Describing Your Data Frequencies Cross Tabulations And-Books Pdf

Describing Your Data Frequencies Cross Tabulations and
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A Brief History of,Florence Nightingale 1820 1910,Florence Nightingale nicknamed the lady with the. lamp is known for her work in nursing During the,Crimean War 1853 1856 Nightingale sent re. ports of the conditions and treatment of patients, back to Britain As part of her reports Nightingale. used visual presentations of her data in the form of. variations of pie charts In order to present monthly. deaths she used a more elaborate pie chart that,included different forms of death by month She. called these pictures coxcombs see example on rate had dropped from 69 to 18 deaths per 1 000. the right soldiers, After the war Nightingale lobbied hard for san In 1859 Florence Nightingale became the first.
itary reforms in the hospitals In 1873 while work female to be elected to the Royal Statistical Society. ing on the improvement of sanitary conditions Shortly after that she became an honorary member. in India Nightingale reported that the mortality of the American Statistical Association 1. Introduction, Researchers use a variety of different methods such as surveys interviews exper. Empirical data iments databases etc to gather empirical data For example a sociologist. is gathered from objects gathers data on cultural norms a political scientist on voting behaviour an econ. or participants for a omist on stock fluctuation and an educational psychologist on gender difference. research study, in academic performance All social science disciplines gather some form of em. pirical data from the real world Once gathered the data needs to be organized and. presented in a manner that can provide summary information about the phenom. ena of interest, In this chapter we will focus on different ways to present summary informa. tion about your data using frequency tables cross tabulations and graphs How. ever before we do that we need to review how data gets from the collection stage. to a dataset that we can work with Figure 2 1 provides four examples of how. variables with different levels of measurement can be measured coded and. entered in a dataset Here you can see that the variable Age measured at the or. dinal level is given a specific coding and entered in a data analysis program. such as SPSS or Microsoft Excel We code variable responses in order to. have numeric information to work with The coding you use is largely based on. what makes the most sense to you At this stage it is important to keep notes. of which codes match which responses often called a data dictionary in order to. make the correct interpretations, 38 Chapter 2 Describing Your Data Frequencies Cross Tabulations and Graphs. FIGURE 2 1 Measurement and Coding,Question Example Coding Dataset.
Nominal Gender n Gender,Gender Male Male 1 1 1,Female Female 2 2 2. Ordinal Please state your age n Age,Age 20 to 25 20 to 25 1 1 1. 26 to 35 26 to 35 2 2 2,36 to 45 36 to 45 3 3 2, Interval I am satisfied with my life n Life Satisfied. Satisfied with life Strongly Disagree Strongly disagree 1 1 4. Disagree Disagree 2 2 4,Neutral Neutral 3 3 3,Agree Agree 4 4 2. Strongly Agree Strongly Agree 5 5 4, Ratio How many hours per week Record actual n Internet Hours.
Internet hours do you spend on the number of hours 1 3. Internet 2 15,n respondent number, Chapter 2 Describing Your Data Frequencies Cross Tabulations and Graphs 39. FIGURE 2 2 n Gender Age Life Satisfied Internet Hours. Example of a Dataset,2 2 2 4 15,3 1 2 3 12,6 2 2 1 10. 7 2 3 5 11,10 2 2 2 8,n respondent number, FIGURE 2 3 Variables Measured at the Create This Type of Data. Measurement Level,and Type of Data Nominal Level Nominal Data. Ordinal Level Ordinal Data,Interval Level Interval Data.
