Inferential Statistics - DAY 4 - B.Ed - AIOU

 Inferential statistics is of vital importance in educational
research.
 It is used to make inferences about the population on
the bases of data obtained from the sample.
 inferential statistics helps researchers to make
generalization about a population based on the data
obtained from the sample.

 Descriptive statistics only gives us the central values,
dispersion or the variability of the data
 But
 inferential statistics leads us to take a decision about the whole
population and in the end to any conclusion
 Inferential statistics enables us to infer from the data obtained
the sample what the population might think

 Inferential statistics has two broad areas
 i) Estimating Parameter
 This means taking a statistics from the sample data (e.g. the sample mean)
and
 saying something about population parameter (e.g. the population mean).
 ii) Hypothesis testing
 This is where a researcher can use sample data to answer research
questions.
Inferential statistics deals with two or more than two variables. If in an
analysis there are two variables it is called bivariate analysis and if the
variables are more than two it is called multivariate analysis

 The logic of inferential statistics starts with a
hypothesis about a relationship of two or more attributes
or concepts observed in a population

 The purpose of inferential statistics is to
determine whether the findings from the sample
can generalize - or be applied - to the entire
population. There will always be differences in
scores between groups in a research study

 Inferential statistics allows us to
use what we've learned from descriptive statistics.
 Using data from the past and the resulting descriptive stats I.e.,
mean, mode, median, standard deviation, etc. infential statistics
extend beyond the immediate data.
 Inferential stats are used to infer from the sample data what the
population might think.

 Hypothesis testing is a statistical method that uses
sample data to evaluate a hypothesis aboutt a population
parameter (Gravetter & Wallnau, 2002)
 A hypothesis test is usually used in context of a research
study. Depending on the type of research and the type of
data, the details of the hypothesis test will change from
one situation to another.
 Hypothesis testing is a formalized procedure that
follows a standard series of operations

 The process of hypothesis testing goes through
following four steps.
 i) Stating the Hypothesis
 The process of hypothesis testing begins by stating a
hypothesis about the unknown population.
 Usually, a researcher states two opposing hypotheses.
And both
hypotheses are stated in terms of population parameters.

 The first and most important of two hypotheses is called null hypothesis.
A null hypothesis states that the treatment has no effect.
 The null hypothesis is denoted by the symbol Ho (H stands for
hypothesis and 0 denotes that this is zero effect).
 The null hypothesis (Ho) states that in the general population there is no
change, no difference, or no relationship. In an experimental study, null
hypothesis (Ho) predicts that the independent variable (treatment) will
have no effect on the dependent variable for the population.

 The alternative hypothesis (H1) states that
there is a change, a difference, or a
relationship for the general population. In an
experiment, H1 predicts that the independent
variable (treatment) will have an effect on
the dependent variable.

In a common practice, a researcher uses the data from the sample to evaluate
the authority of null hypothesis.
The data will either support or deny the null hypothesis.
To formalize the decision process, a researcher will use null hypothesis
 to predict exactly what kind of sample should be obtained if the treatment
has no effect.
 In particular, a researcher will examine all the possible sample means that
could be obtained if the null hypothesis is true.

 The next step in hypothesis testing is to obtain the sample data.
 The raw data are summarized with appropriate statistics such as
mean, standard deviation etc.
 Then it is possible for the researcher to compare the sample
mean with the null hypothesis.

 In the final step the researcher decides, in the light of analysis
of data, whether to accept or reject the null hypothesis. If
analysis of data supports the null hypothesis, he accepts it and
vice versa.

 As hypothesis test uses information obtained from the
Sample in this situation, there is always the probability
of reaching incorrect conclusion.

 Generally two kinds of errors can be made
 i) Type I Errors
 A type I error occurs when a researcher rejects a null hypothesis that is actually
true. It means that the researcher concludes that the treatment does have an effect
when in fact the treatment has no effect.
 Type I error is not a stupid mistake in the sense that the researcher is overlooking
 something that should be perfectly obvious.
 ii) Type II Errors
 A type II error occurs when a researcher fails to reject the null hypothesis that is
really false. It means that a treatment effect really exists, but the hypothesis test
has failed to detect it. This type of error occurs when the effect of the treatment is
relatively small.

