Question

There is a statistical difference in these perceptions between North Africa and Southern Africa. The results of the independent-sample t-test were significant, p = 0.00, that perceptions between North African (M= 4.90 , SD = 3.09, N = 5418) and Southern Africa (M= 5.78 , SD = 2.80 , N = 15979) is statistical different regarding perceptions about current levels of democracy. The results were statistically significant and the effect size is strong, mean difference 0.879, leading to a meaningful results.

Based on the above is are the results meaningful? I know it is statistically signficant but not sure if it is meaningful.

How can you tell I the mean difference is meaningful?

Answer 1

Answer)

Null hypothesis Ho : u1 = u2

Alternate hypothesis Ha : u1 not equal to u2

Test statistics t = (m1-m2)/(standard error)

Standard error = √{(s1^2/n1)+(s2^2/n2)}

M1 = 4.9, M2 = 5.78

S1 = 3.09, S2 = 2.8

N1 = 5418, N2 = 15979

After substitution

Test statistics t = -18.51

Degrees of freedom is = smaller of n1-1, n2-1 = 5417

For 5417 dof and -18.51 test statistics

P-value is 0 from t distribution

As the obtained p-value is extremely small, we reject the null hypothesis

So we can conclude that there is a difference.

{We can also find p-value through z table as sample size is large and as the sample size increases, t distribution approaches z distribution}

From z table, P(z<-18.51) = 0

As the test is two tailed, p-value = 2*0 = 0