This assessment consists of answering three questions:
a) (750 words) Critically discuss the rationale for
null hypothesis significance testing. Your answer needs to include a brief description of the underlying statistical theory as well as limitations associated with this approach to inferential testing. Please, make sure to add any references at the end of your answer.
b) (750 words) Explain and critically discuss
the application of confidence intervals (CIs)to inferential testing. Your answer should explain what CIs are, their strengths and factors which influence the width of a CI. Please, make sure to add any references at the end of your answer.
c) (1000 words). Suppose that you are invited to be part of a research project. Your task is to examine the relationship between care provision and gender. As part of this project, you are asked to
write a report
based on results from analysis of a secondary dataset, i.e. the first wave of the English Longitudinal Survey of Ageing (ELSA).
This assessment consists of answering three questions: a) (750 words) Critically discuss the rationale for null hypothesis significance testing. Your answer needs to include a brief description of the underlying statistical theory as well as limitations associated with this approach to inferential testing. Please, make sure to add any references at the end of your answer. b) (750 words) Explain and critically discuss the application of confidence intervals (CIs) to inferential testing. Your answer should explain what CIs are, their strengths and factors which influence the width of a CI. Please, make sure to add any references at the end of your answer. c) (1000 words). Suppose that you are invited to be part of a research project. Your task is to examine the relationship between care provision and gender. As part of this project, you are asked to write a report based on results from analysis of a secondary dataset, i.e. the first wave of the English Longitudinal Survey of Ageing (ELSA). The dataset has a sample of n = 2078 participants who reported valid information for how long they had looked after anyone in the past week (including their partner or other people in the household). Those are the older people (aged 50+ in England) who have been actively involved in care provision. There are three variables in the analysis: disex: gender (1=Male, 2=Female); spcac: a continuous variable reporting the number of hours spent on caring for others in the past week. Care_cat: a categorical variable also reporting the number of hours spent caring for others during the past week (1=0-20 hours, 2=21-50 hours, 3=51-168 hours). In order to complete the report, you are recommended to read some relevant articles in the references list to learn the background of the topic, or find other articles that are relevant yourself. You will need to read the codebook section of the output to familiarise yourself with the variables. The suggested structure of your written report is: introduction, data and methods, findings, discussion and references. The report should address the following points: · Introduce the topic and research question and develop appropriate research hypotheses, justifying them with reference to the literature. · Identify the level of measurement of variables and describe data. · Identify the bivariate analysis tests and explain why they were selected, considering both the characteristics of data and statistical tests. · Report the results of these tests using the SPSS output and critically interpret the findings. References list for Question c) Dahlberg, L., Demack, S. and Bambra, C. (2007), Age and gender of informal carers: a population‐based study in the UK. Health & Social Care in the Community, 15: 439-445. https://doi.org/10.1111/j.1365-2524.2007.00702.x Langner, L. A., & Furstenberg, F. F.. (2020). Gender Differences in Spousal Caregivers’ Care and Housework: Fact or Fiction?. The Journals of Gerontology: Series B, 75(1), 173–183. https://doi.org/10.1093/geronb/gby087 Accessing the output You can download the Word version of the output under the ‘Quantitative Assignment Submission, Resources and Support’ section. Please see next attached document assignment SPSS output *get the information of variables CODEBOOK disex [n] spcac [s] Care_cat [n] /VARINFO POSITION LABEL TYPE FORMAT MEASURE ROLE VALUELABELS MISSING ATTRIBUTES /OPTIONS VARORDER=VARLIST SORT=ASCENDING MAXCATS=200 /STATISTICS COUNT PERCENT MEAN STDDEV QUARTILES. Codebook disex Value Count Percent Standard Attributes Position 1 Label Subject~s sex Type Numeric Format F1 Measurement Nominal Role Input Valid Values 1 Male 778 37.0% 2 Female 1325 63.0% Missing Values -9 Refusal 0 0.0% -8 Don't Know 0 0.0% -1 Not applicable 0 0.0% spcac Value Count Percent Standard Attributes Position 32 Label How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Type