The Data from Amsterlaw & Wellman (2006) being studied in Psyc20008 Developmental Psychology
(a) Contingency Table
Figure 1: The Contingency Table
Type of Explanation
Desire
Situational
a = 9
b = 5
a + b = 14
Comparison
c = 3
d = 10
c + d = 12
Total
a + b = 11
b + d = 15
a + b + c + d = 26
(b) Observed Chi-Square Test Statistics
Using the formula x2 = (ad – bc)2 (a + b +c) / (a + b)(c + d)(b + d(a + c)
Chi-Square (x2) =26[(9)(10) - (5)(3)]2 / (14)(12)(15)(11) = 0.0858
The percentage Derivation is got by the formula:
X 100
Hence:
(c) The Odds of Giving a Desire Explanation for Children Who Are in the Comparison Group
Under Compassion we take desire number and then subtract the corresponding expected number (3- 11).
Square the difference [(-8)2] = 64
Divide the squares obtained for desire by the expected number for desire [64/11].
The Answer = 5.8181 chances of giving a desired explanation for children in Compassion.
(d) The Odds for Children in the Microgenetic Group Giving a Desire Explanation
Under Microgenetic we take desire number and then subtract the corresponding expected number (9- 11).
Square the difference [(-2)2] = 4
Divide the squares obtained for desire by the expected number for desire [4/ 11]
The Answer = 0.3636 chances of giving a desired explanation for children in Microgenetics.
PART B
Correct Response, and Brief Explanation of the Response
(a) The Relative p Value for the Second Hypothesis Test
In this case the relative p value for the second hypothesis test might be negative or a number lower than 0.036, this is because in the calculation of p values in other words hypothesis testing, the null hypotheses might be expressed and then rejected and the alternative or relative p value is certainly not certain, because the first p value (null hypothesis) might have, accidental, produced the results (its value).
(b) The Lower and Upper Bound Values
The upper and the lower values of a 2X2 cross-classified with a Chi-squire of 10.51, and a sample size of 56, must be less than 56, simply because they can not be more than the sample size, the upper and the lower values are also very close, they have no big difference due to the value of the higher Chi-squire and the low sample size.
(c) Null Hypothesis Test
(i) H: m + 2.0 = 0, and 0
This will imply that there is no relationship or correlation between the two aspects of the data being compared.
(ii) H: m = -1.0?
This will imply that the negative hypothesis is true; the unexpected outcome has been proved as possible.
Researcher with More Meaningful Result
Dr. Nina Nomoneyworries with a sample 80 people will have more meaningful results, than Professor Chuck Cheapskate who had 20 people in his sample. This is because; the sample size depends on the confidence level and confidence interval. A higher confidence level of 95% will imply a much higher sample size from the population, and the main advantage for this is that the research gets a higher power of accepting the particular hypothesis.
Standardized Multiple Regression Equation
(a) Interpretation of the Three Regression Coefficients in this Model
68 TELD is the education level factor, it analyses the education related norms to give a score that represents the same, and it mainly implies that above average education thus a score is worth making a meaning impact in life. The .11Age factors in the child age, and it implies the higher the age of a child, the more the chances of being productive in the society. And lastly .45Siblings factors in the number of children in a family, as it can affect various socio-economic aspects of a population.
(b) Two Equivalent Interpretations of the Regression Coefficient for Age in the Regression Model Equation
Age can be interpreted as children can contribute or have economic value that is explained as the higher the age of the child the more the economic stress that he posses to the rest of the other coefficients like education, this can also be interpreted as: the older the child becomes, the more resources needed to support his basic needs like education.
Multiple Linear Regression
Given:
5 independent variables
Sample size of 43 the multiple correlation coefficient equaled 0.57 95% confidence interval for this point estimate equaled (0.13; 0.69)
The R-Squared is also called the multiple R2 and is got by the formula: R2 = (SS (Total) - SS (Residual)) / SS (Total).
(a) The R2 Values for both the Point and Interval Estimates of the Population R2 Value
The R2 value for estimated point of 0.13 is:
R2 = (SS (Total) - SS (Residual)) / SS (Total).
SStotal = Sum of Squared Derivations
SStotal = 0.101
SSresidual = 5(0.57) + 1(0.57)
= 2.85 + 0.57
SSresidual = 3.42
R2 = (0.101 – 3.42) / 0.101
R2 = 32.86%
The R2 value for estimated point of 0.69 is:
SStotal = Sum of Squared Derivations
SStotal = 2.8566
SSresidual = 5(0.57) + 1(0.57)
= 2.85 + 0.57
SSresidual = 3.42
R2 = (2.8566 – 3.42) / 2.8566
R2 = 19.72%
(b) Inferential Interpretation of the Strength of Prediction of the Linear Regression Model In Terms of the Sample R2 Value
The value of R2 gives some information about the effectiveness of a model. In regression, in our case the value of R2 squared increases the limits raised from the lower to the higher, this is the difference in the value of R2 in the two instances. Lastly, a value R2 that is close 1.0 designates that the; if it was to be plotted the regression line would have perfectly fitted the data, hence 0.13 best suits this model than 0.69.
(c) Multiple Correlation Coefficient Value in the Second Sample
(i) The 95% Confidence Interval for the Sample R2 Value
Just as a reminder R2 value is used as a measure of the strength of prediction, thus the 95% confidence can imply various points: this is observable for very predictable comparison, and there is a very strong correlation between the preceding values in that table. This percentage suggests that the model is very effective and it was rightly chosen and applied for the right data type.
(ii) The Adjusted R2 Value for this Second Replicated Sample Compared to the First Sample
The adjusted value of R2 mainly highlights the errors that exist in the calculation of R2 , Its is also worth noting that R2 is just the portion of the entire squared error that is clarified by the model.
