Full Text PDF - Government College University

The Scientific Ravi 2012 

Statistics 

Test of significance 

Aamir Sanaullah 

Lecturer, Department of Statistics 

GCU, Lahore 

The results of analysis and interpretation of the 

results of our study should be related to the 

objectives. We may find some interesting 

results. For example, in a study on smoking, we 

may find that 30% of the men included in the 

sample are smoking more than four cigarettes a 

day compared to only 20% of the women. How 

can we interpret this result? 

The difference of 10% might be a 

TRUE DIFFERENCE, which is also 

existed in the total population from 

which the sample was taken. 

The difference might be DUE TO 

CHANGE. In reality, there is no 

difference between men and women, but 

the sample of men just happened to 

differ from that of women. One can also 

say that the observed difference is due to 

sampling variation. 

The third possibility maybe due to 

defects in the study design (also 

referred to as BIAS). For example, only 

male interviewers may have been used 

or the pre-test might have been omitted. 

May be with an appropriate study design 

no such difference would be found. 

If we think that this observed difference between 

two groups cannot be explained by bias, we will 

check out whether this difference can be 

considered as a true difference or not. We only 

conclude that this is the case if we can explain 

this chance of occurrence. We accomplish it by 

applying a significance test. 

N.M. Kapoor once said, “Procedures which 

enables us to decide, on the basis of sample 

information, whether to accept or reject 

hypothesis or to determine whether observed 

sampling results differ significantly from 

expected result are called tests of significance, 

rule of decision or test of hypothesis.” 

“A significance test may be defined as the 

probability of obtaining a statistic as different or 

more different from the null hypothesis (given 

that the null hypothesis is correct) than the 

statistic obtained in the sample. If this 

probability is sufficiently low, then the 

difference between the parameter and the 

statistic is said to be statistically significant” 

How The Test Of Significance Works! 

Procedure of significance test can be 

summarized in following steps below 

1. We state our hypothesis (statistical 

hypothesis, null hypothesis). 

2. Decide level of significance. 

3. Choose suitable test statistic. 

4. Complete required calculation from 

the selected sample/probability form. 

5. Complete the results / calculated 

probability from sample information 

with alpha level. 

6. Conclusion. 

7. Interpretation. 

TYPE 1 AND TYPE 2 Errors (Which One Is 

Worse Off?) 

There is always a possibility of mistake made by 

the researcher even in their best projects, 

concerning relationship between the two 

variables. There are two types of errors. 

“The first is called a Type 1 error. This occurs 

when the researcher assumes that a relationship 

exists when in fact the evidence is that it does 

GC University Lahore Page 189


Statistics 

not. The probability of committing a Type 1 

error is called alpha.” 

“The second is called Type 2 error. This occurs 

when the researcher assumes that a relationship 

does not exist, when in fact the evidence shows 

that it does. The probability of committing Type 

2 error is called beta.” 

If we reduce the possibility of committing Type 

1 error, this may result an increase in the 

possibility of committing a Type 2 error and 

vice versa. 

Things may be worse off than before, when 

chances to verify that a relationship exists is 

missing; the researcher generally tries to 

minimize the Type 1 error. But in Type 2 error, 

there is nothing worse than before, when chance 

to verify that a relationship exists has been 

missed by the researcher. 

Let’s take an example. In this example, which 

type of error would you think that you would 

like to commit? 

“Someone has reduced crop yields in County X, 

for making it eligible for the Government 

disaster relief.” 

“Someone has not reduced crop yields in County 

X, for making it ineligible for Government 

disaster relief.” 

If the researcher has committed Type 1 error, 

then the County would be assumed to qualify for 

tragedy release or “disaster relief”, when it 

actually wasn’t eligible (the null hypothesis has 

been rejected, as it should be acknowledged). 

The Government may be spending disaster relief 

funds when it should not, and taxes may be 

increased. 

If the researcher has committed Type 2 error, 

then the County would be assumed to be 

disqualified for tragedy release or “disaster 

relief”, although it was eligible (we have 

rejected the null hypothesis, when it should be 

acknowledged). The Government may be not be 

spending disaster relief funds when farmers 

needed it. 

