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# Descriptive Statistics and Inferential Test Questions Assessment Answer

Ryerson University

Daphne Cockwell School of Nursing CNUR 860 Fall 2019 Statistics Assignment

Bivariate Descriptive statistics and Inferential t test and ANOVA

Prepare your assignment as per APA 6^{th} format, inclusive of a title page, pages numbered, double spaced, reference page etc.

DO NOT RECOPY Question format and DO NOT INSERT ANSWERS IN POINT FORM;

Reference your Salkind text appropriately. Note: all charts and graphs must have a complete title. It is not adequate to use only the variable name for a title. It is not adequate to include chart or graph embedded within a sentence with the chart or graph as the end of the sentence. Follow APA 6^{th} for chart and graphs. Title must convey what the chart is telling the reader.

NOTE: do not use a downloaded copy of this word document as the foundation document on which you prepare and submit your paper (to do so may be considered plagiarism).

Create your own new word document.

**Use of personal tutors: **you may use a tutor ONLY for the explanation and understanding of statistical principles and NOT for the completion or production of this or any assignment in part or in whole. If you cite either an instructor or tutor you must quote as per APA (not to do so, will be considered plagiarism).

For assignment 1 use the C NUR 860 statistics assignment 1 database with data dictionary. This is fictional data.

**Grading: 4.0 marks automatic deduction if APA ****6th ****not followed, Assignments completed in point form will NOT be accepted for grading.**

**This is an individual assignment, not a group assignment, see course syllabus re directions to **__not share files, papers, or any part of your assignment with another__* *__student, in this or any other semester, as that may constitute academic misconduct.__

**Question 1. (Five marks total)**

a. Create a contingency (pivot in excel) tables, cut, and paste the excel output for the variables: (**You must decide which variables are independent and dependent in each pivot table) (1 mark for each pivot table for a total of 4 marks for all pivot tables). All charts must be labeled completely for full**** ****marks.**

1. age group’ and ‘gender’.

2. 'age group’ and ‘transition type”’

3. ‘age group’ and ‘ family support for transition’

4. 'gender’ and choose any other categorical variable that may be of interest to the researcher to describe this sample

(other than age group as conducted in i)

b. For **ONE **of the above tables, discuss (critically interpret the statistics) the findings of the descriptive analysis for this sample. Based upon these descriptive results for this sample, for that same table, suggest possible nursing implications for practice and one possible research question. (As this is bivariate analysis, must discuss bivariate practice and research implications ie discuss both variables in their association with each other). **1**** ****mark**

Question 2.**(Five marks**** ****total)**

The research question:

Is physical readiness for transition predictive of psychological readiness for transition?

1. Create summary statistics reports of descriptive data for the two variables:

a.‘physical readiness for transition’**0.25****Marks**

b. ‘psychological readiness for transition’**0.25 marks**

2. Explain the standard error (S.E.) number in relation to the sample means for each variable. **1**** ****mark**

3. Write a null hypothesis for the variables in question 2a and b.

State which variables are the independent and dependent and the levels of measure for each **0.5 marks**

4. Write a research (an alternate) hypothesis for the variables in question 2c. State if hypothesis is directional or not, (and if so, which direction). Logic of independent and dependent variables must be consistent between null and research hypotheses. **0.5**** ****marks**

5. For the two variables above, based upon the research hypothesis you created, calculate the Pearson r, and explain relationship in terms of strength and direction. Explain the relationship between the two variables in words. *(Note: you are not being asked to test the hypothesis you created above, just to calculate and** **explain the r) 1** ***mark**

6. Determine the coefficient of determination for the Pearson’s r calculated in question 2e. Explain its meaning in terms of the relationship between the two variables. (this number is found in excel output for the regression as the r squared) **0.5 marks**

7. For the two variables above, based upon the research hypothesis you created, create a scatter plot **0.5 marks**

Remember to decide which variable is logically the independent variable (or factor) and which is the dependent variable in order to decide which variable goes on the x- axis and which variable goes in the y-axis, as indicated by the hypothesis you created. Label the variables names and codes for each variable’s categories as per the data dictionary either in a legend or on the plot

8. Discuss the relationship between the two variables. You must discuss the relationships in words in terms of the hypothesis you presented, ie use the variable names in your discussion of the relationship to explain it (critically interpret the statistics) and possible implications for a) practice and b) research based on these results. Include a discussion of any of the demographic data that you have analyzed in previous assignments. **0.5**** ****marks**

**Question 3. (Five marks total)**

For the following research scenario, state and complete each step of the hypothesis testing procedure.

