An experiment on information presentation and investor mutual fund selection

Figures & data

Table 1. Fee minimization

Treatments			Minimized fees
Presentation format	Measurement level	n	n	%
table	%	94	16	17
table	$	100	12	12
graph	%	91	10	11
graph	$	94	10	11

Table 2. Descriptive statistics and multiple testing results for Experiment 1

Panel A: Average amount allocated to each fund by treatment.
Treatments						Average allocation
Presentation format		Measurement level		n		Fund 1	Fund 2		Fund 3		Fund 4
table		%		94		1925.96	3673.40		2089.50		2311.14
table		$		100		2338.30	3446.43		1938.48		2276.79
graph		%		91		2000.00	2982.97		2647.25		2369.78
graph		$		94		2545.84	2638.48		2690.10		2125.59
Panel B: Two-sided and one-directional (greater than) adjusted pairwise comparisons among treatment means
t-statistic adjusted p-value (two-sided test) adjusted p-value (one-sided)
Alternative Hypothesis		Treatment 1 (table, %)		Treatment 2 (table, $)		Treatment 3 (graph, %)			Treatment 4 (graph, $)
${\mu }_{Fund2}\ne {\mu }_{Fund1}$ ${\mu }_{Fund2}>{\mu }_{Fund1}$		4.12 (0.0012)* (0.0011)*		2.66 (0.0595) (0.0252)*		2.36 (0.1164) (0.0485)*			0.22 (1.0000) (0.4534)
${\mu }_{Fund2}\ne {\mu }_{Fund3}$ ${\mu }_{Fund2}>{\mu }_{Fund3}$		3.63 (0.0040)* (0018)*		4.06 (0.0012)* (0.0011)*		0.75 (1.0000) (0.4534)			0.12 (**) (1.0000)
${\mu }_{Fund2}\ne {\mu }_{Fund4}$ ${\mu }_{Fund2}>{\mu }_{Fund4}$		3.13 (0.0189)* (0.0080)*		2.90 (0.0336)* (0.0147)*		1.47 (0.7145) (0.2856)			1.28 (0.8116) (0.3045)

*significant at the 0.05 level

**this test was not performed since the mean amount allocated to fund 3 for this treatment was more than the mean amount allocated to the lowest fee fund (fund 2).

Table 3. Allocation of the $10,000 among the four fund choices

Treatment
# subjects that allocated	table, percentage n (%)		table, dollar n (%)	graph, percentage n (%)	graph, dollar n (%)	Total
all $10,000 to fund 1	3 (3.2%)		6 (6%)	5 (5.5%)	7 (7.4%)	21
all $10,000 to fund 2	16 (17%)		12 (12%)	10 (11%)	10 (10.6%)	48
all $10,000 to fund 3	3 (3.2%)		0 (0%)	5 (5.5%)	6 (6.4%)	14
all $10,000 to fund 4	3 (3.2%)		5 (5%)	4 (4.4%)	4 (4.3%)	16
$10,000 to two or more funds (diversified)	69 (73.4%)		77 (77%)	67 (73.6%)	67 (71.3%)	280
Total	94 (100%)		100 (100%)	91 (100%)	94 (100%)

Table 4. Average concentration measures by treatments

Treatment
	table, percentage mean (standard deviation)	table, dollar mean (standard deviation)	graph, percentage mean (standard deviation)	graph, dollar mean (standard deviation)
concentration	0.46 (0.29)	0.44 (0.29)	0.46 (0.29)	0.46 (0.30)

Table 5. Subject’s self-reported responses to PEQs

	Confidence How confident are you in your index mutual fund allocation decision?	Desire to diversify How much influence did a desire to diversify your investments have on your investment allocation decision?	Minimize fees How much influence did a desire to minimize fees have on your investment allocation decision?
	n (%)	n (%)	n (%)
Not confident at all Slightly confident	47 (12) 82 (22)
Somewhat confident Moderately confident Extremely confident	127 (34) 70 (19) 52 (13)
Not at all influential		69 (18)	48 (13)
Slightly influential		77 (20)	79 (21)
Somewhat influential		138 (37)	110 (29)
Very influential		65	75
Extremely influential		(17) 29 (7)	(20) 66 (17)

Table 6. One-way ANOVA for the PEQs

	Minimized fees (all $10,000 to the lowest fee fund)	Diversified (allocated $10,000 to two or more funds)
Question	mean standard deviation	mean standard deviation	F (p-value)
Confidence	3.1 1.4	3.0 1.2	0.88 (0.3484)
Desire to diversify	1.7 0.9	2.4 0.8	22.36 (<0.0001)
Minimize fees	2.8 0.4	2.6 0.5	1.55 (0.2153)

Table 7. Fee minimization

Treatments			Minimized fees
Presentation format	Measurement level	n	n	%
table	%	88	25	28
table	$	92	27	29
graph	%	103	15	15
graph	$	101	21	21

