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# Kinds Of Variable

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### Kinds Of Variable

1. 1. Kinds of variable The independent variable: It is the factor that is measured, manipulated or selected by the experimenter to determine its relationship to an observed phenomenon. It is a stimulus variable or input operates within a person or within his environment to effect behavior. Independent variable may be called factor and its variation is called levels. The dependent variable: The dependent variable is a response variable or output. The dependent variable is the factor that is observed and measured to determine the effect of the independent variable; it is the factor that appears, disappears, or varies as the researcher introduces, removes, or varies the independent variables. Moderate variable: It is the factor that is measured, manipulated or selected by the experimenter to discover whether it modifies the relationship of the independent variable to an observed phenomenon. The term moderate variable describes a special type of independent variable, a secondary independent variable selected to determine if it affects the relationship between the study’s primary independent variable and its dependent variable. Control variable: Control variables are factors controlled by the experimenter to cancel out or neutralized any effect they might otherwise on the observed phenomena. A single study can not examine all of the variables in a situation (situational variable) or in a person (dispositional variable); some must be neutralized to guarantee that they will not exert differential or moderating effects on the relationship between the independent variables and dependent variables. Intervening variable: An intervening variable is the factor that theoretically effects observed phenomena but can not be seen, measured, or manipulated; its effects must be inferred from the effects of the independent and moderate variable on the observed phenomena. Consider the hypothesis Among students of the same age and intelligence, skill performance is directly related to the number of practice trials, the relationship being particularly strong among boys, but also holding, though less directly, among girls’. this hypothesis that indicates that practice increases learning, involve several variables. Independent variable: number of practice trail Dependent variable: skill performance Control variable: age, intelligence Moderate variable: gender Intervening variable: learning
2. 2. Causes relationship effects Independent Variables Moderate Intervening Dependent variables variables variables Control variables Steps in data processing Raw data Editing Coding Analysis Interview Developing a code book Developing a Questionnaires frame of analysis observation Pre-testing the code book Analysis Interview guid Sec.sources Coding the data Computer Verifying the Manual coded data Data There are two types of data. Qualitative Data and Quantitative Data Qualitative Data is further divided into Nominal data and ordinal data. Nominal data As it obvious from the name nominal means “to give names”. In social sciences, the qualitative cannot be measured or simplified. To calculate this type of data, it is named and categorized. This named or categorized data is called nominal data. Ordinal data The friendly term ordinal gives a meaning of “ordered or arranged”. This data is arranged into orders, categorizing individuals as more than or less than one another. After nominalising the data into categories, it is then ordered or arranged to get the desired result. Although ordinal measurement may require more difficult processes but it gives more informative, précised data. Interval data It is the data or score as units of equal appearing magnitude. The interval data can be added subtracted but cannot be multiplied or divided. Ratio Data
3. 3. It has a true zero value, that is, a point that represents the complete absence of the measured characteristics, ratios are comparable at different points. It is much more frequently used in the physical sciences than in behavioral sciences; For example 9 ohms indicates three times the resistance of 3 ohms, while 6 ohms stands in the same ratio to 2 ohms. For example; Listed below are the scores of a group of students on a mid semester English test. 64,61,56,51,52,34,64,31,31,31,59,61,34,59,51,38,38,38,36,36. How many students received a score of 36? Did most of the students receive a score above 50? Unordered data is difficult to tell, to make any sense out of this data. We must put it into some sort of order. One of the most common ways to do this is to prepare a frequency distribution. This is done by listing, in rank order from high to low, with tallies, to indicate the number of subjects receiving each score. Often score in distribution are grouped into intervals. This results in grouped frequency distribution. Example of a frequency distribution Raw score frequency 64 2 61 2 59 2 56 1 52 1 51 2 38 3 36 2 34 2 31 3 -------- N = 20 Table of a Grouped Frequency Distribution Raw Score Intervals of Five Frequencies 60 -- 64 4 55 – 59 3 50 – 54 3 45 – 49 0 40 – 44 0 35 – 39 5 30 – 34 5 ------------- N=20 Frequency Polygon
4. 4. Average It enables a researcher to summarize the data in a frequency distribution with single number. It is of three kinds; Mode Median, Mean. The mode The mode is the most frequent score in a distribution. The score attained by more students than any other score e.g. in a distribution, 25, 20,19,17,16,16,13,12. The mode is 16. What about this distribution? 25, 20, 19, 19, 17, 16, 16, 12, and 11. This distribution has two modes, 19 and 16. Hence it is called bimodal distribution. This mode does not tell us very much about a distribution. However, it is not often used in educational research. Median (the mid point) The median is the point below and above 50% of the score in a distribution fall. This is a distribution 1, 2, 3, 4, 5. The median is 3. If the numbers are even in a distribution then the median is the point halfway between the two middle most scores. In a distribution; 2, 4,6,8,10,12. The median is 7. The Mean It is determined by adding up all of the scores and then dividing this sum by the total number of scores. X where sum of X represents any raw score value, n represents the total number of scores and X represents the mean. All the averages give us ample information data by a single value. But sometimes, the researcher cannot get the required results from the data by using average. Then there is a need for measures researchers can use to describe the spread or variability that exists within a distribution because average tells us the total behavior of data by single unit that sometimes leads to confusion and ambiguity. To calculate the position of the data or deviation there are certain ways. 1. Measures of Data Variability: Knowing central tendencies (mean, median, and 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.
