Uses this information to construct a model.c) The engineer might test whether the bridge

can withstand strong winds, by placing the model in

a wind tunnel.d) it is important that the model is an

accurate representation of the real world.


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Fit of the model

The degree to which a statistical model represent

the data collected is known as thefit of the model. Types of Model based on Fit

Good fit: The If the model is an excellentrepresentation of the real world situation it is saidto be a good fit

Moderate Fit: If the model has some similarities ofthe real world but there are some big differencesto the real world that is called moderate fit.

Poor Fit: If the model bears no structuralsimilarities to the real bridge it is termed as poorfit.


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Population & Sample

As a researcher, we are interested in finding resultsthat apply to an entire population of people or things.

The bridge building engineer cannot make a full sizemodel of the bridge she wants to build and so shebuilds a small scale model and tests this model undervarious conditions. From the results obtained from thesmall scale model(sample) the engineer infers thingsabout how the full size bridge(population) will respond.

The bigger the sample, the more likely it is to reflectthe whole population.


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Simple Statistical Model

Mean

Sum of Squares

Variance Standard Deviations


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Mean

The mean is a hypothetical value that can be

calculated for any data set. It is not have to be

a value that is actually observed.

This can be calculated by adding the values we

obtained and by dividing the number of values

measured.

Formula:

(1+2+3+3+4)/5= 2.6 Hypothetical Mean


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Sum of Squares


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Standard Deviation(S.D)

Standard deviation is the square root of the variance, whichensures that the measure of average error is in the sameunits as the original measure.

Formula:

Interpretation: The S.D is a measure of how well the mean represents the data.

Small S.D indicates that the data points are close to the mean.

The large S.D indicates that the data points are distant from themean.

A S.D of 0 would mean that all of the scores were the same.


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Diagrammatic representation of S.D


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What is a Frequency Distribution?

Also called the histogram, It is simply the

graph plotting the value of observations on

the horizontal axis, with the bar showing how

many times each value occurred in the dataset.

By looking at which score has the tallest bar,

we can immediately see the mode(mostfrequent score).


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When frequency distribution is

Normal?

If we draw a vertical line through the center ofthe distribution then it should look the same on

both sides, this is known as a normal distribution.

It is characterized by the bell shaped curve.

This shape basically implies that the majority of

score lies around the center of the distribution.


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Properties of Frequency distribution

There are two main ways in which the

distribution can deviate from normal.

Skewness: lack of symmetry

Kurtosis: pointyness of the curve.


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Properties of Frequency Distribution

Skewed Distribution: this distribution is not symmetricaland the most frequent scores are clustered at one end ofthe scale.

Types of skewness

Positive skewness: Negative skewness


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Properties of Frequency Distribution

Kurtosis (pointyness): refers to the degree to whichscores cluster in the tails of the distribution.

Types of kurtosis

Platykurtic

Leptokurtic


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Interpretation of Normal Distribution

Ideally we want our data to be normally distributed

that is not too skewed, and not too pointy or flat. In a normal distribution the value of skew and kurtosis is 0. If the

distribution has values of skew or kurtosis above or below 0 then

this indicates a deviation from normal


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The Standard Deviation(S.D) and the

Shape of the Distribution

SD also tells us about the shape of thedistribution

If the mean represents the data well then most of

the scores will cluster close to the mean and theresulting SD is small

When the mean is worse representation of data,the scores cluster more widely around the mean

and the SD is large. Fig shows two distribution that have the same mean

(50) but different SD.


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SD= 25 SD=15


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The Standard Error

What is the difference between SD(Standard

Deviation) and SE(Standard Error)?

Standard error is the SD of the sample means.

This would give you the measure of how much

variability there is between the means of different

samples.


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If we take several samples from

the same population , then each

sample has its own mean.

Population

Mean


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Sampling Distribution is simply the frequency

distribution of sample means from the same

population. Is my sample representative of the population?

It can be asked through Standard Error.

A large Standard error(relative to the sample mean)means that there is a lot of variability between the

means of different samples and so the sample we

have might not be representative of the population

A small SE indicates that the most sample means aresimilar to the population mean and so our sample is

likely to be an accurate reflection of the population.


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Confidence Interval

Confidence Interval tells us with a known

degree of confidence as to where the

population value(parameter) actually lies.

An interval can be computed by adding and

subtracting a margin of error to the point

estimate.

= Point Estimate Margin of error


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Hypothesis

Scientists are usually interested in testing hypothesis:that is, testing the scientific questions that theygenerate. Within these questions, there is usually aprediction that the researcher has made. This

prediction is called experimental hypothesis. The reverse possibility that your prediction is wrong is

called the null hypothesis.

Example: Hamburgers make you fat

The experimental hypothesis is that the more hamburgers you eat,the more you start to resemble a beached whale; the nullhypothesis is that people will be equally fat regardless of howmany hamburgers they eat.


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One and two tail tests

Directional hypothesis uses one tail test

Example

The more someone reads this book, the more they

want to kill its author

Non Directional hypothesis uses two tail test

Example

Reading more of this book could increase or decreasethe reader`s desire to kill its author


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Errors in testing of hypothesis

The Null hypothesis is accepted or rejected on

the basis of the value of the test-statistic(z, t,

F, chi-square). The test-statistic may land in

acceptance or rejection region

In this rejection plan or acceptance plan, there

is the possibility of making any one of the two

errors which are called Type I error and Type IIerror.


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Type I error and Type II error

Type I error:

The null hypothesis Ho may be true but it may berejected. This is an error and is called type I error

Example: We can say type I error is committed when An intelligent is not passed

An innocent person is punished.

Type II error:

The null hypothesis Ho may be false but it maybe accepted. It is an error and is called type IIerror.


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(alpha), Level of Significance:

The probability of making type I error is denoted

by (alpha)

( Beta):

The probability of making type II error is denoted

by

Slides of Discovering Statistics using SPSS by Muhammad Yousaf Abid. Iqra University Islamabad.

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