A Probability Of Error Level (Alpha Level): 

Researchers normally presume that they may be 

able to agree with what is called the probability 

of committing Type 1 error, i.e., the value of 

alpha. Mostly value of alpha is taken as 0.05 

in Social Sciences. 

An alpha of .01 is not unusual in researches 

regarding the public health, because 

researchers don’t want to be incorrect more 

than 0.1% times. 

Good Analyst and Bad Analyst by Gerard E. 

Dallal 

Reject the hypothesis under test, if an observed 

significance level (P value) is less than 0.05. Do 

not discard the null hypothesis, if it is higher 

than 0.05. 

Frequently, researchersare distracted by 

statistical significance and ignore practical 

significance, meaning, the result that is 

statistically significant might be a reason of 

happiness, even if it does not have such 

importance. 

A badresearcher wants a P-value and gives no 

importance to the quality of the data. He only 

considers P0.05 with and does not 

pay much attention for the background in which 

the data were collected or the confidence 

intervals. 

A good analyst considers all the rules of firstclass 

study design. He knows that which test 

procedure is required for the resulting P value to 

be applicable. He takes the P value as 



Statistics 

significant element of the study, but not as a 

whole answer. 

Significance tests are just pieces of the 

problem, not a whole answer to rely on.They 

become unrelated if the outcome has no realistic 

significance. One may say that significance tests 

are useful pieces of problem. 

If some relationship between two variables 

exists, then there is a good possibility that 

findings are correct. But statistical significance 

is not the same as practical significance. 

Statistical significant findings might not have 

important practical implication. They may have 

such finding, but implication of such findings 

may be useless. The researcher must look at 

both significances, statistical and practical, 

for any research. 

“However, they do not assure that the 

research has been carefully designed and 

executed. In fact, tests for statistical 

significance may be misleading, because they 

are precise numbers. But they have no 

relationship to the practical significance of 

the findings of the research.” 

*LAUGHTER BEST MEDICINE* 

Sometimes, because of large sample size those 

differences are small but statistically 

significant. And the differences would not be 

enough to be statistically significant in a small 

sample size. 

Conclusion: 

“Tests for statistical significance are used to 

estimate the probability that a relationship 

observed in the data occurred only by 

chance; the probability that the variables are 

really unrelated in the population. They can 

be used to filter out unpromising hypothesis.” 

We use these tests because they make up 

a measure, which explain about the unwritten 

and understood results by many people, and 

these results present necessary and vital 

information about a research project which 

can be in contrast with the conclusions of the 

other project. 

Probability 

And Everyday Life 

Zeeshan Ali Shams 

People usually make statements that are 

uncertain. A student who is not good at a 

particular subject; after taking an exam of that 

subject says that he is not sure whether he can 

pass the exam or not. Assume a cricket match is 

going to be played between Pakistan and India; 

each team has an equal chance of winning or 

losing. Likewise, if a man applies for a specific 

job, there is a 50% chance of his selection. All 

such uncertain statements are related to the topic 



Statistics 

of Probability. In this article, I shall try to 

exhibit the role of probability in everyday life. 

What probability is? 

Chance, likelihood, percentage and proportion, 

alternative terms of probability, are used by 

people in everyday life, but they rarely know 

what probability is? 

The word ‘probability’ has been derived from 

the word probable.This means likely, chance, 

possible or feasible. Likewise, probability 

implies the chance or occurrence of something. 

This something, in statistical language, is called 

an event. Thus, in statistics, the likely of 

happening of an event is recognized as a 

probability of that event. Such events ought to 

result in stochastic experiments. Stochastic 

experiments mean experiments that give 

different results when repeated again and again, 

under the same conditions. Tossing a wellbalanced 

coin, throwing a favorable dice and 

drawing a card from a well-shuffled pack of 

deck are instances of stochastic experiments. 

What does mean by the likelihood of the 

occurrence of an event? 

The likelihood of occurrence of an event means 

the probability of that event. For understanding 

this, consider a simple instance of tossing a coin. 

When a well-balanced coin is tossed, the chance 

of appearing either head or tail is one out of two. 

While throwing a well-balanced dice, the 

likelihood of occurrence of all points (1, 2, 3, 4, 

5, 6.) is equal, one out of six. Similarly, the 

likelihood of drawing a king from a wellshuffled 

pack of duck is four out of fifty two. 

