An Evaluation of College Students’ Perceptions of Statisticians

Figures & data

Fig. 1 Student gender by gender of statistician in drawing.

Fig. 2 Student race by race of statistician in the drawing.

Fig. 3 Student gender by gender of mathematician in drawing.

Fig. 4 Student race by race of mathematician in the drawing.

Table 1 Keywords by theme for each class.

Mathematics			Statistics
Physical appearance	Teaching	Research	Physical appearance	Teaching	Research
Male	Teaching	Equations	Balding	Board	Analyzing
Smile	Chalkboards	Business	Clothes	Drawing	Calculator
Casual	Classroom	Calculators	Dress	Explaining	Chart
Happy	Whiteboard	Solving	Middle age	Professor	Computer
Curly Hair	Grade	Analyzing	Female	Students	Data
Outfit	Teacher	Professional	Glasses	Taught	Graph
Einstein	School		Guy	Teacher	Idea
Female	Students		Hair	Teaching	Paper
Wizard			Male	Whiteboard	Reading
Glasses			White	Class	Research
Dress					Thinking
White
Gender

Table 2 A 2 × 2 contingency table for calculating the $\varphi$ coefficient.

		Observation j
		1	0	Total
Observation i	1	n11	n10	$n_{1.}$
	0	n01	n00	$n_{0.}$
	Total	$n_{.1}$	$n_{.0}$	n

Fig. 5 Statistics class clustering fit indices.

Fig. 6 Mathematics class clustering fit indices.

Table 3 Statistics Class Clustering Fit Indices.

Statistics Class HCA
		Index	2-Class	3-Class	4-Class	5-Class	6-Class	7-Class	8-Class
Average linkage	Internal validity	Connectivity	7.8548	10.8837	20.6369	48.3575	57.4794	81.0091	82.3282
		Dunn	0.2830	0.2830	0.2432	0.1510	0.1678	0.1708	0.1708
		Silhouette	0.2694	0.1580	0.0950	0.1706	0.1793	0.1804	0.1618
	Cluster stability	ADM	0.0596	0.1588	0.3260	0.4352	0.3635	0.4705	0.4424
	Minimum cluster size	n (%)	4 (3.64%)	1 (0.91%)	1 (0.91%)	1 (0.91%)	1 (0.91%)	1 (0.91%)	1 (0.91%)
Complete linkage	Internal validity	Connectivity	67.2996	80.4770	92.1643	102.8627	110.3373	113.0702	125.0040
		Dunn	0.0813	0.0852	0.0932	0.0987	0.1044	0.1048	0.1059
		Silhouette	0.1324	0.1080	0.1325	0.1486	0.1547	0.1524	0.1428
	Cluster stability	ADM	0.4801	0.6241	0.6875	0.7042	0.7185	0.7279	0.7550
	Minimum cluster size	n (%)	42 (38.18%)	16 (14.55%)	13 (11.92%)	13 (11.92%)	11 (10.00%)	4 (3.64%)	4 (3.64%)
Single linkage	Internal validity	Connectivity	3.3734	6.4024	9.5452	13.1631	15.8393	19.1349	22.5317
		Dunn	0.3426	0.3344	0.3297	0.2830	0.2830	0.2708	0.2708
		Silhouette	0.2557	0.1578	0.1217	0.0643	0.0377	0.0036	–0.0152
	Cluster stability	ADM	0.0325	0.0537	0.0511	0.0754	0.1021	0.1027	0.1171
	Minimum cluster size	n (%)	1 (0.91%)	1 (0.91%)	1 (0.91%)	1 (0.91%)	1 (0.91%)	1 (0.91%)	1 (0.91%)

Note: For the measures of internal validity and cluster stability, a greater number is preferrable to a smaller number except for Connectivity and ADM where the opposite is the case. Bolded values indicate the optimum value for a given metric.

Table 4 Mathematics Class Clustering Fit Indices.

