13. Four young children were monitored closely over a period of several weeks tomeasure how much they watched violent television programs and their amountof violent behavior toward their playmates. The results were as follows:
Weekly Viewing of Number of Violent or Aggressive
Child’s Code Number Violent TV (hours) Acts Toward Playmates
G3368 14 9
R8904 8 6
C9890 6 1
L8722 12 8
(a) Make a scatter diagram of thescores; (b) describe in words the general pattern of correlation, if any; (c) figure
the correlation coefficient; (d) figure whether the correlation is statistically significant(use the .05 significance level, two-tailed); (e) explain the logic of whatyou have done, writing as if you are speaking to someone who has never heard
of correlation (but who does understand the mean, deviation scores, and hypothesistesting); and (f) give three logically possible directions of causality, indicatingfor each direction whether it is a reasonable explanation for the correlation
in light of the variables involved (and why).
(b) It appears from the scatter diagram that there is a positive correlation between Tv hours and Violent acts. Higher the Tv hours, more the number of violent acts is her anxiety.
(c) R = 0.9230 and R^2 = 0.852
We see that R = 0.9230, indicating a high degree of negative correlation between Tv hours and Violent acts. R^2 = 0.852, which implies that 85.20% of the variation in violent acts can be explained by the variation in Tv hours
(d) Hypothesis Testing:
H0: There is no correlation between the variables, that is, β = 0
Ha: variables are correlated, that is, β ≠ 0.
Regression Analysis
r² / 0.853 / n / 4
r / 0.923 / k / 1
Std. Error / 1.673 / Dep. Var. / Violent acts (y)
ANOVA table
Source / SS / df / MS / F / p-value
Regression / 32.4000 / 1 / 32.4000 / 11.57 / .0766
Residual / 5.6000 / 2 / 2.8000
Total / 38.0000 / 3
Regression output / confidence interval
variables / coefficients / std. error / t (df=2) / p-value / 95% lower / 95% upper / std. coeff.
Intercept / -3.0000 / 0.000
Tv hours (x) / 0.9000 / 0.2646 / 3.402 / .0766 / -0.2384 / 2.0384 / 0.923
From the Regression output, we see that the p- value for the population slope is 0.0766. Since 0.0766 > 0.05, we fail to reject Ho
Conclusion: At α = 0.05, there is no sufficient evidence to say that TV hours have a relationship with the number of violent acts
(e) The present study examined if the violent behavior and Tv hours were significantly correlated in the population. A regression hypothesis test was conducted and on the basis of the results, there is insufficient evidence to conclude that the variables are correlated.
(f) We have the following possibilities with respect to the variables x and y:
(i) x and y are not correlated - This appears somewhat improbable because research has shown too much Tv viewing can result in violent behavior.
(ii) x and y are directly correlated - This is logical because we would more Tv viewing with more violent acts
(iii) x and y are inversely correlated - This is not probable.