Ratio Level Ratio Data, Figure 2 2 provides an example of what the combined data for the examples in. Figure 2 1 may look like in a dataset, One final note about the terminology we use regarding variables We know that. variables can be measured at four different levels nominal ordinal interval and. ratio When we assess a variable with a specific level of measurement we say that. it produces a specific type of data Figure 2 3 captures this idea For example. when measuring a variable with an interval level of measurement we say that it. produces interval data Given this we often shorten the phrase a variable with. an interval level of measurement to just an interval variable So when you see. ordinal variable this is referring to a variable that has been measured at the. ordinal level which creates ordinal data,Frequency Distributions and Tables. LO1 Recall from chapter 1 that a variable is a phenomenon of interest that can take on. different values Furthermore nominal and ordinal variables have qualitative cat. egories referred to as just categories as potential values whereas interval and. ratio variables have quantitative values Given that a variable can have different. Frequency refers to, the number of observa values we can count the frequency also referred to as absolute frequency of. tions of a specific value the observed values categories or quantitative values of a variable Consider the. within a variable Some following two examples,textbooks call this.
absolute frequency but Example 1 The variable Gender has two possible qualitative categories male. the meaning is the same and female Suppose we collect data on gender by surveying 100 respondents and. 40 Chapter 2 Describing Your Data Frequencies Cross Tabulations and Graphs. observe that 46 are male and 54 are female In this case there are two values with. differing frequencies, Example 2 Suppose we measure Student Grade with a ratio level of measure. ment and assume that grades do not include decimals or negative numbers There. are then 101 potential quantitative values ranging from 0 to 100 Now imagine. that we sampled 10 students and observed that three students received a grade of. 76 two students received a grade of 79 one student received a grade of 83 and. four students received a grade of 86 In this case we observed four potential val. ues with differing frequencies, Once the data is entered in a software program we want to get a sense of what. the data looks like at a summary level One way to summarize data into a form. that can be easily reviewed is to create a frequency distribution within a table A. Frequency frequency distribution is the summary of the values of a variable based on the. distribution is the frequencies with which they occur It is called a frequency distribution because. summary of the values we are looking at how the values of the variable are distributed across all of the. of a variable based on, the frequencies with cases in the data When we display the frequency distribution in a table format. which they occur we call it a frequency table As an example think back to the survey question in. Figure 1 10 in chapter 1 which measured the variable Political Party Affiliation. If we administered the question to 100 respondents we could calculate the fre. quency f with which each category was selected by the respondent and create. the frequency table in Table 2 1, LO2 Often it is easier to interpret frequency results when they are converted into. relative frequency f n Relative frequency is a comparative measure of the. Relative frequency proportion of observed values category or quantitative value to the total num. is a comparative measure, of the proportion of ber of responses within a variable It provides us with the proportion or fraction.
observed values to of one occurance relative to all occurances You will often hear this referred to as. the total number of a proportion, responses within a The equation for calculating relative frequency f n is. relative frequency 2 1,where f frequency of specific responses. n total number of responses, We use a small n to represent the size of a sample and a capital N to repre. sent the size of a population,Category Frequency f. Frequency of,Political Party Conservative 35,Affiliation Green Party 10.
Le Bloc Qu b cois 10,Liberal Party 33, Chapter 2 Describing Your Data Frequencies Cross Tabulations and Graphs 41. Frequency Relative Frequency,2009 Statistics,Canada Population. Estimates of the Males 22 500 0 517,Northwest Territories Females 21 000 0 483. Total 43 500 1 00,Source 2009 Statistics Canada,Population Estimates of the. Northwest Territories adapted, from Statistics Canada website Consider Table 2 2 which provides the 2009 Statistics Canada population esti.
