Statistical Analysis of Frequency Distributions: Toys and Engineering Students, Lecture notes of Social Statistics and Data Analysis

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TABLE 1.1: RESPONSES OF YOUNG BOYS TO THE REMOVAL OF A TOY. RESPONSE OF CHILD FREQUENCY

Cry 25

Express Anger 15

Withdraw from Play 5

Play with Alternative Toy 5

N= 50

TABLE 1.1: RESPONSES OF REMOVAL OF A TOY BY SEX OF CHILD. RESPONSE OF CHILD SEX OF CHILD MALE FEMALE Cry 25 28

Express Anger 15 3

Withdraw from Play 5 4

Play with Alternative Toy 5 15

N= 50 50

Standardizing Frequency Distributions

 Proportions are useful in testing hypotheses but people have a better grasp of percentages.

 Convert a proportion into a percentage by multiplying the proportion by 100.

 % = f / N (100) where f is the number of cases in category, and N is the total number of cases. (e.g., 15 out of 50 girls found an alternative toy so the percentage is 15 / 50 (100) = 30%; the percentage of boys who found an alternative toy was 5 / 15 (100) = 10%).

SEX OF STUDENTS MAJORING IN ENGINEERING AT UNIVERSITIES “A” AND “B”.

ENGINEERING MAJORS SEX UNIVERSITY “A” UNIVERSITY “B” f f Male 1,082 146

Female 270 37

Total 1,352 183

Ratios

 The ratio directly compares the frequency of cases in one category with the frequency of cases in another category.

 Ratio = f1 / f

 (e.g., ratio of male to female engineering

students at University A is 1,082/270 =

4 ….so there are 4 male students for every

1 female student. Likewise, for University

B, the ratio is 146/37 = 4.

Rates

 Rates compare actual to potential cases (e.g., birth rate relates live births to the population of women 15-49; divorce rate relates number of divorces to married population).

 Usually expressed as the number per 1000. For uncommon events such as suicide or homicide, rates are expressed as the number per 100,0000.

 Rate = (f(actual) / f(potential)) (1000) (e.g., 500/4000 (1000) or .125 (1000) or 125 per 1000.

The Mode

 The mode is the value with the largest or highest frequency count. For our scores in the index variable measuring attitudes toward new reproductive technology: 9, 12, 15, 13, 15, 15, 17, 8, 11, 14, 12, the mode is 15 because more respondents (3) obtained a value of 15 than any other score.

 While the mode can be very useful, in general it is not all that informative in summarizing an entire group.

The Median

 The median is the score that marks the midpoint of a data set. That is to say, ½ of the scores exceed the median and ½ of the scores are below the median.

 In our data set on index scores for new reproductive technology ( 9, 12, 15, 13, 15, 15, 17, 8, 11, 14, 12) the median is 13 because 5 respondents have scores above 13 and 5 respondents have scores below 13.

 The median is usually better than the mode in summarizing a data set.

More on the Mean…..

The mean uses all the information in

a data set. The mean is usually the

most accurate and useful measure of

central tendency.

The mean is usually the most stable

measure of central tendency and

amenable to the greatest range of

statistical analyses.