The researchers are aware that anxiety, “uncertainty about the future, and a lack of control” (p. 22), can be a factor that can negatively affect a patient’s psychological readiness for transition. However, meditation may be an intervention to reduce anxiety and thereby improve psychological readiness for transition. For study participants who had psychological readiness for transition scores =/< 30, the researchers provided a

voluntary meditation class intervention daily for 1 week. After this intervention, researchers measured their psychological readiness for transition again.

The research question is:

Does the intervention, meditation classes, delivered daily for 1 week to patients with psychological readiness for transition scores of =/< 30, improve their psychological readiness for transition?

- Conduct the inferential test by completing EACH step and its sub steps Step 1) To select a test statistic:

State the null hypothesis(0.25 marks) State the research hypothesis.(0.25 marks) Identify the target population(0.25 marks) Identify the sample population(0.25 marks)

Identify the independent variable or factor and level of measure(0.25 marks)

Identify the dependent variable and the level of measure. (0.25 marks)

State the test to be done __and provide your rationale __**(0.25 marks)**

Step 2) To establish the level of significance: **(0.25 marks)**

State the level of significance for the test:

Step 3) To select a one-tailed or two-tailed test: **(0.25)**

State your choice of a one or two tailed test

__Provide your rationale.__

Step 4) Conduct the test in excel and report the calculated test statistic, for either the one-tailed or two- tailed test, as per your choice above

`You must include the excel output **(0.25 marks)**

Step 5) To calculate the degrees of freedom: **(0.25 marks)**

Calculate and state the degrees of freedom for this test __and explain how that number was derived ie show your calculation__

Step 6) State the critical value to be exceeded by the calculated t test statistic, for either the one-tailed or two- tailed test as per your choice above, from the excel output. **(0.25 marks)**

(Look for this critical value manually in the textbook table for t test statistics by using the one or two tailed test, df and alpha which you determined, in order to compare the calculated t test statistic value from your analysis with the critical value as listed in the table, which will confirm your computer critical value.)

(critical value to be exceeded)

Step 7) Compare the calculated t test statistic with the level of significance at which the test statistic fell under the curve; and make a decision to accept or reject the null hypothesis

State the p value at which the test statistic was located under the curve. Report as test statistic score t = , df = , p = **(0.25 marks)**

State 3 decisions: **(0.75 marks)**

- Are the results statistically significant?
- Do you accept or reject the null hypothesis?
- What do you conclude about the research hypothesis?
- Discuss (interpret) your findings. (Interpretation includes discussion of descriptive analyses with all relevant data outputs, possible error sources, generalizability and critique of design that would suggest bias).

Discuss the nursing practice and research implications based on the results from the analysis of this research question.

Include a discussion of any of the demographic data that you have analyzed in previous assignments. **(One mark for total of 3b.)**

__Question 4. __**(Five marks total)**

The researchers want to investigate the potential for an age effect on total readiness for transition.

The research question was:

Are patients who are =/>81 overall less ready for transition, (as measured by their total readiness scores of physical plus psychological readiness), than patients in younger age groups?

- Conduct the inferential test by completing EACH step and its sub steps

Step 1) To select a test statistic:

State the null hypothesis(0.25 marks) State the research hypothesis.(0.25 marks) Identify the target population(0.25 marks) Identify the sample population(0.25 marks)

Identify the independent variable or factor and level of measure (0.25 marks)

Identify the dependent variable and the level of measure. (0.25 marks)

State the test to be done __and provide your rationale __**(0.25 marks)**

Step 2) To establish the level of significance: **(0.25 marks)**

State the level of significance for the test:

Step 3) To select a one-tailed or two-tailed test: **(0.25)**

State your choice of a one or two tailed test

__Provide your rationale.__

__Provide your rationale.__Step 4) Conduct the test in excel and report the calculated test statistic, for either the one-tailed or two- tailed test, as per your choice above

`You must include the excel output **(0.25 marks)**

Step 5) To calculate the degrees of freedom: **(0.25 marks)**

Calculate and state the degrees of freedom for this test __and explain how that number was derived ie show your calculation__

Step 6) State the critical value to be exceeded by the calculated t test statistic, for either the one-tailed or two- tailed test as per your choice above, from the excel output. **(0.25 marks)**

(Look for this critical value manually in the textbook table for t test statistics by using the one or two tailed test, df and alpha which you determined, in order to compare the calculated t test statistic value from your analysis with the critical value as listed in the table, which will confirm your computer critical value.)

