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Lecture 2, Jan 15.docx

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Child and Youth Studies
Patricia Kirkpatrick

3P15, Lecture 2, Jan 15 Haan: An Introduction to Statistics for Canadian Social Scientists Chapter 3 Univariate Statistics Levels of measurement, a brief review • Nominal: responses cannot be ranked, and distance between response categories cannot be measured. • Ordinal: responses can be ranked, but distance between response categories cannot be measured. • Interval: responses can be ranked, distance can be measured, but there is no theoretical zero. • Ratio: same as interval, but there is a theoretical zero. Frequencies with Nominal Data • Frequency tables usually contain two vital pieces of information: the identifier (response category, e.g., sex) and the frequency (count, percentage, and/or proportion). • Identifiers are usually on the left [column], often sorted alphabetically. • The right column contains the frequency distribution. Nominal Frequencies, continued • Table 1: Number of males and females in the Canadian population, 2001 census of Canada SEX f Proportion Percent ---------------------------------------------------------- Female 15074757 0.51 50.86 Male 14564275 0.49 49.14 • Female/(Female+male)=proportion • Female/(Female+male) x 100 = percentage • Always round to two decimal places Necessary Equations for Nominal Frequencies • N= total number f proportion = N f percent = *100 N Nominal Frequencies, continued • Table 1: Number of males and females in the Canadian population, 2001 census of Canada SEX f Proportion Percent ---------------------------------------------------------- Female 15074757 0.51 50.86 Male 14564275 0.49 49.14 Frequencies with Ordinal, Interval, or Ratio Data • Unlike nominal data, the order of response categories is important. • Usually the largest or most positive value is in the top row, followed by descending values. • Eases interpretation. Ordinal frequencies, an example • Table 2: Students’ attitude towards introductory statistics • Attitude f Proportion Percent --------------------------------------------------------------- Excited 49 0.98 98.00 Neutral 0 0.00 0.00 Not Excited 1 0.02 2.00 Cumulative Frequencies • It is often useful to know what percentage or proportion of observations of fall above or below a specified value. Examples: obesity, poverty, adolescents cf = ∑ fi i≤N • Cumulative frequency = the total frequency of all values above or below a specified boundary – Add up the frequencies of each value, up to your boundary Cumulative Percentages • Like cumulative frequencies, except that percentages accumulate. cf c% = N *100 An example with SPSS and the CCHS Province - (G) Cumulative Frequency Percent Valid Percent Percent Valid NEWFOUNDLAND 460130 1.7 1.7 1.7 PEI 119410 .4 .4 2.2 NOVASCOTIA 797601 3.0 3.0 5.2 NEW BRUNSWICK 638566 2.4 2.4 7.6 QUEBEC 6347862 23.9 23.9 31.5 ONTARIO 10278740 38.7 38.7 70.2 MANITOBA 915110 3.4 3.4 73.6 SASKATCHEWAN 799910 3.0 3.0 76.7 ALBERTA 2604212 9.8 9.8 86.5 BRITISH COLUMBIA 3521972 13.3 13.3 99.7 YUKON/NWT/NUNAVT 71917 .3 .3 100.0 Total 26555430 100.0 100.0 • Example Exam Q: If you were to start driving from the Eastern most point of Newfoundland to the West, by the time you have driven across NB but before Quebec, how many people have you driven across? A: 7.6% Interval/Ratio data with many response categories • Often there are too many response categories to meaningfully present results as a frequency. • In these cases, it is necessary to collapse categories, creating “class intervals”. – e.g. do you make between ($10-15), ($15-20), ($20-25), etc. • Examples where this might be necessary: age, education, income, test scores, etc. Other Univariate Statistics -Ratios and Rates Ratio = f1 f 2 • Count of observations in one category per number of observations in another category, • Where f1= number of observations in first category f2=number of observations in second category Ratios-an example • What is the ratio of males to females in the Faculty of Arts at the University of Alberta? • Number of males: 2018 (winter 2006) 2018 Ratio =3397 • Number of females: 3397 (winter 2006) • In the Faculty of Arts, there are 0.59 males for every female. • In computer science, there are roughly eight males for every female. This is the reason the equation works: Rates • Closely related to ratios, except that the denominator is usually a rounded (1,000, 100,000, etc.) or otherwise intuitive number (kilometres per hour, heartbeats per m
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