With the help of above instances, this may be 

inferred easily that the likelihood of happening 

of an event (probability of an event) means 

the number of possibilities of the occurrence 

of that particular event out of the total 

possibilities. If the likelihood of occurrence of 

an event is impossible, its probability will be 

zero. e.g. the probability of occurring 14, when a 

well-balanced pair of dice is thrown, is zero. If 

the likelihood of occurrence of an event is 

certain, its probability will be exactly one. This 

means, in statistical terminology, probability is a 

number from 0 to 1 or from 0% to 100%. 

Probability in Everyday Life 

Probability plays an important role in everyday 

life. We are often affected by probability. 

Suppose you heard in news that there is a 

possibility of rain today. Weather report says 

that there is 80% likelihood of rain. If you have 

some plans for going on trip in some park, will 

you continue to stick to your plan after listening 

to the news or cancel your plan for another day? 

Surely, your answer will be in negative. But it is 

interesting to know how this forecast is made. 

The meteorologists provide such forecasts after 

calculating probabilities. The way of calculating 

probability is simple. They look back in the 

history and collect data of similar weather 

conditions. Then, the probability of rain is 

determined from the formula: the number of 

days it rained in past divided by the total 

number of days having similar weather 

conditions. Take an instance, there is data of one 

hundred days having similar weather conditions. 

There were eighty days when it rained out of one 

hundred. Thus, the probability of raining today, 

when weather has almost similar conditions as it 

had in past one hundred days, is eighty divided 

by hundred, that is, 80%. 

It is human nature that they want to be 

successful within a very short span of time. Most 

of people want to be millionaire or even 

billionaire within a single night. For this 

purpose, one of the most adopted ways is to try 

their lucks in lottery tickets. But do they really 

know what the chances of their winning are? 

Surely, they do not know. If they know, very 

few of them will opt this way. The chance of 

winning a lottery ticket is determined after 



Statistics 

dividing it with the total number of lottery 

tickets. Suppose if there are one hundred lottery 

tickets, the likelihood of winning a lottery ticket 

is one out of one hundred. If there are one 

thousand lottery tickets, the likelihood of 

winning grand prize is one out of one thousand. 

This shows that the chances of winning are 

lesser when there are one thousand lottery 

tickets instead of one hundred. This is only an 

instance, but in real life there are thousands of 

lottery tickets. So the likelihood of winning the 

grand prize can be determined in the similar way 

which implies almost impossible. 

Above two instances show the influence of 

probability in our daily life. There are hundreds 

of instances in our everyday life where 

probability affects our plans. This subject also 

plays a vital role in economics, management, 

operational research, astronomy, physics, 

psychology, sociology and many other 

disciplines. Many business decisions are also 

affected by probability. Almost all entities make 

their policies by using probability. Many 

forecasts depends upon the likelihood. In short, 

every decision that is made without hundred 

percent certainties leads to probability. In other 

word, lack of certainty gives birth to probability. 

Avoid Common Misconceptions regarding 

Probability: 

I have seen many people making common 

mistakes regarding probabilities. It does not 

matter what type of information or data was 

collected or by which technique the researcher 

calculated probability (Subjective approach or 

Objective approaches: classical approach, 

relative frequency approach, axiomatic 

approach). 

This section will help to eliminate some 

misconceptions about probability that are 

usually made by some people. 

If there are merely two outcomes of a stochastic 

experiment, one must give both two equal 

chance occurrences. If one tosses a wellbalanced 

coin, then either the head or the tail 

will appear on the upper face. Thus, there is 

equal likelihood of occurring of head and tail on 

a well-balanced coin. If on the first toss head 

appears, it does not mean that in the second toss 

tail will be appeared because head has already 

been appeared. On the second toss, again, both 

outcomes (head and tail) has 50-50 percent 

chances to appear. Likewise, one should allot 

equal likelihood of occurrence to all possible 

outcomes. For instance, once I asked one of my 

friends, “what is the likelihood of Pakistan 

cricket team winning in the semi-final?” He 

replied that it depends on how Pakistan would 

perform on that day. Perhaps, he thought that he 

was right. But, in statistical language, he was 

quite wrong. Since there are three possibilities of 

the results: Pakistan wins, other team wins or 

match ends at draw. Thus, the chance of winning 

or losing the semi-final of both teams is one out 

of three. Also, the likelihood of drawing the 

match is one out of three. 

