Kinds Of Variables Kato Begum

Kinds of variable:Kinds of variable: The independent variable:The independent variable:It is the factor that is measured, manipulated It is the factor that is measured, manipulated

or selected by the experimenter to or selected by the experimenter to determine its relationship to an observed determine its relationship to an observed phenomenon. It is a stimulus variable or phenomenon. It is a stimulus variable or input operates within a person or within his input operates within a person or within his environment to effect behavior. environment to effect behavior. Independent variable may be called factor Independent variable may be called factor and its variation is called levels.and its variation is called levels.

The dependent variable:The dependent variable:The dependent variable is a response variable The dependent variable is a response variable

or output. The dependent variable is the or output. The dependent variable is the factor that is observed and measured to factor that is observed and measured to determine the effect of the independent determine the effect of the independent variable; it is the factor that appears, variable; it is the factor that appears, disappears, or varies as the researcher disappears, or varies as the researcher introduces, removes, or varies the introduces, removes, or varies the independent variables.independent variables.

Moderate variable:Moderate variable: It is the factor that is measured, manipulated or selected It is the factor that is measured, manipulated or selected

by the experimenter to discover whether it modifies the by the experimenter to discover whether it modifies the relationship of the independent variable to an observed relationship of the independent variable to an observed phenomenon. The term moderate variable describes a phenomenon. The term moderate variable describes a special type of independent variable, a secondary special type of independent variable, a secondary independent variable selected to determine if it affects the independent variable selected to determine if it affects the relationship between the study’s primary independent relationship between the study’s primary independent variable and its dependent variable.variable and its dependent variable.

Control variable:Control variable: Control variables are factors controlled by the Control variables are factors controlled by the

experimenter to cancel out or neutralized any effect they experimenter to cancel out or neutralized any effect they might otherwise on the observed phenomena. A single might otherwise on the observed phenomena. A single study can not examine all of the variables in a situation study can not examine all of the variables in a situation (situational variable) or in a person (dispositional variable); (situational variable) or in a person (dispositional variable); some must be neutralized to guarantee that they will not some must be neutralized to guarantee that they will not exert differential or moderating effects on the relationship exert differential or moderating effects on the relationship between the independent variables and dependent between the independent variables and dependent variables.variables.

Intervening variable:Intervening variable: An intervening variable is the factor that theoretically An intervening variable is the factor that theoretically

effects observed phenomena but can not be seen, effects observed phenomena but can not be seen, measured, or manipulated; its effects must be inferred measured, or manipulated; its effects must be inferred from the effects of the independent and moderate variable from the effects of the independent and moderate variable on the observed phenomena.on the observed phenomena.

Consider the hypothesisConsider the hypothesis

Among students of the same age and Among students of the same age and intelligence, skill performance is directly intelligence, skill performance is directly related to the number of practice trials, the related to the number of practice trials, the relationship being particularly strong among relationship being particularly strong among boys, but also holding, though less directly, boys, but also holding, though less directly, among girls’. this hypothesis that indicates among girls’. this hypothesis that indicates that practice increases learning, involve that practice increases learning, involve several variables.several variables.

Independent variableIndependent variable:: number of number of practice trailpractice trail

Dependent variableDependent variable:: skill performance skill performance Control variableControl variable: : age, intelligence age, intelligence Moderate variableModerate variable:: gender gender Intervening variableIntervening variable:: learning learning

Steps in data processingSteps in data processing

Quantitative Analysis StrategiesQuantitative Analysis Strategies

There are two types of quantitative analysis:There are two types of quantitative analysis:

DescriptiveDescriptive: Utilizes numerical and graphical methods : Utilizes numerical and graphical methods to find patterns in a data set, summarizes the to find patterns in a data set, summarizes the information, and present information in a convenient information, and present information in a convenient form.form.

InferentialInferential: Utilizes a : Utilizes a samplesample to make estimates, to make estimates, decisions, or predictions about decisions, or predictions about populationpopulation. It consists of . It consists of Estimation technique and Hypothesis of testing.Estimation technique and Hypothesis of testing.

