Reference no: EM132311622

Assignment

Assume two-tailed tests with a conventional p critical (alpha of 5%, or .05) unless specified in thequestion.

If the third decimal place (or fourth for p values), where provided, is 5 or greater, round the seconddecimal place upwards. e.g. SPSS reporting a mean of 15.335, results in your rounding to M=15.34.

Numbers representing statistics which have a possible range above 1 should have a zero placeholder, while those with an upper limit of 1 require no zero placeholder. e.g. p=.651 or r=.66 orM=0.78

Exact p values are required to three decimal places. e.g. p=.050

Where SPSS reports 0.000, provide the following as your answer after the equals sign p=.001 (thisfollows the APA 6th edition rules for using p < .001 when p is smaller than .001. For exact p values in this Task, please use the p = .001 noted when SPSS reports .000).

Finally, check the specific question for any question-specific requirements for the submission of youranswer.
 
The Data (SPSS)

The sample size is N=251 cases in the SPSS file. The keyvariables, used across the analyses, feature:

Total Mastery (Tmast): A psychological wellbeing measure of overall environmental mastery inmeeting challenges and goals (taken from seven items, next).

Seven Mastery question items (Mast1to Mast7): Representing the specific survey questions forMastery.

Total Negative Affect (Tnegaff): A measure of negative mood, taken from ten items in the PANAS.

Total Optimism (Toptim): Measure of overall optimism taken from six items.

Educational Group (edgroup): Five educational groups 1(did not complete high school), 2(completedhigh school), 3(some additional training), 4(completed undergrad uni), 5(completed postgrad uni).

Educational Group Dichotomised (edu_2cat): 1 (Up to [including] high school), 2 (Post-high school)

Age: Age of respondent in years.

Sex: Gender of respondent (1=Males; 2=Females)

Stress: Primary source of stress: 1(Work), 2(Relationships), 3(Health), 4(Money).

Total Perceived Stress at time 1 (Tpstress): Initial (time 1) total perceived stress score taken from tenitems.

Total Perceived Stress at time 2 (Tpstress_time2): Total perceived stress score at the second timepoint taken from ten items.

Total Perceived Stress at time 3 (Tpstress_time3): Total perceived stress score at the third timepoint taken from ten items.

Questions

Section 1 (Q1, Q2, Q3)

Q1a/b/c.

Focusing on one of the sub-scales of psychological well-being, Total Mastery (Tmast), complete the following questions using SPSS to provide information on the estimate of skewness, kurtosis; tests of normality; and transformations of the key variable.

Using the skewness and kurtosis scores and their standard errors, is Tmast normally distributed?

(First, generate a 95% confidence interval, or use the Z score approach, each, for skewnessand kurtosis before consulting the K-S Lillefors test for normality).

Q1a. Using a 95% confidence interval of the skewness score (score and standard error provided by SPSS), assess whether Tmast is skewed? Choose 1, below: Positively skewed, Not significantly skewed, Negatively skewed.

Q1b. Using a 95% confidence interval of the kurtosis score, assess whether Tmast is kurtic?Choose 1, below:
Letopkurtic, Not significantly kurtic, Platykurtic.

Q1c. Assess the normality of Tmast using the Kolmogorov-Smirnov test for normality,provided by SPSS (Choose 1, below):
Fail to Reject the Null Hypothesis that Tmast as normally distributed
Reject the Null Hypothesis that Tmast is normally distributed
 
Q2a-g. Focusing on Negative Affect of the PANAS (Tnegaff), complete the followingquestions.

Using the skewness and kurtosis scores and their standard errors, assess whether Tnegaffnormally distributed.
(First, generate a 95% confidence interval, or use the Z score approach, each, for skewnessand kurtosis before consulting the K-S Lillefors test for normality).

Q2a. Using a 95% confidence interval of the skewness score, assess whether Tnegaff isskewed.
Positively skewed, Not significantly skewed, Negatively skewed.

Q2b. Using a 95% confidence interval of the kurtosis score, assess whether Tnegaff is kurtic.
Letopkurtic, Not significantly kurtic, Platykurtic.

