Question

Not only does speaking two languages have many practical benefits in a globalized world, but there is also growing evidence that it appears to help with brain functioning as we age. In one study, 80 participants were divided equally among 4 groups: younger adult bilinguals, older adult bilinguals, younger adult monolinguals, and older adult monolinguals. Each participant was asked to complete a series of color-shape task-switching tests. For our analysis, we’ll focus on the total reaction time (in microseconds) for these experiments; the shorter the reaction time, the better. a) (2 points) Make a table giving the sample size, mean, and standard deviation for each group. Is it reasonable to pool the variances? b) (2 points) If bilingualism helps with brain functioning as we age, explain why we’d expect to find an interaction between age and lingualism. Also create an interaction plot that shows the type of pattern we’d expect. c) (5 points) Analyze the data using an ANOVA. Report the test statistics, degrees of freedom, and p-values (α = 0.10). Write a short paragraph summarizing your findings.

Age   Ling   Time
Young   Mono   828
Young   Mono   849
Young   Mono   839
Young   Mono   878
Young   Mono   723
Young   Mono   826
Young   Mono   913
Young   Mono   792
Young   Mono   869
Young   Mono   748
Young   Mono   803
Young   Mono   786
Young   Mono   827
Young   Mono   865
Young   Mono   831
Young   Mono   848
Young   Mono   813
Young   Mono   736
Young   Mono   825
Young   Mono   815
Young   Bi   748
Young   Bi   784
Young   Bi   741
Young   Bi   833
Young   Bi   795
Young   Bi   845
Young   Bi   748
Young   Bi   688
Young   Bi   777
Young   Bi   758
Young   Bi   806
Young   Bi   767
Young   Bi   783
Young   Bi   769
Young   Bi   818
Young   Bi   769
Young   Bi   838
Young   Bi   846
Young   Bi   841
Young   Bi   759
Old   Mono   1051
Old   Mono   961
Old   Mono   905
Old   Mono   1042
Old   Mono   1049
Old   Mono   1019
Old   Mono   923
Old   Mono   1033
Old   Mono   955
Old   Mono   985
Old   Mono   1050
Old   Mono   1027
Old   Mono   1071
Old   Mono   997
Old   Mono   1056
Old   Mono   902
Old   Mono   985
Old   Mono   930
Old   Mono   1027
Old   Mono   969
Old   Bi   949
Old   Bi   955
Old   Bi   862
Old   Bi   975
Old   Bi   949
Old   Bi   951
Old   Bi   849
Old   Bi   1013
Old   Bi   943
Old   Bi   915
Old   Bi   960
Old   Bi   822
Old   Bi   892
Old   Bi   886
Old   Bi   944
Old   Bi   888
Old   Bi   963
Old   Bi   802
Old   Bi   914
Old   Bi   954

Answer 1

a.

Ling Age Total Count Mean StDev
Bi Old 20 919.3 54.3866

Bi Young 20 785.65   42.0429

Mono Old 20 996.9 53.5952

Mono Young 20 820.7 47.3854

Test for Equal Variances: Time versus Ling, Age

95% Bonferroni confidence intervals for standard deviations

Ling Age N Lower StDev Upper
Bi Old 20 38.5470 54.3866 89.0677
Bi Young  20 29.7983 42.0429 68.8527
Mono Old 20 37.9861 53.5952 87.7717
Mono Young 20 33.5849 47.3854 77.6020

Bartlett's Test (Normal Distribution)
Test statistic = 1.56, p-value = 0.669

Levene's Test (Any Continuous Distribution)
Test statistic = 0.70, p-value = 0.555

Since p-value>0.05 so we can assume population variances of all groups are equal and hence it is reasonable to pool the variances.

b.

Since bilingualism helps with brain functioning as we age, so we can expect that there is an interaction between age and bilingualism.

Interaction Plot for Time Data Means 1000 Ling Bi Mono 950 E 900 850 (ki Young Age

c.

Two-way ANOVA: Time versus Age, Ling

Source DF SS MS F P
Age 1 479880 479880 195.01 0.000
Ling 1 63394 63394 25.76 0.000
Interaction 1 9031 9031 3.67 0.059
Error 76 187023 2461
Total 79 739329

Since p-value of interaction between age and bilingualism=0.059>0.05 so the interaction effect is absent whereas Age and bilingualism are separately significant (since their corresponding p-values<0.05).