Another misconception often observed is to 

think about the patterns. For instance, one 

throws a dice fifteen times and finds outcomes 

as 2,4,6,1,3,5, 2,4,6,1,3,5, 2,4,6. If he asks his 

friend, what the next point may be? Surely, if his 

friend does not know about the probability, he 

will reply that the next point would be 1. But it 

is not the case. Above pattern occurred just by 

chance. The next point may be any one of 1, 2, 

3, 4, 5,6. Since statistics deals with stochastic 

experiments, we know the total possible 

outcomes before performing the experiment; but 

which outcome will occur cannot be said with 

surety. 



Statistics 

Rana Faizan Ahmed 

STATISCAL 

HYPOTHESIS 

In order to understand the term, we need to 

know firstly that what Statistical hypothesis is? 

Hypothesis, as we know is simply the base of 

any investigation, so Statistical Hypothesis is an 

assumption about the population parameter 

(measuring characteristic), that either our 

assumption is true or not. Normally statisticians 

use hypothesis testing to check whether to reject 

the statistical hypothesis or not. The hypothesis 

testing includes 6 steps that are: 

1. Hypothesis 

2. Level of significance 

3. Test statistic 

4. Critical region 

5. P-value 

6. Interpretation 

These are the steps which a Statistician must 

follow for testing, but we won’t discuss the 

detail of hypothesis testing anymore. The 

statistical hypothesis should be performed on the 

whole population and if it is performed using a 

random sample than results might not be true, 

because data is very important to Statisticians 

and if it’s not consistent, then there will be 

errors may lead to a false decision. Generally 

hypothesis may be simple or composite, the 

examples are: 

 

 

The mean score of Pakistan in T 20s is 

130 (Simple hypothesis). 

The Average scoring of students in the 

test of Statistics is 60 (Simple 

hypothesis). 

 

 

The mean score of Pakistan in T 20s is 

greater than or equal to 130 (composite 

hypothesis). 

The average scoring of students in the 

test of Statistics is less than or equal to 

60 (composite hypothesis). 

It is a fact that in any situation there are two 

different results e.g. Pakistan will either win the 

match lose, Ali will either fail or pass the exam 

or Sana will be declared as a position holder or 

not etc. 

So, we can say that statistical hypothesis is the 

statement that explains about relationships, like 

all hypotheses, Statistical hypotheses may 

predict truly or not. In making decisions, 

statistical hypothesis uses the testing approach 

called hypothesis tests. (As discussed above) 

In statistical hypothesis, the decision making 

depends on the data. Data should serve as a 

representative, if doesn’t, our decision might not 

be true. In decision making, we will set up a 

scheme between the matching and mismatching 

of Reality, we believe the true or false 

hypothesis is the reality. Here we uses the phrase 

“Do not reject H0” Or “Reject H0” which means 

the two right decisions that match the reality and 

two wrong decisions that do not, are; 

 

 

 

 

Hypothesis is true and we will not reject 

H0 

Hypothesis is false so we will reject H0 

Hypothesis is true but we won’t reject 

H0 

Hypothesis is false but we reject H0 

DECISION H0 is true H0 is false 

Accept H0: satisfactory error 

Reject H0: error satisfactory 

The mismatching of decisions constitutes an 

Error as our data is not like as it should be. 



Statistics 

Errors have very bad effects on our real life, 

because an error leads us to commit more errors. 

So, in statistical hypothesis we have to focus 

more seriously on errors and make arrangements 

that it will be rejected when it is true, which 

means if there is an error, the hypothesis must be 

rejected. Now we will discuss two types of 

hypothesis: 

Two types of Hypothesis: 

 

Null hypothesis (H0 is true but rejected) 

The hypothesis against which we hope to gather 

evidence is called the NULL HYPOTHESIS 

denoted by H0. 

The definition can be cleared through this 

example; “let us suppose that the Judge has to 

make a decision that either a person is guilty or 

not, his decision would be based on evidences. 

