Review Chapter 2, p. 56 – SPSS MARITAL – How would you describe where most students in the sample were raised? – What percent of the sample is divorced? – What percent of the sample is married? – What percent would you describe as currently being single?

Chapter 5 Homework # 7, p (in slides last week) #9 p #12 p

Projects 1) Perceptions of Western Washington Univ. 2) Presidential campaign – Which candidates mobilize? 3) Opinion on national issues – Which issues of greatest concern?, Why? Guns, Immigration, House GOP, etc.

Review Friday’s Lab How do we measure a country’s level of development? – Define the concept

Review Friday’s Lab How do we measure a country’s level of development? Some measures: – Human Development Index – GDP – ??

Describe the graph – Range, standard deviation – Mean, median, mode Which country at center of distribution? Which countries at the extremes?

GDP

HDI vs GDP What differences? Median countries? Shape of distribution Correlated at.79

Friday, review 3 rd factor that measures ‘development’ Discuss: which measure is best / most valid? Why?

Chapter 6: Normal Distribution Normal curve – Theoretical, not an empirical distribution – Mean = median = mode – Constant proportions of area under normal curve – Standard deviation = fixed relationship between distance from mean and area under the curve

Std Dev & Normal Curve

Normal Curve and z-scores Difference between and observation and the mean can be expressed in standard scores Z scores

Normal curve and z scores Calculate z-score observed score - mean Z =_____________________ Standard deviation

Normal curve and z scores Calculate z-score Y – Y “Hat” Z =_____________________ Standard deviation

Z scores & normal distribution Where is a country with an HDI of.75? – mean =.696 – sd =.186 – Z = ( ) /.186 =.06/.186 =.32 – 0.32 deviations beyond the mean

Z scores & normal distribution What is the raw score for a country with a z score of 1.5 on HDI – Y = Y“hat” + Z(std dev.) – Y= (1.5*.186) = =.975 – so, a country with HDI at.975 = 1.5 standard deviations beyond the mean

Standard Normal Distribution Appendix B in text, p. 480

Z scores & Normal curve Standard normal distribution – Normal distribution represented by z scores

Normal curve and z scores Example: What proportion of countries would we expect to find between the mean and 1.45 std dev. (if normal distribution?) What proportion below the mean? What proportion between mean and Z = +1.45

normal-distribution-table.html normal-distribution-table.html

Normal curve and z-scores 1,200 students in stats class, Mean Median 70 Mode70 Std. deviation 10.27

Translate scores into Zs Score of 40: ( )/10.27 =-2.93 Score of 70: ( ) /10.27 =-0.01 Score of 90: ( ) / = 1.94

Z scores & normal distribution What % of students scored above 90? – Z for 90 is 1.94 – Use standard normal table (p. 480)

B C.500 of total area -Z MEAN + Z = 1.94

B C.500 of total area -Z MEAN + Z = Check table to determine area of B; or area of C

of total area -Z MEAN + Z = Check table to determine area of B

of total area -Z MEAN + Z = = % scored lower than 90

of total area -Z MEAN + Z = = % scored higher than 90

Translate scores into Zs Score of 40: ( )/10.27 =-2.93 Score of 70: ( ) /10.27 =-0.01 Score of 90: ( ) / = 1.94

Z score and normal curve What percent scored below 40 on the stats exam? – Z for 40 = – use standard normal table

B C.500 of total area -Z MEAN + Z 40 70

B:.4983 C: of total area -Z MEAN + Z Area C = of area; Area B = % scored lower than 40

Z scores and normal curve Standard Normal Table expressed in proportions Easily translated into percentages – multiply by 100 Easily translated into percentiles

Z scores and normal curve Find the percentile rank of a score of 85: – Z = (score-mean) / std. deviation – Z = ( ) / = 1.45 Find the percentile rank of a score of 90 – Z = (score-mean) / std. deviation – Z = ( ) / = 1.94

. 0262, or 2.62% of total area = 97.38% -Z MEAN + Z = Score of 90 higher than 97.38% who took stats test th percentile B C

. 0735, or 7.35% of total area = 92.65% -Z MEAN + Z = Score of 80 higher than 92.65% who took stats test th percentile B C

Normal curve: percentiles OK, a score of 70 (mean = 70.07) – Z = ?? A score of 60 (below the mean, sd = 10.27) – Z = ?? positive or negative guess

Normal curve: percentiles A score of 70 – Z = A score of 60 (below the mean) – Z = (score – mean) / st dev. ( ) / =

. Z = MEAN + Z Score of 60 higher than 16.35% who took stats test th percentile B:.3365; 33.65% C:.1635, 16.35%

Percentiles Range from 0 to 100 Percent of observations above a point Example – SAT math score in 82nd percentile – SAT writing score in 88th percentile – SAT vocabulary score in 75th percentile

Percentiles SAT scores – mean 500 – st dev 100 What % score above 625?

Percentiles SAT scores (p. 203 Q 8) – mean 500 – st dev 100 What % score above 625? Translate 625 into z score ( ) / 100 = 1.25 Use table: Z 1.25 – Area B.3944 ( =.8944 = th percentile – Area C.1056 (10.56% of scores higher)

Percentiles SAT scores – mean 500 – st dev 100 What percent between 400 and 600? – Find Z for 400 – Find Z for 600 – Use table