Mathematics Class HCA
		Index	2-Class	3-Class	4-Class	5-Class	6-Class	7-Class	8-Class
Average linkage	Internal validity	Connectivity	6.9714	25.0210	25.0210	57.3778	59.4996	69.9778	91.2484
		Dunn	0.2265	0.1001	0.1001	0.0857	0.0857	0.0857	0.0857
		Silhouette	0.3253	0.2104	0.1188	0.1108	0.0903	0.0706	0.0792
	Cluster stability	ADM	0.0158	0.0176	0.0170	0.0200	0.0198	0.0289	0.0411
	Minimum cluster size	n (%)	3 (1.73%)	3 (1.73%)	2 (1.16%)	2 (1.16%)	2 (1.16%)	2 (1.16%)	2 (1.16%)
Complete linkage	Internal validity	Connectivity	96.7944	137.0567	149.5702	152.6214	178.2806	181.7333	182.9302
		Dunn	0.0752	0.0799	0.0849	0.0876	0.0917	0.0917	0.0942
		Silhouette	0.0928	0.0843	0.0890	0.0600	0.0680	0.0694	0.0781
	Cluster stability	ADM	0.0225	0.0283	0.0382	0.0430	0.0440	0.0446	0.0445
	Minimum cluster size	n (%)	74 (42.77%)	49 (28.32%)	23 (13.29%)	9 (5.20%)	9 (5.20%)	8 (4.62%)	3 (1.73%)
Single linkage	Internal validity	Connectivity	3.3873	6.7925	9.9575	13.6865	18.0238	21.9528	23.3817
		Dunn	0.2984	0.2503	0.2609	0.2554	0.2544	0.2544	0.2544
		Silhouette	0.3360	0.2803	0.2303	0.0672	0.0116	–0.0101	–0.0167
	Cluster stability	ADM	0.0149	0.0152	0.0154	0.0162	0.0162	0.0163	0.0170
	Minimum cluster size	n (%)	1 (0.58%)	1 (0.58%)	1 (0.58%)	1 (0.58%)	1 (0.58%)	1 (0.58%)	1 (0.58%)

Note: For the measures of internal validity and cluster stability, a greater number is preferrable to a smaller number except for Connectivity and ADM where the opposite is the case. Bolded values indicate the optimum value for a given metric.

Fig. 7 Dendrogram for statistics class.

Table 5 Statistics class cluster variable proportions.

Cluster	White students	White females drawing
theme	drawing white	white males
	(unhappy) females	with whiteboards
N	42	68
% Male students	42.86%	26.47%
% White students	80.95%	60.29%
% Male drawings	30.95%	85.29%
% White/Caucasian drawings	69.05%	76.47%
% Drew glasses	21.43%	38.24%
% Drew calculator	9.52%	11.76%
% Drew whiteboard	35.71%	75.00%
% Drew desk	33.33%	16.18%
% Drew messy hair	14.29%	14.71%
% Drew computer	23.81%	8.82%
% Physical appearance comments	16.67%	33.82%
% Teaching comments	38.10%	32.35%
% Research comments	54.76%	23.53%
% Drew students	0.00%	4.41%
% Drew unhappy mood	66.67%	41.18%

Fig. 8 Dendrogram for mathematics class.

Table 6 Mathematics class cluster variable proportions.

Cluster	Drawings of white	Drawings by females
theme	male mathematicians	of happy, white
	who are unhappy	teachers at a whiteboard
N	99	74
% Male students	41.41%	37.84%
% White students	49.49%	52.70%
% Male drawings	67.68%	44.59%
% White/caucasian drawings	60.61%	64.86%
% Drew glasses	34.34%	9.46%
% Drew calculator	8.08%	1.35%
% Drew whiteboard	56.57%	97.30%
% Drew desk	21.21%	4.05%
% Drew messy hair	12.12%	24.32%
% Drew computer	7.07%	0.00%
% Physical appearance comments	55.56%	48.65%
% Teaching comments	37.37%	67.57%
% Research comments	33.33%	12.16%
% Drew students	1.01%	21.62%
% Drew unhappy mood	74.75%	39.19%

Table

Age of statistician	Gender of statistician	Race of statistician

Table

Table

Your age	Your Gender	Your Race