Table 8. Descriptive statistics and multiple testing results for Experiment 2

Panel A: Average amount allocated to each fund by treatment.
Treatments					Average allocation
Presentation format	Measurement level		n		Fund 1		Fund 2	Fund 3		Fund 4
table	%		88		1977.38		4939.18	1405.78		1677.66
table	$		92		2296.74		4802.42	1203.93		1696.90
graph	%		103		2059.03		4128.16	1733.69		2079.13
graph	$		101		1865.01		4354.54	1677.23		2103.22
Panel B: Two-sided and One-directional (greater than) adjusted pairwise comparisons among treatment means
t-statistic adjusted p-value (two-sided) adjusted p-value (one-sided)
Alternative Hypothesis		Treatment 1 (table, %)		Treatment 2 (table, $)		Treatment 3 (graph, %)			Treatment 4 (graph, $)
${\mu }_{Fund2}\ne {\mu }_{Fund1}$ ${\mu }_{Fund2}>{\mu }_{Fund1}$		6.19 (0.0004)* (0.0004)*		5.06 (0.0004)* (0.0004)*		5.44 (0.0004)* (0.0004)*			5.88 (0.0004)* (0.0004)*
${\mu }_{Fund2}\ne {\mu }_{Fund3}$ ${\mu }_{Fund2}>{\mu }_{Fund3}$		8.13 (0.0004)* (0.0004)*		8.26 (0.0004)* (0.0004)*		6.80 (0.0004)* (0.0004)*			6.46 (0.0004)* (0.0004)*
${\mu }_{Fund2}\ne {\mu }_{Fund4}$ ${\mu }_{Fund2}>{\mu }_{Fund4}$		7.44 (0.0004)* (0.0004)*		7.01 (0.0004)* (0.0004)*		5.97 (0.0004)* (0.0004)*			5.58 (0.0004)* (0.0004)*

*significant at the 0.05 level

Table 9. Allocation of the $10,000 among the four fund choices

Treatment
# subjects that allocated	table, percentage n (%)	table, dollar n (%)	graph, percentage n (%)	graph, dollar n (%)	Total
all $10,000 to fund 1	5 (5.7%)	7 (7.6%)	1 (0.9%)	4 (4.0%)	17
all $10,000 to fund 2	25 (28.4%)	27 (29.3%)	15 (14.6%)	21 (20.8%)	88
all $10,000 to fund 3	0 (0%)	1 (0%)	1 (0.9%)	3 (3.0%)	5
all $10,000 to fund 4	1 (1.1%)	1 (1.1%)	0 (0%)	1 (0.9%)	3
$10,000 to two or more funds (diversified)	57 (64.7%)	56 (60.9%)	86 (83.5%)	72 (71.3%)	271
Total	88 (100%)	92 (100%)	103 (100%)	101 (100%)

Table 10. Concentration measures by treatments

Treatment
	table, percentage mean (standard deviation)	table, dollar mean (standard deviation)	graph, percentage mean (standard deviation)	graph, dollar mean (standard deviation)
concentration	0.49 (0.31)	0.50 (0.30)	0.39 (0.30)	0.48 (0.30)

Table 11. Subject’s self-reported responses to PEQs

	Confidence How confident are you in your index mutual fund allocation decision?	Desire to diversify How much influence did a desire to diversify your investments have on your investment allocation decision?	Minimize fees How much influence did a desire to minimize fees have on your investment allocation decision?
	n (%)	n (%)	n (%)
Not confident at all Slightly confident	39 (10) 74 (19)
Somewhat confident Moderately confident Extremely confident	127 (33) 83 (22) 58 (15)
Not at all influential		83 (22)	34 (9)
Slightly influential		79 (21)	57 (15)
Somewhat influential		121 (32)	100 (26)
Very influential		62	98
Extremely influential		(16) 36 (9)	(26) 91 (24)

Table 12. One-way ANOVA for the PEQs

	Minimized fees (all $10,000 to the lowest fee fund)	Diversified (allocated $10,000 to two or more funds)
Question	mean standard deviation	mean standard deviation	F (p-value)
Confidence	3.4 1.3	3.1 1.1	5.39 (0.0208)
Desire to diversify	1.6 0.8	2.3 0.8	45.82 (<0.0001)
Minimize fees	2.7 0.5	2.6 0.5	0.05 (0.8304)

Table A2.1. Consequences and decisions for statistical tests

Actual
	H0 is true	H0 is false
Decision
Reject H0	Correct (1-$\alpha )$=confidence	Error=$\beta$ Type II Error
Do not reject H0	Error=$\alpha$=level of significance Type I Error	Correct (1-$\beta$)=power

Table A2.2. Hypothesized response means for the 2 × 2 ANOVA for Experiment 1

Factor 2 (unit of measurement)
Factor 1 (presentation format)	$	%
table	$6500	$4500
graph	$8500	$5500

Figure A2.1. SAS code and output to calculate the required sample size for Experiment 1.