Variable, Data & types of dataVariable, Data & types of data Variable:Variable:

Characteristic or property of an individual population unitCharacteristic or property of an individual population unit The value of the characteristic may vary among units in a population.The value of the characteristic may vary among units in a population.Kinds of variable:Kinds of variable:The independent variable:The independent variable:The dependent variable:The dependent variable:Moderate variable:Moderate variable:Control variable:Control variable:Intervening variable:Intervening variable:

Data:Data: The values of the observations recorded for The values of the observations recorded for variablesvariables or a bunch of values for one or more variables. or a bunch of values for one or more variables.

Types of Data:Types of Data: Quantitative or QualitativeQuantitative or Qualitative

Quantitative Data (Measurement):Quantitative Data (Measurement): Data that are measured on a naturally occurring numerical scale.Data that are measured on a naturally occurring numerical scale.

Qualitative Data (Categorical):Qualitative Data (Categorical): Data that cannot be measured on a naturally occurring numerical scale.Data that cannot be measured on a naturally occurring numerical scale. Can only be classified into a group of categories (classes).Can only be classified into a group of categories (classes).

Examples of qualitative and quantitative dataExamples of qualitative and quantitative data

Examples of quantitative data: Temperature, Height, Weight, Examples of quantitative data: Temperature, Height, Weight, Age, Student score, Total students in the school etc.Age, Student score, Total students in the school etc.

Examples of qualitative data: Sex, Grades (A, B, C, D or E), Examples of qualitative data: Sex, Grades (A, B, C, D or E), Competency in English (Full, moderate, little, not at all) etc.Competency in English (Full, moderate, little, not at all) etc.

Identify qualitative or quantitative from the following:Identify qualitative or quantitative from the following:

Type of institution (public or private), System of education Type of institution (public or private), System of education (Pakistani, British or American), Medium of instruction (Pakistani, British or American), Medium of instruction (English, Urdu, Other), Importance of communication skills (English, Urdu, Other), Importance of communication skills (not at all, a little, quite, very, most), number of teachers in the (not at all, a little, quite, very, most), number of teachers in the institution, Years of schoolinginstitution, Years of schooling

More on Qualitative and Quantitative DataMore on Qualitative and Quantitative Data

Qualitative data may be:Qualitative data may be: Nominal DataNominal Data

Categories cannot be ranked.Categories cannot be ranked. Ordinal DataOrdinal Data

Categories can be ranked or meaningfully ordered.Categories can be ranked or meaningfully ordered.

Quantitative data may be:Quantitative data may be: Interval DataInterval Data

Differences between values have meaning, but ratios between values have Differences between values have meaning, but ratios between values have none.none.

Zero is arbitrary.Zero is arbitrary. Can add/subtract but cannot multiply/divide. Can add/subtract but cannot multiply/divide.

Ratio DataRatio Data Ratios between values have meaning.Ratios between values have meaning. Zero is the absence of the characteristic being measured.Zero is the absence of the characteristic being measured. Can add/subtract/multiply/divide.Can add/subtract/multiply/divide.

Summary of Data ClassificationSummary of Data Classification

N om in a l O rd in a l

Q u a lita t ive

In te rva l R a tio

Q u an tita tive

D ata

Increasing Complexity

Presentation of DataPresentation of Data

Statistical data are generally presented by: Statistical data are generally presented by:

TablesTables-- Frequency table:Frequency table:-- Cross tabulationCross tabulation

GraphsGraphs-- For Qualitative dataFor Qualitative data-- For Quantitative dataFor Quantitative data

Frequency table and cross tabulationFrequency table and cross tabulation

What is a Frequency table?What is a Frequency table?

It is a tabular summary of a set of data showing the frequency (or number) It is a tabular summary of a set of data showing the frequency (or number) of items in each of several non-overlapping (with each data value of items in each of several non-overlapping (with each data value belonging to one and only one group or class) groups or classes.belonging to one and only one group or class) groups or classes.

Note: In Note: In qualitative dataqualitative data, class is one of the category of the variable and in , class is one of the category of the variable and in quantitative dataquantitative data it is the range of values established to divide the data into it is the range of values established to divide the data into categories.categories.