Q2c. Assess the normality of Tnegaff using the Kolmogorov-Smirnov test for normality:
Fail to Reject the Null Hypothesis that Tnegaff as normally distributed
Reject the Null Hypothesis that Tnegaff is normally distributed

Q2d. Using the skewness or kurtosis score (and respective standard error), does a square-roottransformation of Tnegaff result in (Answer each, below):
A non-skewed distribution (using Skewness score method): Y/ N
A non-kurtic distribution (using Kurtosis score method): Y /N

Q2e. Test the null hypothesis of univariate normality using the Kolmogorov-Smirnovnormality test (Choose 1, below):
Accept (it is normal)
Reject (not normal)

Q2f. Using the skewness or kurtosis score (and respective standard error), does a natural log(i.e. ln) transformation of Tnegaff result in (Answer each, below):
A non-skewed distribution (using Skewness score method): Y/ N
A non-kurtic distribution (using Kurtosis score method): Y /N

Q2g. Test the null hypothesis of univariate normality using the Kolmogorov-Smirnovnormality test (Choose 1, below):
Accept (it is normal)
Reject (not normal)

Q3a/b/c. Seven questions (MAST1 to MAST7) were used to indicate the Tmast overall scale.Using SPSS to calculate the Cronbach's Alpha reliability coefficient, what is the overall initialreliability of the total seven (MAST1 to MAST7) items?

Q3a. Report Cronbach's Alpha (use two decimal places) of the seven MAST questions:(MAST1 to MAST7)= ___

Q3b. Would this be regarded as an acceptable inter-item reliability? Choose 1, below:
Yes / No

Q3c. Using the statistics provided by SPSS Reliability (Cronbach's Alpha), Scale if itemremoved, remove items systematically to improve the Cronbach's Alpha. Be sure torecalculate Cronbach's Alpha each time an item is removed, if any are removed at all. Do notremove any more items if Cronbach's Alpha is decreased.
Final number of items: ___
Cronbach's Alpha: ___
Would this be regarded as an acceptable inter-item reliability? Choose 1, below:
Yes / No
 
Q4a-f. Conduct a Pearson correlation and simple linear regression between the PANASnegative affect (tnegaff) and the dependent variable Total Mastery (Tmast) to answer thefollowing questions.

Q4a. Is there a significant linear association between Tnegaff and Tmast? Choose 1, below:
Y / N

Q4b. Complete the following statistical summary (ensure you use the df and not N in theparentheses, and use .001 for p, when SPSS provides a significance of .000 or lower) forPearson's correlation coefficient:
r(___) = ___, p=____

Q4c. Using a simple linear regression with the dependent variable Tmast and the
independent variable Tnegaff, complete the following statistical summary:
F(___, ___)=____, p= ____

Q4cii. Do you Fail to Reject (Accept) or Reject the null hypothesis that there is no linearassociation between Tnegaff and Tmast?
Write Accept or Reject: ___

Q4di. Using a regression between the dependent variable Tmast and the independentvariable Tnegaff, if significant, what is the unadjusted r squared (put NA if not significant)?
R squared = ___

Q4dii. According to this R squared provided in Q4di, what percent of variation in the
dependent variable is associated or accounted for by the independent variable (put NA ifyou put NA in the previous question, do not include the ‘%' in your answer, just use anumerical answer with zero decimal places)?
% = ___

Q4e. Complete the following unstandardised prediction equation based on a linear
regression of the dependent variable Tmast on the independent variable Tnegaff (be sure toinclude any negative signs in your answers, as appropriate). Complete this questionregardless of any significance or non-significance in answered previous questions. Enteryour Constant and Tnegaff Regression Coefficient (unstandardised), below:
Tmast = ____ + ( ____ xTnegaff)

Q4f. Using standardised residuals greater than +/- 3 to indicate influential cases, provide thecase_ID value (note: this is not CASE, as in row number, but the value within a variablecalled case_ID within the dataset) numbers of the two most extreme standardised residuals(in order of most extreme and second-most extreme):
Case numberof the Highest standardised residual: ___
Case numberof the Second-Highest standardised residual: ___
 
Q5a-g. ANCOVA
The research team wish to test the group differences (based on education) in Mastery(Tmast) removing the effects of a covariate, AGE of person in years. To check initialassumptions, you should have the following simple one-way ANOVA of Edgroup differencesin mean Mastery as follows: DV: Mastery (Tmast); IV: Educational Group: F(4,244)=2.11.p=.080; (use a conventional alpha, p critical, of 5% or .05 throughout this assessment).

