Organizing Data

Lecture 2Vernon E. Reyes

Collecting Data

• Collecting data entails a serious effort to organize information

• Data collection also entails that “raw” materials are organized in order to analyze data… obtain results and test the hypotheses.

Frequency Distribution

• Frequency distribution is simply counting the number of incidences or occurrence

• This can be done on nominal level and ordinal level of measurements.

• Making a frequency distribution makes our data easy to understand

• First step is to construct a frequency distribution table.

Frequency distribution of Nominal Data

• Frequency distribution table:• Example: response of you boys tyo removal of

toy

-------------------------------------------Response of Child f-------------------------------------------Cry 25Express Anger 15Withdraw 5Play with another toy 5 N = 50

Notice the elements

• Heading/title• 2 columns• f = frequency• N = TOTALThe table therefore shows a clear indication that

boys cry or show anger as compared to withdrawal or playing with other toys in response to toy removal

----------------------------------------------------------- Gender of ChildResponse of Child Male Female-----------------------------------------------------------Cry 25 28Express Anger 15 3Withdraw 5 4Play with another toy 5 15 N = 50 50

Comparing Distributions

Proportions and percentages

• When we study distributions of equal size, its easy to compare groups. (e.g. 50 children each group)

• However, when they are not equal (this is often the case) we can use proportions and percentages

Proportions and percentages

• Proportion: compares the number of cases in a given category with the total size. We convert any frequency into a proportion (P) by dividing the number of cases in a category (f) by the total number of cases (N).

Formula: P = f /NExample: .30 = 15/50 girls that play with

another toy

• However many people prefer to see categories in terms of percentages, a frequency of occurrence per 100 cases. To compute simply multiply by 100.

• Formula % = (100)f/N• Example 30% = (100) 15/50

---------------------------------------------------------------------

Engineering Majors Gender of student Col. A Col. B

f % f %--------------------------------------------------------------------

-Male 1,082 ? ? 80Female 270 ? ? 20 Total 1,352 100 183 100

Gender of students majoring in Engineering at College A and B

Simple frequency distribution of ordinal and interval data

• For nominal data, they can be listed in ANY order. Any of these are acceptable!

Religion f Religion f Religion fProtestant 30 Catholic 20 Jewish 10Catholic 20 Jewish 10 Protestant 30Jewish 10 Protestant 30 Catholic 20 Total 60 Total 60 Total 60

For ordinal and interval• Arrange from highest to lowest or lowest to

highest (based on the categories) to increase readability! Which one is correct?

Attitude towards Attitude towardsa tuition hike f a tuition hike fSlightly favorable 2 Strongly favorable 0Somewhat favorable 21 Somewhat favorable 1Strongly favorable 0 Slightly favorable 2Slightly unfavorable 4 Slightly unfavorable 4Strongly unfavorable 10 Somewhat favorable 21Somewhat favorable 1 Strongly unfavorable 10 Total 38 Total 38

Grouped frequency distribution• Most interval data a spread over a wide range,

thus single frequency distribution is long and difficult

• ExampleGrade f Grade f Grade f Grade f99 0 85 2 71 4 57 098 1 84 1 70 9 56 197 0 83 0 69 3 55 096 1 82 3 68 5 54 195 1 81 1 67 1 53 094 0 80 2 66 3 52 193 0 79 8 65 0 51 192 1 78 1 64 1 50 191 1 77 0 63 290 0 76 2 62 089 1 75 1 61 088 0 74 1 60 287 1 73 1 59 386 0 72 2 58 1

Simply groupedClass Interval f %95 – 99 3 4.2390 – 94 2 2.8285 – 89 4 5.6380 – 84 7 9.8675 – 79 12 16.9070 – 74 17 23.9465 – 69 12 16.9060 – 64 5 7.0455 – 59 5 7.0450 – 54 4 5.63 Total 71 100 %

-------------------------------------------------------------------- Gender of ChildResponse of Child Male Female Total--------------------------------------------------------------------Cry 25 28 53Express Anger 15 3 18Withdraw 5 4 9Play with another toy 5 15 20 N = 50 50 100You can also get the percentages of each (row,

column, total)

Cross Tabulations

Graphic presentationsA. Pie Charts: a cicular group whose pieces add

up to 100%. This is usually helpful in presenting percentages!

Graphic presentationsB. Bar graphs (histogram): can accommodate

any number of categories at any level of measurement and widely used than pie charts

Graphic presentationsB. Bar graphs (histogram): it can also look like

this!

Graphic presentationsB. Bar graphs (histogram): this can also be used

to compare groups

Graphic presentationsB. Frequency Polygon: usually shows continuity

rather than being different