Andrea Meld, PhDAssessment Analyst, OSPI

andrea.meld@k12.wa.us

Description of Statewide Sample:

A cohort of 43,754 students tested in both Reading and Math WASL who were:

Grade 4 students in Spring 2000 Grade 7 students in Spring 2003, and Grade 10 students in Spring 2006

51% female, 49% male

2% Native American, 4% African American 8% Asian, 9% Hispanic and 77% White.

This sample may be different in some ways from Washington state students as a whole because a cohort (by definition) does not contain students whose families are mobile.

Descriptive Statistics for Reading and Math WASL Grade 4, 7 and 10 Cohort

Reading Min Max Med Mean SD

Grade 4 311 478 410 410.2 18.80

Grade 7 314 470 402 400.5 17.93

Grade 10 291 525 437 436.2 32.18

Math Min Max Med Mean SD

Grade 4 190 519 399 396.9 33.19

Grade 7 168 624 394 393.6 50.23

Grade 10 228 575 407 406.1 35.62

Pearson Correlations Statewide Cohort

WASL Reading Scale Scores

WASL Math Scale Scores

Grade 7 Grade 10

Grade 4 .649 .569

Grade 7 .637

Grade 7 Grade 10

Grade 4 .745 .694

Grade 7 .778

Thought experiment

 You’re a teacher at Emerald Elementary in the Green School District.

100 students in your school take the WASL in 2000 as 4th graders.

Imagine them lined up in order of their WASL Reading Scores and then again in the order of their WASL Math, Students who receive the same rank stand side by side.

Now, do your two lines look the same? Are the students in the same order?

Thought experiment continued

Jump ahead to 2003. You now teach at Sage Middle School.

These same 100 students now attend Sage as 7Th grade students and take the Reading and Math WASL.

Again, imagine the students lining up in rank order of WASL Reading and WASL Math scores.

You see familiar faces, but are these students in the same order as they were in grade 4?

Thought experiment continued

It’s now 2006, and you are now the District Assessment Coordinator for Emerald SD.

The WASL is a major part of your work. You would like to know to what extent is the rank

order of the students in the 2000-2003-2006 cohort the same as in previous WASL Reading and Math Assessments.

Correlations among rank-ordered variables

WASL Reading Rank WASL Math Rank

Grade 7 Grade 10

Grade 4 .757 .702

Grade 7 .790

Grade 7 Grade 10

Grade 4 .733 .692

Grade 7 .801

Math Rank Grade 4 by Grade 10 Reading Rank Grade 4 by Grade 10

Questions, Observations, Comments?

Appendix – SPSS Syntax to Create Rank Variables and Spearman vs. Pearson

SPSS Syntax

Rank

RANK order (1=highest value and 100 is lowest value)

VARIABLES=rscale6 (A) /RANK /PRINT=YES

/TIES=MEAN .

Percentile AKA Fractional Rank

RANK percentile (100=highest value and l is lowest value)

VARIABLES=rscale6 (A) /RFRACTION /PRINT=YES

/TIES=MEAN .

Pearson vs. SpearmanSyntax for Pearson correlation -- r Use when you have equal interval scale, measures are the same or equivalent. Large sample or population Magnitude of association is important

CORRELATIONS /VARIABLES=mtraw6 sscale6

/PRINT=TWOTAIL NOSIG

/MISSING=PAIRWISE .

Syntax for Spearman correlation -- rho Use when you have ordinal scale, measures may be different. Good for survey data, e.g, Likert scales, agree/disagree Smaller sample or population (~ 100) Need to reject Null Hypothesis that two measures are not related.

NONPAR CORR /VARIABLES=mtraw6 sscale6

/PRINT=SPEARMAN TWOTAIL NOSIG

/MISSING=PAIRWISE .

NOTE: Running Pearson correlation on ranked variables = Spearman correlation.

For more information on Spearman correlationhttp://www.google.com/search?hl=en&q=spearman+pearson&btnG=Google+Search

http://www.google.com/search?hl=en&q=spearman+assumptions&btnG=Search

http://www.google.com/search?hl=en&q=spearman+rank+order&btnG=Search

http://www.google.com/search?hl=en&q=spearman+rho&btnG=Google+Search