Question

To test whether memory changes with age, a researcher conducts an experiment in which there are four groups of six subjects each. The four groups are listed below. All subjects are in good health and matched in other important variables such as years of education, IQ, gender and motivation. Each subject is shown a series of nonsense syllables (a meaningless combination of three letters such as DAF or FUM) at a rate of one syllable every 4 seconds. The series is shown twice after which the subjects are asked to write down as many of the syllables as they can remember. The number of syllables remembered by each subject is shown below.

30 Years Old	40 Years Old	50 Years Old	60 Years Old
14	12	17	13
13	15	14	10
15	16	14	7
17	11	9	8
12	12	13	6
10	18	15	9

Please use SPSS to compute the test statistic for the following problems. For those questions, please turn in the appropriate SPSS output.

1. Perform the appropriate analysis
2. Wherever appropriate, calculate and report effect size(s)
3. Make a decision regarding the null hypothesis and write an APA-style conclusion interpreting your statistical results with regard to the aims of the experiment and as you would write it up in a report, including the statistical evidence to back it up.

Answer 1

Here we use one way anova test in SPSS,

Enter data in SPSS in one column and corrosponding group in next column.

Hypothesis :

Ho : There is no difference in means of these four group.

i.e. (memory does not change with age)

V/s

H1 : There is difference in at least one mean among these four group.

    i.e. (memory change with age)

SPSS => Analyze => Compare mean => One-way Anova => one box is open => choose dependent list as our data column and factor as group column => if we want multiple comparison then Post-hoc and tick as you need =>option descriptives => ok

The output as given above we see anova table from anova table,

ANOVA
Data
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	108.333	3	36.111	5.403	.007
Within Groups	133.667	20	6.683
Total	242.000	23

we see that,

test stat = F = 5.403

and see last column Sig = 0.007 it is p-value of that test.

We know that if p-value < alpha then we reject Ho.

Here at alpha = 0.05 level

p-value = 0.007 < alpha = 0.05 then we reject Ho.

We have to find effect size,

From above anova,

Effect size is approximatly medium.

45% of the total variance is accounted for by the age group effect.

Here at 0.05 level we conclude that,

There is difference in at least one mean among these four group  i.e. (memory change with age).

If we want to see there is significant difference in mean of these age group we carry out post-hoc analysis

In above given table we observe column 4 Sig. it is significance (p-value) for each group if our Sig < alpha then there is significant effect in group means.

at alpha = 0.05

We see that there is significant difference in 1 and 4, 2 and 4,3 and 4.

In this problem our aim is to find whether the memory change with age group and we have given 4 age groups with there corrosponding scores. Then here we used a One-way-Anova analysis and observe output anova then we see that our aim is satisfied i.e.memory change with age group.

At 0.05 level of significance result is statistically significant .There is no sufficient evidance to warrent the rejection of the claim that memory changes with age.