Q5a. Conduct an ANCOVA using the covariate: AGE, examining education group (edgroup)differences in Total Mastery (Tmast) added to the above to provide the following results.Provide the key results and interpretations as requested:
For the Covariate, Age: F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis in regards to the relationship between thecovariate and the Mastery dependent variable
(write Accept or Reject in this space):___
For Edgroup: F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis for Edgroup differences in (adjusted) Masterycontrolling for Age:
(Write Accept or Reject in this space): ___

Q5b. Conduct a statistical test to test the assumption that there is no significant differencesbetween education groups (Edgroup) and the covariate, Age:
F(___, ___)=____, p= ____

Is your answer, above, indicative of a violation of one of the assumptions of the ANCOVA
(Write Yes or No in the space): ___

Q5c. Replace the Age covariate, used in your original ANCOVA in Q5a, with Total LifeSatisfaction (Tlifesat). I.e. Remove Age from now on. This new ANCOVA examines theEdgroup differences in Tmast, controlling for Tlifesat.

Provide the key results and interpretations as requested:
For the Covariate, Tlifesat, in the ANCOVA:
F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis in regards to the relationship between thecovariate and the Mastery dependent variable
(write Accept or Reject in this space): ___
For Edgroup: F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis for Edgroup differences in (adjusted) Masterycontrolling for Total Life Satisfaction
(Write Accept or Reject in this space): ___

Q5d. Conduct a statistical test to test the assumption that there is no significant differencesbetween education groups and the covariate:
F(___, ___)=____, p= ____

Is your answer, above, indicative of a violation of one of the assumptions of the
ANCOVA (Write Yes or No in the space): ___

Q5e (i). Check the homogeneity of regression slopes assumption, "generally" are theregression slopes between the covariate and the dependent variable the same across thedifferent groups? To be specific, are all of the slopes either positive, or negative (i.e. noslopes go in opposite sign directions)?
(Write Yes or No in the space): ___

Q5e(ii). Using your Tmast and Tlifesat plot showing sub-group regression slopes forEdgroup, which Edgroup has the flattest slope? (i.e. alternatively, which subgroup ofEdgroup has the lowest [closest to zero] beta coefficient for Tlifesat?) Choose one of thefollowing:
1 'did not complete high school'
2 'completed high school'
3 'some additional training'
4 'completed undergrad uni'
5 'completed postgrad uni'

Q5f. Regardless of any potential lack of overall model significance, or any potential failurewith assumptions, using Bonferroni adjusted post-hoc tests between education groups(edgroups) on Total Mastery, controlling for Total Life Satisfaction, was group 4 (unibachelor) significantly higher than group 1 (did not complete high school) in the adjustedmean Tmast?
(Write Yes or No in the space): ___

Q5g. Identify the two adjusted means this specific test used and provide them in the spacesprovided:
M(group 4): ____ ;
M(group 1): ____
 
Q6a-h. ANOVA1
The lead researcher has argued that participants with different types (groups) of Stress, anddifferent Genders (Sex) will have different mean levels of Tmast, and that further, the meanTmast differences between Males and Females (Sex) will vary across the Stress groups, i.e.there will be a Sex-by-Stress interaction in mean Tmast. Assess the main effects (if any) andinteraction effects (if any) using a Factorial Between Groups ANOVA. Assumptions aretested at the end of the analysis.