Numeric Format F3 Measurement Scale Role Input N Valid 2078 Missing 25 Central Tendency and Dispersion Mean 55.62 Standard Deviation 68.206 Percentile 25 6.00 Percentile 50 16.00 Percentile 75 168.00 Labeled Values -9 Refusal 0 0.0% -8 Don't Know 25 1.2% -1 Not applicable 0 0.0% Care_cat Value Count Percent Standard Attributes Position 78 Label Hours of care in last week in 3 categories Type Numeric Format F3 Measurement Nominal Role Input Valid Values 1 0-20 hours 1149 54.6% 2 21-50hours 317 15.1% 3 51-168hours 612 29.1% Missing Values System 25 1.2% *get the descriptive statistics of nominal level variables FREQUENCIES VARIABLES=disex Care_cat /ORDER=ANALYSIS. Frequencies Statistics Subject~s sex Hours of care in last week in 3 categories N Valid 2103 2078 Missing 0 25 Frequency Table Subject~s sex Frequency Percent Valid Percent Cumulative Percent Valid Male 778 37.0 37.0 37.0 Female 1325 63.0 63.0 100.0 Total 2103 100.0 100.0 Hours of care in last week in 3 categories Frequency Percent Valid Percent Cumulative Percent Valid 0-20 hours 1149 54.6 55.3 55.3 21-50hours 317 15.1 15.3 70.5 51-168hours 612 29.1 29.5 100.0 Total 2078 98.8 100.0 Missing System 25 1.2 Total 2103 100.0 *the descriptive statistics of ratio level variables and check the outliers and normality EXAMINE VARIABLES=spcac BY disex /PLOT HISTOGRAM NPPLOT /COMPARE GROUPS /STATISTICS DESCRIPTIVES /CINTERVAL 95 /MISSING LISTWISE /NOTOTAL. Explore Subject~s sex Case Processing Summary Subject~s sex Cases Valid Missing Total N Percent N Percent N Percent How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Male 768 98.7% 10 1.3% 778 100.0% Female 1310 98.9% 15 1.1% 1325 100.0% Descriptives Subject~s sex Statistic Std. Error How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Male Mean 56.68 2.510 95% Confidence Interval for Mean Lower Bound 51.75 Upper Bound 61.61 5% Trimmed Mean 53.58 Median 15.00 Variance 4837.689 Std. Deviation 69.553 Minimum 0 Maximum 168 Range 168 Interquartile Range 163 Skewness .894 .088 Kurtosis -1.078 .176 Female Mean 55.00 1.863 95% Confidence Interval for Mean Lower Bound 51.35 Upper Bound 58.66 5% Trimmed Mean 51.70 Median 16.00 Variance 4545.781 Std. Deviation 67.422 Minimum 0 Maximum 168 Range 168 Interquartile Range 144 Skewness .986 .068 Kurtosis -.880 .135 Tests of Normality Subject~s sex Kolmogorov-Smirnova Shapiro-Wilk Statistic df Sig. Statistic df Sig. How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Male .276 768 .000 .683 768 .000 Female .272 1310 .000 .684 1310 .000 a. Lilliefors Significance Correction How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Histograms Normal Q-Q Plots *carry out t test T-TEST GROUPS=disex(1 2) /MISSING=ANALYSIS /VARIABLES=spcac /ES DISPLAY(TRUE) /CRITERIA=CI(.95). T-Test Group Statistics Subject~s sex N Mean Std. Deviation Std. Error Mean How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Male 768 56.68 69.553 2.510 Female 1310 55.00 67.422 1.863 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Equal variances assumed 4.296 .038 .540 2076 .589 1.675 3.100 -4.405 7.755 Equal variances not assumed .536 1566.303 .592 1.675 3.126 -4.456 7.805 Independent Samples Effect Sizes Standardizera Point Estimate 95% Confidence Interval Lower Upper How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Cohen's d 68.218 .025 -.065 .114 Hedges' correction 68.242 .025 -.065 .114 Glass's delta 67.422 .025 -.064 .114 a. The denominator used in estimating the effect sizes. Cohen's d uses the pooled standard deviation. Hedges' correction uses the pooled standard deviation, plus a correction factor. Glass's delta uses the sample standard deviation of the control group. *Nonparametric Tests: Independent Samples. NPAR TESTS /M-W= spcac BY disex(1 2) /MISSING ANALYSIS. NPar Tests Mann-Whitney Test Ranks Subject~s sex N Mean Rank Sum of Ranks How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Male 768 1018.14 781930.50 Female 1310 1052.02 1378150.50 Total 2078 Test Statisticsa How many hours in the past week did you do this? @/@/IF ALL THE TIME , ENTER 168 Mann-Whitney U 486634.500 Wilcoxon W 781930.500 Z -1.254 Asymp. Sig. (2-tailed) .210 a. Grouping Variable: Subject~s sex * carry out chi-square test CROSSTABS /TABLES=care_cat BY disex /FORMAT=AVALUE TABLES /STATISTICS=CHISQ /CELLS=COUNT EXPECTED ROW COLUMN TOTAL SRESID /COUNT ROUND CELL. Crosstabs Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Hours of care in last week in 3 categories * Subject~s sex 2078 98.8% 25 1.2% 2103 100.0% Hours of care in last week in 3 categories * Subject~s sex Crosstabulation Subject~s sex Total Male Female Hours of care in last week in 3 categories 0-20 hours Count 430 719 1149 Expected Count 424.7 724.3 1149.0 % within Hours of care in last week in 3 categories 37.4% 62.6% 100.0% % within Subject~s sex 56.0% 54.9% 55.3% % of Total 20.7% 34.6% 55