5. 5. • 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 s2. Note: Deviations are squared to remove effects of negative differences. 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 - s Application of mean & standard deviation to observe the behavior ofthe 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 Score: It uses a common scale to indicate how an individual compare to other individual in group. These scores are particularly helpful in comparing an individual’s relative position. The two standards score are the most frequently used in educati nal research, o 1. 1 Z – Score 2. T- Score Z – Score The simplest form of standard score is the Z – score. It expresses how far a raw score is from the mean in standard deviation units. A big advantage of Z – Score is that they allow raw scores on different tests to be compared. Researchers use a formula to convert a raw score into z-score Z score = raw score – mean Standard deviation For example a student received raw scores of 60 on a biology test and 80 on a chemistry test. A naïve observer might be inclined to infer that the student was doing better in chemistry than in biology. But this might be unwise, for how well the student is comparatively cannot be determined until we know the mean and standard deviation for each distribution of score. Let us suppose the mean is 50 in biology and 90 in chemistry. Also assume the standard deviation on biology deviation is 5 and on chemistry is 10. What does this tell us? The comparison of raw score and Z score on two tests. Test score Raw score Mean SD Z Score % rank Bio 60 50 5 2 98 Chemistry 80 90 10 -1 16 Probability and Z score.
6. 6. Probability: It refers to the likely hood of an event occurring and a percentage stated in decimal form. For example if there is a probability that an event will occur 25 percent of the time, this event can be said to have a probability of .25. Hypothesis: There are two kinds of hypothesis; one is the predictive outcome of the study called research hypothesis where as the null hypothesis is the assumption that there is no relationship between the variables or in the population.. Co relational analysis: It shows the existing relationship between the variables, with no manipulation of variables. It is also used to analyze data containing two variables as well as examine the reliability and validity of the data collection procedure. Types of correlation: Highly positive; (When the variables are directly proportional to each other) Low correlation; (When there is no correlation between the variables) Negative correlation; (When the variables are inversely proportional to each other) When the researcher wants to make inferences to the population, he will have to examine their statistical significance. Statistical significance can be determined if correlation have been obtained from the randomly selected samples. Depends on the size of the correlation Significance of correlation Size of the sample Level of significance is very important since it relates directly to whether the null hypothesis is rejected or not. Multivariate analysis: It is used to find out the relationship between more than two variables as in correlation analysis. There are two ways; Multiple regressions Factor analysis Multiple regressions: Through multiple regressions it is possible to examine the relationship and predictive power of one or more independent variables with the dependent variables. it shows which variables are significant in their contribution explaining the variance in the dependent variable and how much they contribute. Discriminate analysis Which contribution of variables distinguishes between one or more categories of dependent variables? Factor analysis: In it independent variable is not related to dependent variables as in regression, but rather operates within a number of independent variables without a need to have dependent variables. In factor analysis the interrelationships between and among the variables of the data are examined in an attempt to find out how many independent dimensions can be identified in the data. It thus provides
7. 7. information on the characteristics of the variables. This type of analysis is based on the assumption that variables measuring the same factor will be highly related. Whereas variables measuring different factors will have low correlations with one another. Referential Technique: As we know that different designs call for different methods of analysis. A statistical technique appropriate for quantitative data will generally inappropriate for categorical data. Types of Inferences Techniques: There are two types of Inferences techniques that a researcher uses. Parametric technique Non- Parametric technique Parametric It is the most appropriate for interval data. It makes various kind of assumptions about the nature of population from which the sample involved in the research study, are drawn they are generally more powerful than non- Parametric techniques because it reveals a true difference or relationship if really exist. Non-Parametric It is the most appropriate for nominal and ordinal data. It makes few assumptions about the nature of the population from which the sample are taken. T-Test: It is used to compare the means of the two groups. T test is used to determine the probability - that the difference between the groups of subjects rather than a chance variance in data it is used to compare. Types: T-test for independent means; It is used to compare the mean scores of two different independen groups. t T-test for correlate means; It is used to compare the means scores of the same group before and after a treat mint of some sort is given to see if any observed gain is significant or when the researcher design involve two matched groups. The result of t-test provides the researcher with a t-value. Example A researcher is comparing the performance of the two randomly selected groups learning French by two different methods. The experimental group learns wit the aid of computer while the control group h is exposed to the teacher. The researcher investigates the effects of the computer practice on students’ achievement on French. After three months both the groups undergo an achievement test. The researcher uses t- test to examine whether there are differences in the achievements of the two groups. To have a deep insight of the data through descriptive statistics, first it have a mean X, SD and sample size N of the data .There must be a mean of experimental or control group. ANOVA :( one way analysis of variance) One way analysis of variance is used to examine the differences in more than two groups. The analysis is performed on the variances of the groups, focusing on whether the variability between the groups is greater that the variability within the groups value is the ratio between variances over the within the variances. F= between group variance
8. 8. Within group variance If the difference between the groups is greater than the difference within the groups, than F value is significant and the researcher can reject the null hypothesis. If the situation is inverse than F value is significant. Chi-Square (Non-Parametric Technique) The chi test allows analysis of one, two or more nominal variables. It is based on the comparison between expected frequencies and actual, obtained frequencies. Example A researcher might want to compare how many male and female teachers favor a new curriculum, to be instituted in a particular school district. he asks a sample of 50 teachers ,if they favor or oppose new curriculum. if they do not differ significantly in their responses, then we would expect hat about the same proportion of males and females would be in favor(or opposed to)instituting the curriculum. Degree of freedom Number of scores in a distribution that are free to vary-that is, that are not fixed.