Q6a. Conduct a Factorial Between Groups ANOVA using Stress and Sex as groupingindependent variables and Total Mastery (Tmast) as the dependent variable, and answerthe following questions:
Report the Main effect Stress Types:
F(___, ___)=____, p= ____

Accept or Reject the null hypothesis that groups based on different Stress Groups have thesame Mean Tmast.
Write Accept or Reject: ___

What is the strength of the relationship (effect size) in this instance? Use proportions to twodecimal places and not percentages in your answer; put NA if reporting the strength of theeffect is not appropriate.
Partial η2 : ___
Report the Main effect Sex: F(___, ___)=____, p= ____

Accept or Reject the null hypothesis that groups based on different Sex Groups have thesame Mean Tmast.
Write Accept or Reject: ___

What is the strength of the relationship (effect size) in this instance? Use proportions to twodecimal places and not percentages in your answer; put NA if reporting the strength of theeffect is not appropriate.
Partial η2 : ___
Report the Interaction Effect: F(___, ___)=____, p= ____

Accept or Reject the null hypothesis that the mean Tmast differences between Males andFemales across the Stress Type groups are the same.
Write Accept or Reject: ___

What is the strength of the relationship (effect size) in this instance? Use proportions to twodecimal places and not percentages in your answer; put NA if reporting the strength of theeffect is not appropriate.
Partial η2 : ___
Q6b. Which of the following best explains the nature of any significant interaction found in Q6a(Choose 1 below):
There were no significant interactions
The differences between males and females were significantly larger in the MoneyStress Type than other Stress Types
The differences between males and females were significantly larger in the
Relationships Stress Type than other Stress Types
The differences between males and females were significantly larger in the WorkStress Type than other Stress Types

Q6c. Check (test) the assumption of the normality of the distribution of the dependentvariable within each of the Sex-by-Stress groups (i.e. not the main Stress groups OR Sexgroups but within each of the eight groups) using formal tests of normality. To do this, useSPSS Explore, Plots, Normality Plots with Tests, but ensure you also include your groupingvariables in the Factor box in Explore (i.e. not just the dependent variable alone).
Tick any of the following which fail the test of normality (i.e. would reject the nullhypothesis that the particular group is normally distributed).
Sex-by-Stress Group (indicate which of the following fail normality i.e. reject the nullhypothesis in the formal normality test requested)

• Male - Work
• Male - Relationships
• Male - Health
• Male - Money
• Female - Work
• Female - Relationships
• Female - Health
• Female - Money

Q6d. Check (test) the assumption of the homogeneity of variance for this ANOVA
undertaken in Q6a.:
F(___, ___)=____, p= ____

Do you Accept or Reject that the variances between the groups are the same:
(Write Accept or Reject): ___
 
ANOVA2
Q6e. It has been argued that Males and Females have different mean levels of Optimism(Toptim) at different educational levels (Edu_2cat). For example (and this is not to betreated as a directional hypothesis), females might become more optimistic with highereducational credentials. Conduct a Factorial Between Groups ANOVA examining the mainand interaction effects of Education (Edu_2cat) and Sex (Sex) on respondents' TotalOptimism (Toptim: higher is more optimistic) and answer the following questions:

Report the Main effect of Education (Edu_2cat) Groups :
F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis that groups based on different EducationGroups have the same Mean Optimism (Toptim).
Write Accept or Reject: ___

What is the strength of the relationship (effect size) in this instance? Use proportions to twodecimal places and not percentages in your answer; put NA if reporting the strength of theeffect is not appropriate.
Partial η2 : ___

Report the Main effect of Sex:
F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis that groups based on different Sex Groups havethe same Mean Optimism (Toptim).
Write Accept or Reject: ___

What is the strength of the relationship (effect size) in this instance? Use proportions to twodecimal places and not percentages in your answer; put NA if reporting the strength of theeffect is not appropriate.
Partial η2 : ___
Report the Interaction Effect (Sex-by-Edu_2cat):
F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis that the mean Optimism (Toptim) differencesbetween Males and Females across the Education groups are the same.
Write Accept or Reject: ___

What is the strength of the relationship (effect size) in this instance? Use proportions to twodecimal places and not percentages in your answer; put NA if reporting the strength of theeffect is not appropriate.
Partial η2 : ___

