PRP4014: Statistics - Research Methods - Assessment Answer

From the above chart it can be easily shown that there is a decreasing trend for mean also the confidence interval or the lower and upper bounds are decreasing

But, for the standard deviation there is no specific trend.

The line of best fit for mean is y = -9.85x + 108.6

& standard deviation is y = -1.108x + 11.02

And hence the trend analysis is informative for mean and not for standard deviation.

1. 1. State the name and design of the statistical test performed below (3 marks)

One way ANOVA F – Test

One-factor analysis of variance or one-way analysis of variance is a special case of ANOVA for one factor of variable of interest and a generalization of the two sample t-test.

A One–Way ANOVA is a statistical technique by which we can test if three or more means are equal. It tests if the value of a single variable differs significantly among three or more levels of a factor.

We can say we have a framework for one way ANOVA when we have a single factor three or more levels & multiple observations at each level.

In this kind of layout, we can calculate the mean of the observations within each level of our factor.

The linear mathematical model for one-way classified data can be written as

Yij=µi + eij

The null hypothesis is given by

H0: µ1= µ2=µ3=…….µK

Against the alternative hypothesis

H1: µ1? µ2?µ3?…….µK

1. 1. Briefly summarize the main findings of the data below. (7 marks)

We can draw below mentioned interpretations from the given data:

• The mean for different levels of impulsivity is following a decreasing trend

Considering part (c) there is a decreasing trend for mean also the confidence interval or the lower and upper bounds are decreasing

But, for the standard deviation there is no specific trend.

• Using the given ANOVA table the value of calculated F is 26.874

And the tabulated value of F (2, 57) at 5% level of significance is 2.99

Since the calculated F (i.e.26.8874) is greater than the tabulated value of F (i.e. 2.99) therefore we reject the null hypothesis at 5 % level of significance. So the effects of different levels of impulsivity are different and we need to test which level of impulsivity has significant effect.

Hence there is a need to perform pair-wise comparison.

• From contrast coefficients, we can say that the contrasts coefficients are orthogonal because they have a zero sum of the products of their coefficients (2x0 + -1x1 + -1x-1 = 0).

• Ho: The means for different level of impulsivity are same.

H1: The means for different level of impulsivity are different.

From the contrast tests, the calculated value of t when variances are assumed to be equal and when variances are assumed to be different:

From the table above we can see that the calculated value of t is less than the tabulated value of t for all the contrast and assumptions.

Hence we can accept the null hypothesis Ho: The means for different level of impulsivity are same.

4. The data analysis provided on the following pages relates to subjective (Self-report) and objective (Skin Conductance Response) emotional responses to social stimuli. High emotional reactivity is measured by higher scores on each of the variables. Data was collected from two groups of participants: Psychopaths and Non-Psychopaths.

The output on the following pages is taken from a series of analyses attempting to understand the relationships between these variables:

1. State the percentage of variability of self-report responses explained by Skin Conductance in each of the two models in Regression 1 (2 marks)

From the model summary the adjusted R2 for non-psychopath & psychopath are 0.207 & 0.170.

Therefore by the definition of adjusted R2 the percentage of variability of self- report responses for the two models is:

(b) From the data presented in Regression 1, state the basic linear model equation and predict the Self-report emotional response for BOTH a Psychopath and Non-Psychopath with an SCR score of 9.

(6 marks)

The equation for simple linear regression model is Y=a+bX

From the given regression analysis the unstandardized coefficients are

The linear model equation for non-psychopath is Y=19.334+0.1077X

And for psychopath is 17.7742-00.118X

Self-report emotional response for both psychopath and non-psychopath is given by:

(c) Explain why the best predictors chosen by a Backwards regression does not have to be the same as that suggested by the Forced entry regression. (4 marks)

In backward regression method all p variables are included in the model then the least important variable is deleted if its contribution to the sum of squares is not significant. At the second stage the next least important variable whose contribution is not significant is deleted this process goes on till a variable cannot be deleted from the model.

It is considered to be an economical procedure as it attempts to examine only the best regression equation containing a certain number of variable.

In forced entry method all the variables are forced into the model simultaneously,

This method relies on good theoretical reasons for including the chosen variable but here the experimenter makes no decision about the order in which variables are entered.

Hence the above two methods of selection of independent variables provides us with different predictors.

(d)Sketch two plots you would find if the regression assumptions hold for these analyses. (3 marks)

(e) Summarise the key findings of the data presented in Regression analyses 1 and 2. Sketch an appropriate scatterplot with lines of best fit which illustrate these key findings. (10 marks)

Regression 1

(Cont.)

Regression 2

(Cont.)

The key findings for the two regression analysis are:

• The percentage of variability of self- report responses for the two models ( Non Psychopath & psychopath) for regression 1 are 21% & 17 % respectively.

• The percentage of variability of self- report responses for the two models ( Non Psychopath & psychopath) for regression 2 are 41% & 53 % respectively.

• Testing of Hypothesis

H0: ?=0

H1: At least one of the regression coefficients is not zero.

For regression 1

The calculated value of F for model 1 and model 2 are 8.5550 & 6.942 respectively.

And the tabulated value of F (1, 28) is 4.20

Since the calculated value of is greater than the tabulated value

Therefore, we may reject H0

Hence at least one of the regression coefficients is not zero.

For regression 2

The calculated value of F for model 1 and model 2 are 21.641 & 22.982 respectively.

And the tabulated value of F (2, 57) is 3.162 and F (3, 56) is 2.776

Since the calculated value of is greater than the tabulated value

Therefore, we may reject H0

Hence at least one of the regression coefficients is not zero.

• For Regression 1

The linear model equation for non-psychopath is Y=19.334+0.1077X

And for psychopath is 17.7742-00.118X