Question

Using the below data I need a statistical formula to show which of these categories a total of 50 people did the best in in a memory test of words vs. pictures vs. numbers or if it is statistically not able to be proven "reject the null hypothesis"

Words Out of 20 Male & Female N=50	Pictures out of 18 Male & Female N=50	Numbers out of 18 Male & Female N=50
Words	Pictures	Numbers
16	17	12
15	16	12
17	15	11
14	16	14
17	14	14
16	17	16
17	14	8
14	16	9
19	17	15
10	9	15
12	16	13
14	15	12
11	14	9
11	14	10
14	15	17
11	13	14
13	13	12
13	13	12
12	16	12
15	17	11
11	14	10
16	16	10
12	13	16
12	9	8
9	11	11
341	360	303 totals
6.82	7.2	6.06 mean
2.564	2.2546	2.5219 Std. Deviation

Answer 1

here we use one-way anova with

null hypothesis H0: all three groups mean are equal

alternate Hypothesis Ha: atleast one group mean is different from other

since p-value between groups is less than typical alpha=0.05, so we reject H0 and conclude that atleast one group mean is different from other.

( here number of observation in each of the group is 25 accordingly analysis has been done, if it is different please revert back at earliest)

following information has been generated using ms-excel

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	25	341	13.64	6.573333
Column 2	25	360	14.4	5.083333
Column 3	25	303	12.12	6.36
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	67.38667	2	33.69333	5.610361	0.00544	3.123907
Within Groups	432.4	72	6.005556
Total	499.7867	74

if number of observation is 50 then following information has been generated and found the p-value is more than typical alpha=0.05, so we accept H0 ( fail to reject H0)

					within SS		between SS
Group	nj	mean(xj-)	s2	nj*xj-	(n-1)s2	(xj--x-)	nj(xj--x-)2
1	50	6.82	6.5733	341	322.0917	0.126667	0.80222222
2	50	7.2	5.0833	360	249.0817	0.506667	12.8355556
3	50	6.06	6.36	303	311.64	-0.63333	20.0555556
sum	150	20.08	18.0166	1004	882.8134	0	33.6933333
grand mean(x-)	6.693333
		ANOVA
SOURCE	DF	SS	MS	F	CRITICAL F(0.05)	p-value
BETWEEN	2	33.69	16.84667	2.81	3.06	0.063737
WITHIN(ERROR)	147	882.81	6.005533
TOTAL	149	916.51