http www40 statcan ca l01 cst, 01 demo31a eng htm extracted mates for the Northwest Territories The right column provides the relative fre. May 18 2011 quency of males and females Given that relative frequencies must add to 1 0 it is. generally easier to visualize the comparison of relative frequency than raw num. bers For example it is likely easier to see the magnitude of difference in 0 517. males versus 0 483 females than it is in 22 500 males versus 21 000 females. Similar to relative frequency percentage frequency f also provides a useful. A percentage way of displaying the frequency of data A percentage frequency commonly. frequency is the referred to as percentage is the relative frequency expressed as a percentage value. relative frequency out of 100 and can be calculated as follows. expressed as a percent,age value f,where f frequency of responses. n total number of responses within the variable, Since relative frequencies are written as a decimal e g 0 10 we can convert. them to percentage frequencies by multiplying the relative frequency by 100 For. example 0 10 becomes 10 percent 0 10 100 It is also useful to show the cu. mulative percentage frequency c f commonly referred to as cumulative pre. The cumulative per centage The cumulative percentage frequency gives the percentage of. centage frequency observations up to the end of a specific value Table 2 3 provides the 2009 Statistics. gives the percentage of Canada population estimates for the Northwest Territories with the percentage fre. observations up to the, end of a specific value quency added Again we can see that it is easier to see the difference in males ver. sus females when we state that 51 7 percent are male and 48 3 percent are female. rather than 22 500 are males versus 21 000 are females. Now that we have covered some of the basics of frequency tables we need to. focus on how to create frequency tables for nominal ordinal interval and ratio. variables In this section we will focus two types of frequency tables simple fre. TABLE 2 3 quency tables and cross tabulations,2009 Statistics.
Canada Population,Estimates of the Cumulative, Northwest Territories Relative Percentage Percentage. Frequency Frequency Frequency Frequency,Source 2009 Statistics Canada f f n f c f. Population Estimates of the, Northwest Territories adapted Males 22 500 0 517 51 7 51 7. from Statistics Canada website, http www40 statcan ca l01 Females 21 000 0 483 48 3 100 0. cst01 demo31b eng htm Total 43 500 1 000 100 0,extracted May 18 2011.
42 Chapter 2 Describing Your Data Frequencies Cross Tabulations and Graphs. Take a Closer Look, Example of Population Estimates by Province Looking at the relative frequency and percentage. To show the value of relative frequency and per frequency we can see that just over 77 percent. centage frequency Table 2 4 provides the Statistics of the population age 65 and older live in British. Canada 2009 population estimates by province and Columbia Ontario and Quebec. territory for individuals 65 years of age or older. TABLE 2 4 Statistics Canada 2009 Population Estimates. Source Statistics Canada 2009 Population Estimates adapted from Statistics Canada website http www40 statcan gc ca l01 cst01 demo31a eng htm. extracted May 18 2011,Cumulative,Population 65 Relative Percentage Percentage. Frequency Frequency f n Frequency f Frequency c f,Newfoundland and Labrador 75 200 0 0160 1 60 1 60. Prince Edward Island 21 600 0 0046 0 46 2 07,Nova Scotia 147 900 0 0316 3 16 5 22. New Brunswick 116 400 0 0248 2 48 7 70,Quebec 1 170 400 0 2497 24 97 32 67.
Ontario 1 787 900 0 3814 38 14 70 82,Manitoba 168 500 0 3590 3 59 74 41. Saskatchewan 151 900 0 0324 3 24 77 65,Alberta 385 200 0 0822 8 22 85 87. British Columbia 656 300 0 1400 14 00 99 87,Yukon 2 700 0 0006 0 06 99 93. Northwest Territories 2 300 0 0005 0 05 99 98,Nunavut 1 000 0 0002 0 02 100 00. Total 4 687 300 1 0000 100 00, LO3 Simple Frequency Tables for Nominal and Ordinal Data.
A simple frequency table displays the frequency distribution of one variable at a. time These variables can be nominal ordinal interval or ratio To create a fre. quency table list the possible values the variable can have in one column and. record the number of times frequency that each value occurs in another column. Figures 2 4 and 2 5 provide examples of frequency tables for nominal and ordinal. The range of the data, These figures provide a diagrammatic view of how data goes from the collection. is the value of the, largest observation stage in this case by survey question to data entry and then to the frequency table. minus the value of the As you can see it is easy to create frequency tables for nominal and ordinal. smallest observation variables as they have a limited range of potential values. Describing Your Data Frequencies Cross Tabulations and Graphs Learning Objectives By the end of this chapter you should be able to 1 Define and describe the terms frequency and frequency distribution 2 Define and describe the terms relative frequency percentage frequency and cumulative percentage frequency 3 Construct frequency tables for nominal and ordinal data 4 Construct

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