For this, he would assume that both of them are 

not guilty. Then when the case would start, 

every lawyer would give evidences that his 

client is not guilty. After evidences given by 

both lawyers, the judge would decide that who is 

guilty. If he gives a decision that a person is 

guilty who actually hadn’t committed the crime 

and is sentenced to death, then this is just like 

Null hypothesis (H0 is true but rejected, means 

he hasn’t actually committed that but according 

to the given evidences he was found guilty. As 

the lawyer of the person who commits crime, 

gave evidences and got his client saved). 

H0 = committed crime but saved 

H = won’t committed crime but sentenced to 

death 

In accordance with the above example, a person 

who didn’t commit the crime was sentenced to 

death, this is what Alternative hypothesis is (in 

actual, he didn’t commit but got punished). 

Here the error occurred in making the right 

decision, why? The evidences presented might 

not be true. Those errors are referred to as Type 

I and Type II, which will be discussed later. 

Now I will describe these types of Hypothesis 

through a scheme, it is: 

Decision:H0 is true 

Accept H0: satisfactory 

Reject H0: Type I error 

H0 is false 

Type II error 

satisfactory 

So, from this scheme it turns out that we are 

making a decision about a belief that what’s the 

truth and what’s not regarding the hypothesis. 

Now, let’s see what this scheme says to us, 

firstly “reject H0 means that I have decided to 

reject H0 as it is false but it does not mean H0 is 

actually false because it’s our decision. 

Similarly, “accept H0” means that I have 

decided to accept H0 (do not reject), as it is true 

but, it does not mean that H0 is true, in actual. 

There are some errors which are big obstacles in 

making good decisions. These errors are named 

as type I error and type II error as already 

mentioned above. 

Type I error (Reject H0 when it is true, Not 

believing the truth) 

Type II error (Accept H0 when it is False, 

Believing the untruth) 

 

Alternative Hypothesis (H0 is false but 

accepted) 

Type I error: 

The hypothesis for which we wish to gather 

supporting evidence is called the alternative 

hypothesis, and is denoted by H1. 



Statistics 

The above mentioned graph shows type II error, 

in which the value of variable x is in the region 

of known population, and it is in the critical 

region, that’s why we will accept the Alternative 

Hypothesis. But it is not from known population 

as it is under the curve of Unknown population. 

This graph shows us that the value of a variable 

‘x’ is falling out of the region by 5 percent. So, 

we will reject Null hypothesis because the value 

does not fall in the acceptance region, it will be 

more clear through another graph. 

This region is called beta, the probability of 

Type II error. 

This graph shows us that the region represented 

by x is now under the curve of an unknown 

population, it still lies under the same curve of 

Known Population but the value is beyond the 

critical region so it will be rejected because we 

are not accepting the values of this range.This 

area is called Alpha (α), the probability of type I 

error. We will reject the null hypothesis in this 

case. 

Type II error: 

Type I error is usually delicate and more serious 

than that of Type II error, so special care should 

be taken in carrying out a hypothesis. These 

errors would not be eliminated but reduced so; 

reduction of these errors might lead us to the 

right decision. Type I error is called False 

positive and type II error is also called False 

negative. 

Example regarding Type I and Type II errors: 

Suppose that you have an appointment with the 

doctor and the doctor tells you that you are 

suffering from a sore throat, but in actual you 

are not. This will be a type I error which simply 

shows an effect, whenever a test is performed. 

Similarly opposite to this situation will be a type 

II error. That’s all about the Statistical 

hypothesis and it should be considered in 

hypotheses for making right decisions. 



Statistics 

.Statistics - Explained 

In a Magnifying Glass! 

A Case of NIKE Shoes 

Qurat-ul-Ain 

When we talk about numbers /integers /order / 

analysis, the first word that clicks in our mind is 

MATHEMATICS or STATISTICS. Both the 

words originated from Latin / Greek words. 

STATISTICS refers to a systematical 

arrangement of numerical facts. Or we can also 

describe Statistics as “a discipline which 

includes procedures, techniques, inferences and 

making hypothetical statements to reach a 

decision in the face of any uncertainty.” For 

example, in Vital Index Theory, we have birth 

ratio, death ratio and other ratios pertaining to 

population and gender. 