What is Cross tabulation?What is Cross tabulation?

It is the tabular summary of a set of data when two or more variables are It is the tabular summary of a set of data when two or more variables are observed at the same time.observed at the same time.

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Central Tendency & its Central Tendency & its typestypes

Value(s) that define the tendency of Value(s) that define the tendency of the data to cluster around or center the data to cluster around or center about certain numerical values.about certain numerical values.

Main types of central tendency are:Main types of central tendency are: Mean (arithmetic mean),Mean (arithmetic mean), Median, andMedian, and ModeMode

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Mean (or Arithmetic Mean)Mean (or Arithmetic Mean)

Sum of the values of all the Sum of the values of all the observations in a data set divided by observations in a data set divided by the total number of observations. the total number of observations. Mathematically:Mathematically:

The Sample Mean ( ) = =The Sample Mean ( ) = =

The Population Mean ( ) = = The Population Mean ( ) = =

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MedianMedian The middle point of the set of data, i.e. The middle point of the set of data, i.e.

exactly half of the data points are above exactly half of the data points are above the median and exactly half are below.the median and exactly half are below. If the number of observations are odd, it If the number of observations are odd, it

is the middle point of the ordered set of is the middle point of the ordered set of data. data.

Median = observationMedian = observation If the number of observations are even, If the number of observations are even,

it is the average (mean) of the two it is the average (mean) of the two middle points of the ordered set of data. middle points of the ordered set of data.

Median = Median = observationsobservations

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ModeMode

The measurement(s) which occurs The measurement(s) which occurs with the greatest frequency in the with the greatest frequency in the sample, i.e. the most common sample, i.e. the most common point(s):point(s): A uni-modal data set contains only one A uni-modal data set contains only one

mode.mode. A bimodal data set contains two modes.A bimodal data set contains two modes. And so on….And so on….

Decision about data Decision about data symmetry using mean and symmetry using mean and

medianmedian If the median is less than the mean, the If the median is less than the mean, the

data set is skewed right (extreme data data set is skewed right (extreme data in right tail which increases the mean).in right tail which increases the mean).

If the median is greater than the mean, If the median is greater than the mean, the data set is skewed left (extreme the data set is skewed left (extreme data in the left tail which decreases the data in the left tail which decreases the mean).mean).

If median equals the mean, the data If median equals the mean, the data set is said to be set is said to be symmetrical.symmetrical.

Measures of Data Variability

• Knowing central tendencies (mean, median, mode) isn’t enough. Also need a method for determining how close the data is clustered around its center point(s).

• The most typical measures of data variability:– Range,– Variance, and– Standard Deviation.

Range• Simplest measure of variability.

• Calculated by subtracting the smallest measurement from the largest measurement.

• It is not a good measure of variability. i.e. if two ranges are same, it does not mean that the spread is same.

Variance

• It is the sum of the square of the deviation from the mean divided by (n-1) for a sample and is denoted by s2.

• Similarly, the sum of the square of the deviation from the mean divided by N for the population and is denoted by 2.

Note: Deviations are squared to remove effects of negative differences.

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Standard Deviation• While variance does not provide a useful metric (i.e. “units

squared”), taking the positive square root of the variance provides a metric which is the same as the data itself (i.e. “units”).

– Sample Standard Deviation - s

– Population Standard Deviation -

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Application of mean & standard deviation to observe the behavior of

the data

• Data can be standardized using mean & standard deviation. Thus, for a single data set, variability can be discussed in terms of how many members of the data set fall within one, two, three, or more standard deviations of the mean.

