Analyzing Propositions Underlying the Theory of Statistics

Figures & data

Table 1. Number of Subitems Answered Correctly by the Nine Students

Student ID	S1	S2	S3	S4	S5	S6	S7	S8	S9
Number correct	8	7	3	11	8	10	11	2	10

Table 2. Number of Students who Correctly Responded to the 15 Subitems

Subitem	1	2A	2B	2C	2D	3A	3B	3C	4A	4B	4C	4D	5A	5B	5C
Number of correct responses	3	7	6	0	7	5	5	6	6	7	3	6	4	3	2

Table 3. Number of Students who Mentioned a Proposition at Least Once (propositions presented in order of decreasing familiarity)

Prop	Freq	Prop	Freq	Prop	Freq
P7	8	P3	7	P17	6
P8	8	P4	7	P18	5
P9	8	P5	7	P21	5
P10	8	P23	7	P15	1
P11	8	P1	6	P16	1
P12	8	P6	6	P20	1
P22	8	P13	6	P19	0
P2	7	P14	6

Table 4. Number of Different Propositions Recalled by the Nine Students

Student ID	S1	S2	S3	S4	S5	S6	S7	S8	S9
Number of different propositions recalled	18	14	10	17	16	21	20	0	19

Table 5. Implicit Propositions

Proposition	Explicitly Mentioned	Implicitly mentioned
P1	0	6
P7	0	8
P8	1	7
P12	2	11
P13	0	6
P14	1	5
P15	0	3
P16	0	3

Table 6. Additional Propositions Mentioned by More than One Student

Item 2
P24	−1 ≤ rxy ≤ +1 (2 students)
P25	An |rxy| of 1 denotes a strict linear relationship (2 students)
P26	The larger the value of rxy, the better the prediction of Y on the basis of X (4 students)
P27	If X gives a good description of variation in Y, than Sy, should be approximately equal to Sy (2 students)
Item 4
P28	The Z‐transformation changes the scale values of X and Y (3 students)
P29	After Z‐transformation the scores are expressed as standard deviations from the mean (2 students)
P30	The relative amount of variance explained in Y by X does not change after transformation of scale values (4 students)
P31	z‐transformation leaves the value of rxy unchanged (3 students)

Table 7. Erroneous Propositions(F) Mentioned by More Than One Student

Item 3
F1	Irrespective of the chosen loss function, in case of a linear regression model, rxy^2 = Sy'^2/Sy^2 (2 students)
F2	Irrespective of the chosen regression model, when the least squares criterion is met, rxy^2 = Sy'^2/Sy^2 (6 students)
F3	If the least squares criterion has not been used, than the regression model that has been used cannot be linear (2 students)
Item 4	F4	After Z‐transformation all ratio's between quantities remain the same (2 students)
F5	Two students concocted an incorrect formula for Se^2
Item 5	F6	In case of a linear regression model, rxy^2 = Sy'^2/Sy^2 (3 students)
F7	rxy^2 gives the maximum proportion of variance in Y that can be explained by X on the basis of any possible regression model, linear or otherwise (2 students)