A Correlation Matrix

A small study was conducted to examine the effects of polybrominated biphenyl flame retardants (PBBs) on the neuropsychological development of young children exposed in utero and in infancy. [Seagull EA: Developmental abilities of children exposed to polybrominated biphenyls (PBB). Am J Public Health. 1983;73(3): 281–285. Link to full article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1650564/pdf/amjph00638-0057.pdf ]

The author stated:

"To investigate whether ingestion of polybrominated biphenyls has an adverse effect on the neuropsychological development of young children exposed in utero and in infancy, five tests of the McCarthy Scales of Children's Abilities were administered to a group of 19 PBB-exposed Michigan children."

The author wanted to correlate the level of PBBs in biopsies of fat with multiple continuous measures of cognitive development as measured by standardized tests; she also wanted to correlate the cognitive tests with each other to demonstrate their association. The results were reported in a matrix table summarizing all of the correlations and their p-values. The table is a modified version in which the p-values are reported in parentheses for each association.

	Block Building	Puzzle Solving	Word Knowledge	Draw a Design	Draw a Child
Log of PBB fat level	-0.40 (0.045)	-0.50 (0.015)	-0.48 (0.018)	-0.30 (0.106)	-0.52 (0.011)
Block Building	-	0.62 (0.002)	0.46 (0.023)	0.52 (0.011)	0.54 (0.009)
Puzzle Solving		-	0.47 (0.021)	0.62 (0.002)	0.46 (0.023)
Word Knowledge			-	0.80 (0.001)	0.54 (0.009)
Draw a Design				-	0.45 (0.025)

Notice that not all of the cells are filled in, because there is no point in reporting that a measure correlates with itself, and there is no point in reporting correlations twice. The correlations for the blank cells are reported above.

Also notice that the author used the log of PBB concentration in the fat biopsies, probably to normalize the skewed distribution of fat concentrations. A logarithmic transformation is often used to normalize skewed data.

Finally, notice that the various cognitive tests all correlate negatively with PBB concentrations, but the cognitive testes correlate with one another positively.

Test Yourself

A random sample of 50 year old men (n=10) was taken. Weight, height, and systolic blood pressure were measured, and BMI was computed. In this analysis, the independent (or predictor) variable is BMI and the dependent (or outcome) variable is systolic blood pressure (SBP).

X = BMI	Y = SBP
18.4	120
20.1	110
22.4	120
25.9	135
26.5	140
28.9	115
30.1	150
32.9	165
33.0	160
34.7	180

Is there an association between BMI (kg/m²) and systolic blood pressure in 50 year old men?

Link to Answer in a Word file

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