Standard ScoreStandard Score

It uses a common scale to indicate how an It uses a common scale to indicate how an individual compare to other individual in group. individual compare to other individual in group. These scores are particularly helpful in These scores are particularly helpful in comparing an individual’s relative position. The comparing an individual’s relative position. The two standards score are the most frequently two standards score are the most frequently used in educational research,used in educational research,

1. 1 Z – Score1. 1 Z – Score 2. T- Score2. T- Score 1. Z – Score1. Z – Score The simplest form of standard score is the 1. Z – The simplest form of standard score is the 1. Z –

Score. It expresses how far a raw score is from Score. It expresses how far a raw score is from the mean in standard deviation units. A big the mean in standard deviation units. A big advantage of Z – Score is that they allow raw advantage of Z – Score is that they allow raw scores on different tests to be compared Z – scores on different tests to be compared Z – ScoreScore

ExampleExample a student received raw scores of 60 on a biology test a student received raw scores of 60 on a biology test

and 80 on a chemistry test. A naïve observer might be and 80 on a chemistry test. A naïve observer might be inclined to infer that the student was doing better in inclined to infer that the student was doing better in chemistry than in biology. But this might be unwise, chemistry than in biology. But this might be unwise, for how well the student is comparatively cannot be for how well the student is comparatively cannot be determined until we know the mean and standard determined until we know the mean and standard deviation for each distribution of score. Let us suppose deviation for each distribution of score. Let us suppose the mean is 50 in biology and 90 in chemistry. Also the mean is 50 in biology and 90 in chemistry. Also assume the standard deviation on biology deviation is assume the standard deviation on biology deviation is 5 on chemistry is 10. What does this tell us? 5 on chemistry is 10. What does this tell us?

Comparison of raw scores and Z scores on two tests.Comparison of raw scores and Z scores on two tests. Test Score Raw Score Mean SD Z. Score Percentile Test Score Raw Score Mean SD Z. Score Percentile

RankRank BioBio 60 50 5 2 98 60 50 5 2 98 Che 80 90 10 -1 16 Che 80 90 10 -1 16

Probability and z scoreProbability and z score.. Probability:Probability:

It refers to the likely hood of an event occurring It refers to the likely hood of an event occurring and a percentage stated in decimal form. For and a percentage stated in decimal form. For example if there is a probability that an event example if there is a probability that an event will occur 25 percent of the time, this event can will occur 25 percent of the time, this event can be said to have a probability of .25.be said to have a probability of .25.

HypothesisHypothesisThere are two kinds of hypothesis; one is the There are two kinds of hypothesis; one is the predictive outcome of the study called research predictive outcome of the study called research hypothesis where as the hypothesis where as the null hypothesisnull hypothesis is the is the assumption that there is no relationship assumption that there is no relationship between the variables or in the population..between the variables or in the population..

Co relational analysisCo relational analysis

It shows the existing relationship between the It shows the existing relationship between the variables, with no manipulation of variables. It variables, with no manipulation of variables. It is also used to analyze data containing two is also used to analyze data containing two variables as well as examine the reliability and variables as well as examine the reliability and validity of the data collection procedure.validity of the data collection procedure.

TypesTypes Highly positiveHighly positive (when the variables are (when the variables are

directly proportional to each other)directly proportional to each other) Low correlationLow correlation (when there is no correlation (when there is no correlation

between the variables)between the variables) Negative correlationNegative correlation (when the variables are (when the variables are

inversely proportional to each other)inversely proportional to each other)

When the researcher wants to make When the researcher wants to make inferences to the population, he will have inferences to the population, he will have to examine their statistical significance.to examine their statistical significance.

Statistical significance can be determined Statistical significance can be determined if correlation have been obtained from the if correlation have been obtained from the randomly selected samples. randomly selected samples.

Level of significance is very important Level of significance is very important since it relates directly to whether the null since it relates directly to whether the null hypothesis is rejected or not.hypothesis is rejected or not.

Depends on the size of the correlationSignificance of correlation

Size of the sample

There are two waysThere are two ways Multiple regressionsMultiple regressions Factor analysisFactor analysis Multiple regressionsMultiple regressions Through multiple regressions it is possible to Through multiple regressions it is possible to

examine the relationship and predictive power of examine the relationship and predictive power of one or more independent variables with the one or more independent variables with the dependent variables. it shows which variables are dependent variables. it shows which variables are significant in their contribution explaining the significant in their contribution explaining the variance in the dependent variable and how much variance in the dependent variable and how much they contribute.they contribute.

Discriminate analysisDiscriminate analysis Which contribution of variables distinguishes Which contribution of variables distinguishes

between one or more categories of dependent between one or more categories of dependent variables?variables?

