Enumeration Data Analysis
9
ENUMERATION DATA ANALYSIS Expressed in the form of frequencies, which represents the number of items in specified qualitative description of categories. CLASSIFICATION – based on the number of variables described. •ONE-WAY – has only one variable described by at least two categories. •TWO-WAY – has two variables described by their respective categories
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Transcript of Enumeration Data Analysis
ENUMERATION DATA ANALYSIS
Expressed in the form of frequencies, which represents the number of items in specified qualitative description of categories.
CLASSIFICATION – based on the number of variables described.•ONE-WAY – has only one variable described by at least two categories.•TWO-WAY – has two variables described by their respective categories
ENUMERATION DATA ANALYSIS
EDA is done through the chi-square test.
USES OF EDA1. To test the goodness of fit to a normal
curve, that is to find out whether or not a sample distribution conforms to the hypothetical situation.
2. To find out whether or not an observed proportion is equal to some given ideal or expected proportion.
3. To test the independence of one variable from another variable.
ENUMERATION DATA ANALYSIS
STEPS FOR EDA1. State the null and alternative hypothesis. It
may be stated in any of this way:a. For ONE-WAY:1. The sample distribution conforms with the hypothetical or theoretical distribution.2. The actual observed proportion is not significantly different from the ideal or expected proportion.b. For TWO-WAY:1. One variable does not depend from another variable.2. The two variables are independent from each other.
ENUMERATION DATA ANALYSIS
2. Determine the level of significance.3. Determine the degrees of freedom using the following formula.For ONE-WAY: df = c-1For TWO-WAY: df = (r-1)(k-1)
where c –number of categories r – number of rows k – number of columns
4. Locate the tabular values, in the chi-square distribution table by getting the intersection of degrees of freedom and level of significance.
ENUMERATION DATA ANALYSIS
5. Calculate the chi-square value using x2=(O-E)2/E
where O –actual observed frequency E – expected/ideal frequency
•In two-way classification, the expected frequency is computed by multiplying the sub-total of the intersecting categories, then dividing the product by the total frequency represented by the grand total of the contingency table.
•NOTE: If there is only one degree of freedom, Yate’s correction factor is applied
grandtotal
totalBsubtotalAsubE
ENUMERATION DATA ANALYSIS
E
EOX
22 )50.0/(/
6. State the conclusion arrived at by the acceptance or rejection of Ho.
NOTE: 1. If x2 computed value is less than the tabular value, accept Ho.
2. If x2 computed value is greater than the tabular value, reject Ho.
ENUMERATION DATA ANALYSIS
Example 1: Based on the table, is the actual observed proportion significantly from the expected proportion, if the ideal expected proportion is 30% married, 50% single, 10 % widow, and 10 legally separated.
STATUS FREQUENCY
Single 18
Married 24
Widowed 5
Legally Separated 3
TOTAL 50
ENUMERATION DATA ANALYSIS
Example 2: Does attitude toward household chores depend on the sex for the 50 children being considered in the table?
BOYS GIRLS TOTAL
Positive 9 21 30
Negative 9 11 20
TOTAL 18 32 50
ENUMERATION DATA ANALYSIS
DIGIT PROBABILITY OBSERVED FREQUENCY
EXPECTED FREQUENCY
0 0.10 21 251 0.10 28 252 0.10 24 253 0.10 33 254 0.10 23 255 0.10 21 256 0.10 23 257 0.10 23 258 0.10 21 259 0.10 33 25
250 250
Example 3:The table of random variables, which is constructed in such a way that each digit is a value of a random variable which takes on the values 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 with equal probabilities of 0.10. Test whether the discrepancies between the observed and expected frequencies can be attributed to chance at 0.05 level of significance.