Q6f. Which of the following best explains the nature of any significant interaction found(Choose 1, below):
There were no significant interactions
Females were more optimistic (toptim) than Males at lower Education levels andMales were more optimistic (toptim) than Females at higher Education levels(Edu_2cat)
Males were more optimistic (toptim) than Females at lower Education levels andFemales were more optimistic (toptim) than Males at higher Education levels(Edu_2cat)

Q6g. Check (test) the assumption of the normality of the distribution of the dependentvariable within each of the main effect groups (i.e. Edu_2cat groups, and then Sex groups).To do this, use SPSS Explore, Plots, Normality Plots with Tests, but ensure you also includeyour grouping variables in the Factor box in Explore (i.e. not just the dependent variablealone).
Tick any of the following which fail the test of normality (i.e. would reject the null
hypothesis that the particular group is normally distributed).
Sex-by-Education (Sex by Edu_2cat) Group (indicate which group(s) fail normality)
•Male - Up to HighSchool
•Male - Post-High School
•Female - Up to HighSchool
•Female - Post-High School

Q6h. Check (test) the assumption of the homogeneity of variance for this ANOVA:
F(___, ___)=____, p= ____

Do you Accept or Reject that the variances between the groups are the same:
Write Accept or Reject: ___

Q7a/b. A study of respondents' Total Perceived Stress, before (TPSTRESS), during
(TPSTRESS_Time2) and after (TPSTRESS_Time3) Christmas has hypothesised that
respondents' stress changes over the three time points. The null hypothesis is that the meanstress is the same over the three time points (repeated measures). Further, it is hypothesizedthat the mean Total Perceived Stress between respondents with different educational levels(Edu_2cat) might vary over time, particularly in the context of Christmas (i.e. perhaps thosewith higher education are less likely to ruminate than those with lower education under orafter stressful experiences?).

Q7a. Conduct a repeated measures ANOVA of the three total perceived stress variables(TPSTRESS, TPSTRESS_time2, TPSTRESS_time3), with the addition of a between groupseducational grouping variable (edu_2cat), testing the main effects of stress (be sure to usethe TPStress variables and not the stress variable) over the time points, educationalgrouping (edu_2cat), and the interaction of educational grouping over stress-time points.(taking care to check, or take action in relation to, Mauchly's test of sphericity first (useGreenhouse-Geisser epsilon if required) before interpreting within subject effects).

Mauchly's Test of Sphericity:
Test the null hypothesis that the variances of differences in stress measures over the threetime points were the same:
Write Accept or Reject: ___

What is the specific epsilon which is used to adjust the degrees of freedom on the withinsubjects F ratios (use three decimal places, or use NA if not applicable)?
Epsilon = ___

Report the Main effects (Within Subjects) of Stress over time:
F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis in this instance? (Main effect Stress):
Write Accept or Reject: ___

If appropriate (write NA if not appropriate to undertake specific post-hoc tests), conductpost-hoc tests, with Bonferroni adjustments, to examine which time points are differentamong the three measures of stress.
Do you Accept or Reject the null hypothesis that pairwise stress comparisons are the same.Specifically test this null hypothesis comparing:

Time 1 to Time 2 (null hypothesis)
Write Accept or Reject: ___
Time 2 - Time 3 (null hypothesis)
Write Accept or Reject: ___
Time 1 - Time 3 (null hypothesis)
Write Accept or Reject: ___

Main effects of Education group:
F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis in this instance (Main effect of Educationgroup):
Write Accept or Reject: ___

Interaction effects of Stress (over time) by Education Group.
F(___, ___)=____, p= ____

Do you Accept or Reject the null hypothesis in this instance (Interaction effects):
Write Accept or Reject: ___

Q7b. Which of the following best explains the nature of any significant interaction found (ifthere are no significant interactions choose NA):
NA: There are no significant interactions
Education differences in mean Total Perceived Stress are greater at the first timepoint in comparison to the last time point
Education differences in mean Total Perceived Stress are greater at the last timepoint than the first time point

Attachment:- SPSS Data set.rar