Factor analysisFactor analysis In it independent variable is not related to In it independent variable is not related to

dependent variables as in regression, but rather dependent variables as in regression, but rather operates within a number of independent operates within a number of independent variables without a need to have dependent variables without a need to have dependent variables. In factor analysis the interrelationships variables. In factor analysis the interrelationships between and among the variables of the data are between and among the variables of the data are examined in an attempt to find out how many examined in an attempt to find out how many independent dimensions can be identified in the independent dimensions can be identified in the data. It thus provides information on the data. It thus provides information on the characteristics of the variables. This type of characteristics of the variables. This type of analysis is based on the assumption that variables analysis is based on the assumption that variables measuring the same factor will be highly related. measuring the same factor will be highly related. Where as variables measuring different factors will Where as variables measuring different factors will have low correlations with one another.have low correlations with one another.

T-testT-test It is used to compare the means of the two groups. It is used to compare the means of the two groups. TypesTypes T-testT-test for independent means for independent means T-testT-test for correlate means for correlate means The result of t-test provides the researcher with a t-value.The result of t-test provides the researcher with a t-value. ExampleExample A researcher is comparing the performance of the two A researcher is comparing the performance of the two

randomly selected groups learning French by two different randomly selected groups learning French by two different methods. The experimental group learns with the aid of methods. The experimental group learns with the aid of computer while the control group is exposed to the computer while the control group is exposed to the teacher. The researcher investigates the effects of the teacher. The researcher investigates the effects of the computer practice on students’ achievement on French. computer practice on students’ achievement on French. After three months both the groups undergo an After three months both the groups undergo an achievement test.achievement test.

The researcher uses t- test to examine whether there are The researcher uses t- test to examine whether there are differences in the achievements of the two groups.differences in the achievements of the two groups.

To have a deep insight of the data through descriptive To have a deep insight of the data through descriptive statistics, first it have a mean X,S D and sample size N of statistics, first it have a mean X,S D and sample size N of the data .there must be a mean of experimental or control the data .there must be a mean of experimental or control group.group.

ANOVA (one way analysis of ANOVA (one way analysis of variance)variance)

One way analysis of variance is used to examine the One way analysis of variance is used to examine the differences in more than two groups.differences in more than two groups.

The analysis is performed on the variances of the The analysis is performed on the variances of the groups, focusing on whether the variability between the groups, focusing on whether the variability between the groups is greater that the variability within the groups groups is greater that the variability within the groups value is the ratio between variances over the within the value is the ratio between variances over the within the variances.variances.

F = F = between group between group variancevariance

Within group varianceWithin group variance If the difference between the groups is greater than the If the difference between the groups is greater than the

difference within the groups, than F value is significant difference within the groups, than F value is significant and the researcher can reject the null hypothesis. if the and the researcher can reject the null hypothesis. if the situation is inverse than F value is significant.situation is inverse than F value is significant.

ChiChi--squaresquare The chi test allows analysis of one, two or more nominal The chi test allows analysis of one, two or more nominal

variables. it is based on the comparison between variables. it is based on the comparison between expected frequencies and actual, obtained frequencies.expected frequencies and actual, obtained frequencies.

ExampleExample A researcher might want to compare how many male A researcher might want to compare how many male

and female teachers favor a new curriculum, to be and female teachers favor a new curriculum, to be instituted in a particular school district. he asks a instituted in a particular school district. he asks a sample of 50 teachers ,if they favor or oppose new sample of 50 teachers ,if they favor or oppose new curriculum. if they do not differ significantly in their curriculum. if they do not differ significantly in their responses, then we would expect hat about the same responses, then we would expect hat about the same proportion of males and females would be in favor(or proportion of males and females would be in favor(or opposed to)instituting the curriculum.opposed to)instituting the curriculum.

Degree of freedomDegree of freedom Number of scores in a distribution that are free to vary-Number of scores in a distribution that are free to vary-

that is, that are not fixed.that is, that are not fixed.

Use SPSS Programme Use SPSS Programme For CalculationFor Calculation For AnalysisFor Analysis

The EndThe End

Allah HafizAllah Hafiz

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