Let me tell you where and to what extent 

Statistics and statistical concepts influence 

decision making at various national centers. In 

the weather radar station, we have hypothetical 

statements about weather conditions pertaining 

to whether; it would rain or not or whether it 

would be cloudy or sunny. In the head quarter of 

geology, we find anticipation and forecast in 

terms of confirmation about the earthquakes, 

tsunami, floods and storms. Their intensities are 

also predicted in the same way. In trade and 

commerce, marketing strategies and 

management decision largely depend on the 

statistics. For instance, descriptive statisticsis 

used in the production homes, whereas 

inferential statistics come into play when dealing 

with concepts and methods concerned with the 

summarization and description of important 

numerical data. Sometimes these discussions are 

based on the whole population or sometimes just 

one product is chosen, known as a “sample”. 

Let’s have a very practical yet common example 

which is based on our daily routine life; the 

footwear. I know the questions which are just 

coming to your mind that how small and 

everyday use stuff like “shoes” can carry 

Statistics with it? Now let me tell you how 

important role does stats play in small matters to 

the greater ones. 

When a production house / production 

management aims to launch a new product or a 

new range of its existing product, it carries out 

extensive research. During the research phase, 

descriptive stats is used. Production persons 

carry out data analysis, gather data sources, 

prepare dichotomous and multiple choice 

questionnaires and set down time frame and a 

sampling frame to perceive correctly what 

market requires, and how well their new product 

can cater to the needs of the consumers. 

Questionnaire is of two types, open ended 

(which allows respondents to answer in his/her 

own way, which are sometimes difficult to 

tabulate and interpret) and closed ended (all the 

answers are pre-specified and can easily be 

interpreted and tabulated). Ideally, the 

combination of both types is considered as the 

best way to collect primary data. On the rating 

scale, we basically describe the response on 

scale such as “high, low, satisfied, unsatisfied, 

efficient, very efficient, inefficient and etc.” The 

marketing research must define target 

population, and the time frame describes the 

time and duration for which the survey should 

be conducted. 

For setting out the sampling frame, samples are 

chosen. Sampling techniques help in choosing 

the respondents. In this case, sampling is done 

on the basis of probability sampling. In the 

probability sampling design, the sampling 

design is chosen as stratified sampling, because 

sampling includes different age groups / gender / 

profession etc. 

Here for better understanding and in order to 

keep reader’s interest, I would include an 



Statistics 

example of favorite sports wear ‘NIKE’. From 

data analysis and primary research, we found out 

the reason which contributes towards the low 

sales of NIKE footwear among ‘women’. One 

reason is the poor marketing and promotional 

strategies for ladies’ shoes as compared to men’s 

variety. Unfamiliarity is also another major 

reason for the low sales of NIKE ladies’ shoes. 

After this, data of the management structure was 

gathered from the information through 

secondary data, recent developments, the 

company profile, consumer perception and 

behavior, future plans, competitors, trend and 

product profile which was then analyzed. 

Having collected that, the management made an 

‘Executive Summary’. 

Afterwards, a theoretical framework was 

prepared to analyze the dependant and 

independent factors. With respect to NIKE 

ladies footwear, a statistical study shows that 

lack of proper marketing, planning, plus high 

cost, low affordability for middle and lower 

classes and lack of knowledge are the main 

independent factors for low sales. Here ‘low 

sale’ is a dependent factor. 

Now we make a hypothesis development: 

Interviewing and Moderating Variables: 

Null and Alternative Hypothesis: 

H0: MSS = 0 

H1: MSS ≠ 0 

H0: improvement in sale strategies will not 

cause any improvement in sales of ladies shoes. 

H1: improvement in sale strategies will cause an 

improvement in sales volume of NIKE ladies 

shoes. 

The data generated by using primary research 

method, through questionnaires, is then 

processed on SPSS (statistical program). The 

data can then be presented as follows: 

Areas of 

Behavio 

r 

Know 

how 

about 

Nike 

Shoes 

Advertis 

ement 

likelines 

s 

Before 

and 

After 

sale 

service 

Highly 

Dissati 

sfied 

Dissati 

sfied 

Satis 

fied 

1 2 3 4 

1 2 3 4 

1 2 3 4 

High 

ly 

Satis 

fied 

In the sample of 50, 5% responded as 

‘satisfied’, while 3% as ‘highly dissatisfied’. 