 A t-test is a useful statistical technique used for comparing
mean values of two data sets obtained from two groups.
 The comparison tells us whether these data sets are different
from each other.
 It further tells us how significant the differences are and if
these differences could have happened by chance.

 There are a number of t-test available but two main types
independent sample t-test and
paired sample t-test are most commonly used.
 i) Independent sample t-test
 Independent sample t-test is used when there are two different
independent groups
of people and the researcher is interested to compare their scores.
In this case the
 researcher collects information from two different groups of
people on only one occasion.

 ii) Paired sample t-test
 Paired sample t-test is also called repeated
measures.
 It is used when the researcher is interested in
comparing changes in the scores of the same group
tested at two different occasions

 A correlation is a relationship between two variables. The
purpose of using correlation in research is to determine the
degree to which a relationship exists between two or more
variables.
 observed as they naturally exist in the environment.
 Correlation requires two separate scores for each individual
(one score from each of two variables). These scores are
normally identified as X and Y and can be presented in a table
or in a graph.

 A correlation measures three characteristics of the relationship between X
and Y.
 i) The Direction of the Relationship
 The direction of the relationship can be classified into two basic categories:
positive and negative
 Inn a positive correlation both variables tend to change into same direction.
When variable X increases, the variable Y also increases. And if the
variable X decreases, the variable Y also decreases. In other words we can
say that both variables are directly proportional to each other

 In a negative correlation both variables do not tend to change into same
direction.
 They go in opposite direction of each other. When the variable X
increases, the variable Y decreases. And if the variable X decreases, the
variable Y increases. In other words we can say that both variables are
indirectly proportional to each other.
 The direction of the relationship is identified by the sign of the
correlation. A positive sign (+) indicates positive relationship. A negative
sign (−) indicates negative relationship.

 ii) The form of the Relationship
 The form of correlation measures how well the data fit the specific form being
considered.
 For example, a linear correlation measures how well the data points fit
 on a straight line
 iii) The Degree of the Relationship
 The degree of relationship is measured by the numerical value of the correlation.
 This value varies from 1.00 to – 1.00.
 A perfect correlation is always identified by a correlation of 1.00 and indicates a
perfect fit. + 1.00 will indicate perfect positive
 correlation and –1.00 will indicate perfect negative correlation.
 A correlation of 0 indicates no correlation or no fit at all.

 The most commonly used correlation is the Pearson Correlation. It is also known
as Pearson product-moment Correlation. It measures the degree and the
direction of linear relationship of between two variables. It is denoted by r, and r
= degree to which X and Y vary together / degree to which X and Y vary
separately = co-variability of X and Y / variability of X and Y vary separately
 To calculate the Pearson correlation we use the formula
 where SP is the sum of the product of deviation
 SS is sum of squares, SSx is the sum of squares of the variable X and SSy is the
sum of squares of variable Y

 i) Prediction
 If two variables are known to be related in some systematic way, it is
possible to use one variable to make prediction about the other.
 For example, when a student seeks admission in a college, he is required
to submit a great deal of personal information, including his scores in
SSC annual/supplementary examination. The college officials want this
information so that they can predict that student’s chance of success in
college.

ii) Validity
One common technique for demonstrating validity is to use correlation.
iii) Reliability
A measurement procedure is reliable if it produces stable and consistent
measurement. It means a reliable measurement procedure will produce the
same (or
nearly same) scores when the same individuals are measured under the same
Conditions.

 iv) Theory Verification
 Many psychological theories make specific predictions about the
relationship between two variables.
 For example, a theory may predict a relationship between
brain size and learning ability; between the parent IQ and the child IQ etc. In
each
case, the prediction of the theory could be tested by determining the
correlation
between two variables

 The most commonly used measure of relationship is the Pearson
correlation. It measures the degree of linear relationship between two
variables and is used with interval or ratio data.
 i) The Spearman correlation is designed to measure the relationship
between variables measured on an ordinal scale of measurement.
 ii) The Spearman correlation is used when the researcher wants to
measure the consistency of a relationship between the variables X and Y

Inferential Statistics - DAY 4 - B.Ed - AIOU

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Inferential Statistics - DAY 4 - B.Ed - AIOU