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# Sfl level of measurement

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### Sfl level of measurement

1. 1. Variable & Levels of Measurement1. Variable Suppose that we have a research problem namely: The Relationship between Attitude toward Instruction and English Writing Ability, so we have one independent variable (X), and one Dependent variable (Y). Alternatively, we can write them as follow: X : Attitude toward English Instruction Y : English Writing Ability What is Variable? (Hatch and Farhady, 1982: 12-15) Variable can be defined as an attribute of a person or of an object which ‘varies’ from person to person or from object to object. The syntactic, semantic, and phonological elements of language, for example, are variables. They are attributes of language and they are also something which people may possess (to some varying degree of proficiency)… The more specific variable is, the easier it will be to locate and measure. Independent Variable : is the major variable which you hope to investigate. It is the variable which is selected, manipulated, and measured by the researcher. Dependent Variable : on the other hand, is the variable which you observe and measure to determine the effect of the independent variable. Before using any statistical technique (chi-square, product moment, t-test, regression, etc.), we have to determine the Variable Scales or sometimes termed as Scale of Measurement/ Levels of Measurement. 3
2. 2. 2. Levels of Measurement The concept of level of measurement or scales of measurement is central to statistical analysis and helps to determine the types of procedure that may be carried out on particular variables. (Miller, et.al., 2002:59) There three broad levels of measurement. They are: 1. Nominal/Categorical  Classification into categories  Numerical labels are sometimes used to identify the categories (e.g., 1 = male and 2 = female)  The numbers are merely labels and have no intrinsic meaning.  Examples of variables measured on the nominal scale are: sex, race, religion, marital status. 2. Ordinal  Classification into categories  The categories have meaningful order (for example, from highest to lowest)  We cannot determine the degree of difference between the categories.  Example of variables measured on the ordinal scale are: social class, attitude, opinion, etc. 4= strongly agree; 3 agree; 2 disagree; 1 strongly disagree Learning English is to get a good job 4 3 2 1 We can also use such order as: Very happy – happy – unhappy Poor – fair – good – excellent 3. Interval  Shares all the qualities of nominal and ordinal variable  Precise distance between each categories  Examples of variables commonly measured on the interval scale are: age, test score, income, etc. 4
3. 3. According to Hatch and Farhady, 1982: 12-15 “Whether a variable is placed on a nominal, ordinal, orinterval scale is sometimes determined by the type of variable, butmore frequently the researcher must decide on the mostappropriate scale for the variable. For example, if bilingualism isthe variable you wish to research, you could place it on a nominalscale – your Ss (students,_pen.) either are or not bilingual—andassign a 1 or 2 value to variable. You could also assign it to anordinal scale and either rank order your Ss in relation to eachother on how bilingual you think they are or assign them to ascale of extremely to not very bilingual. Or you could give them atest to measure proficiency in each language and thus obtain dataon an interval scale for the variable.” “Whatever the variables are that you want to investigateand whatever scale you select for the variables, you will need todefine them further in terms of your research design. You must beclear about the function of each variable in your investigation.”3. Implication of Level of Measurementa. Chi-Square X2; Statistical Test of Nominal Data When we measure nominal variables, we are concerned notwith how much but with how many or how often. Our data is interms of frequency counts rather than scores (Hatch and Farhadi,1982: 165)Case example: In Academic Year of 2003/2004, 1032 students enrolled atthe English Department of STAIN Jurai Siwo Metro. Aftergrouping them according to their type of schools, we know that543 students are from MAN, 437 from SMUN, and 52 from SMK. We want to know the relationship between the type ofschool and the enrolled students at the English Department ofSTAIN Jurai Siwo Metro . For this, we use Chi-square by doingthe following steps: 5
4. 4. Hypotheses Ha = There is a significant relationship between the type of school and the enrolled students at the English Department of STAIN Jurai Siwo Metro. Ho = There is not a significant relationship between the type of school and the enrolled students at the English Department of STAIN Jurai Siwo Metro.b. T-test The t-test is one of the most frequently used statisticalprocedures in our field. (Hatch and Farhadi, 1982: 114). It is mostoften used to compare two groups. It is most commonly used toexamine whether the means of two groups of data aresignificantly different from one another. (Miller, at.al., 2002: 119)With a t-test the independent variable is nominal or categoricaland the dependent variable is measured at interval or ratio scaleof measurement. (Miller, at.al., 2002: 119) X = nominal/categorical scale and Y = Interval or ratio scale.Case example:We want to know whether there is a difference between malestudents and female students in learning English. We, then,observe the students’ grades of English and try analyze themusing t-test.X1 : male students (nominal)X2 : female students (nominal)Y : English grades (interval)Hypothesis: Ha = There is a significant different between female and male students in learning English. Ho = There is not a significant different between female and male students in learning English. 6
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