Then, data processing methodology was used as 

data was random. In data analysis, there were; 

demography of respondents, CIL, shopping 

season, brand collection, factors and forces 

influencing comparison with other bands. The 

data was then presented with the help of bar 

charts and pie charts which ultimately helped 

management in the decision making process 

before, launching its new product in the market. 

In the end, I would like to say that statistics is 

not just about counting numbers on fingertips. 

Instead, it is about the manipulation of data in 

different fields based on your daily routine life. 

The sample data selection support H1 and reject 

H0. We can use α = 0.05 and z-test of H1 as 

sample size is more than 30. 



Statistics 

Does IQ Matter? 

Mehvish Rizvi and Samra Qadir 

“An intelligence quotient (IQ) is a score 

derived from one of several different 

standardized tests designed to assess 

intelligence. When modern IQ tests are 

constructed, the average score within an age 

group is set to 100 and the standard deviation to 

15. Today almost all IQ tests adhere to the 

assignment of 15 IQ points to each standard 

deviation (SD), but this has not been the case 

historically. Approximately 95% of the 

population has scores within two SDs of the 

mean, i.e., an IQ between 70 and 130.’’ 

Regression analysis is also used to understand 

which among the independent variables are 

related to the dependent variable, and to explore 

the forms of these relationships. In restricted 

circumstances, regression analysis can be used 

to infer causal relationships between the 

independent and dependent variables.” 

We will check the evidence that Does IQ play 

any role in the progress (GPA) of student, that 

is,how much the progress of any student 

depends upon his IQ? 

Here, intelligence and hard work complement 

each other. They both work side by side. One is 

God gifted and the other requires self 

disciplining. Many psychologists say that IQ 

does not matter in good progress report; it plays 

only a little role as compared to the struggle 

made by them. 

Now let us define what is IQ? 

We have taken an example to check the 

relationship between the students’ IQ and their 

Progress report (GPA). We can measure this 

relationship by Regression Analysis. Now, what 

is Regression analysis 

“In statistics, Regression analysis includes 

many techniques for modeling and analyzing 

several variables, when the focus is on the 

relationship between a dependent and one or 

more independent variables. Regression analysis 

is widely used for prediction and forecasting. 

We did a research on how IQ levels affect the 

GPA of any student and to what extent the GPA 

depends upon the IQ level. As statisticians, we 

defined our hypothesis “IQ affects the GPA 

report” and by using the application of 

regression analysis we estimated a regression 

line. One advantage of Regression line is that it 

tells us the dependence of response variable. 

(GPA) on Predictor Variable (IQ): 

For this purpose we selected 10 students of 

different IQ levels, having different GPA as 

well. The data is as shown below: 



Statistics 

No. of student GPA IQ Level 

1 3.40 123 

2 3.00 125 

3 3.50 118 

4 2.89 80 

5 3.00 130 

6 2.70 101 

7 3.70 129 

8 3.10 108 

9 2.93 105 

10 3.02 107 

From the above data we have estimated our 

regression line “GPA = 1.81 + 0.0117 IQ”. In 

this regression line, the dependent variable is 

GPA and the independent variable is IQ. This 

relationship shows that GPA depends only 1.1% 

on IQ levels. Intelligence is only a tool for 

success. The main role is played by the ‘hard 

work’ done by the student. Now, it’s on him that 

how much he uses this tool to move ahead. 

In our research, we tested the IQ levels 

by a simple IQ test; the results are shown in the 

table above. Higher the IQ, higher was the GPA 

level. Although intelligence is blessed by 

Almighty Allah to which there is no alternative, 

but one can improve the results by his own 

struggle and hard work. The results can be even 

better if we work hard along with using the 

intelligence gifted to us. 

NEW METRIC FOR OBESITY 

Researchers have developed a new metric to 

measure obesity, called A Body Shape Index, 

or ABSI, that combines the existing metrics of 

Body Mass Index (BMI) and waist 

circumference and shows a better correlation 

with death rate than do either of these 

individual measures.

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