(critical value to be exceeded)

Step 7) Compare the calculated t test statistic with the level of significance at

which the test statistic fell under the curve; and make a decision to accept or reject the null hypothesis

State the p value at which the test statistic was located under the curve. Report as test statistic score F = , df = , p = **(0.25 marks)**

State 3 decisions: **(0.75 marks)**

- Are the results statistically significant?
- Do you accept or reject the null hypothesis?
- What do you conclude about the research hypothesis?
- Discuss (interpret) your findings. (Interpretation includes discussion of descriptive analyses with all relevant data outputs, possible error sources, generalizability and critique of design that would suggest bias).

Discuss the nursing practice and research implications based on the results from the analysis of this research question.

Include a discussion of any of the demographic data that you have analyzed in previous assignments. **(One mark for total of 4b.)**

## Answer

**Question 1**

**Part A**

**1.i**

Age group | |||||

Gender | 16-30 | 31 - 60 | 61- 80 | > 81 | Grand Total |

Female | 4 | 9 | 4 | 13 | 30 |

Male | 3 | 9 | 4 | 7 | 23 |

Grand Total | 7 | 18 | 8 | 20 | 53 |

**Figure ****1**** Age group & gender**

**Question 1.ii**

Age group | |||||

Transition type | 16-30 | 31-60 | 61-80 | 81+ | Grand Total |

Internal | 3 | 7 | 4 | 3 | 17 |

External | 4 | 11 | 4 | 17 | 36 |

Grand Total | 7 | 18 | 8 | 20 | 53 |

**Figure ****2**** Age group & Transition**

**Question 1.iii **

Age group | |||||

Family support for transition | 16-30 | 31-60 | 61-80 | 81+ | Grand Total |

Supports | 2 | 4 | 6 | 14 | 26 |

Doesn't support | 5 | 14 | 2 | 6 | 27 |

Grand Total | 7 | 18 | 8 | 20 | 53 |

**Figure ****3**** Age group & Family support**

**Question 1.iv **

The age group and gender are combined and discussed in the pivot table

Count of family support for transition | Gender | ||

family support for transition | 1 | 2 | Grand Total |

Supports | 15 | 11 | 26 |

Doesn't support | 15 | 12 | 27 |

Grand Total | 30 | 23 | 53 |

**Part-B**

This part will discuss the Age group and the type of transition among the patients. The type of transition is a key factor for recovering patients. This descriptive analysis aims to understand it with the help of pivot table between the age group and how the internal and external support varies among the patients. The external transition is mostly preferred over the internal transition. At the age of 16-30, 3 choose for external and 4 choose internally. At the age of 31-60, 7 choose internally and 11 choose external. The patients from 61-80 are equally selected and for age 81+ three choose internal and 17 choose external.

**Question 2**

**2.a.i**

physical readiness for transition | |

Mean | 34.83019 |

Standard Error | 1.544158 |

Median | 35 |

Mode | 50 |

Standard Deviation | 11.24164 |

Sample Variance | 126.3745 |

Kurtosis | -0.99557 |

Skewness | -0.21823 |

Range | 40 |

Minimum | 10 |

Maximum | 50 |

Sum | 1846 |

Count | 53 |

** 2.a.ii **

psychological readiness for transition | |

Mean | 33.67925 |

Standard Error | 1.95723 |

Median | 40 |

Mode | 50 |

Standard Deviation | 14.24885 |

Sample Variance | 203.0298 |

Kurtosis | -1.26555 |

Skewness | -0.41135 |

Range | 40 |

Minimum | 10 |

Maximum | 50 |

Sum | 1785 |

Count | 53 |

**2.b**

The standard error in the table above aims to measure the dispersion of sample mean around the population mean. The standard error for the variable physical readiness is 1.544158 and for the psychological readiness is 1.95. The dispersion of the sample means is higher for psychological readiness than physical readiness.

**2.c Null hypothesis**

H0= The physical readiness for transition is not predictive of psychological readiness for transition

Psychological readiness is the independent variable and the physical readiness is the dependent variable. The p-value can be considered for the case can be 0.05

**2.d Alternate hypothesis**

H1= The physical readiness for transition is predictive of psychological readiness for transition

Psychological readiness is the independent variable and the physical readiness is the dependent variable. The p-value can be considered for the case can be 0.05

**2.e Correlation**

| physical readiness for transition | psychological readiness for transition |

physical readiness for transition | 1 | |

psychological readiness for transition | 0.641478 | 1 |

The correlation between the physical readiness for transition and the psychological readiness for transition is at 0.641. The relationship between the two variables is positive and moderately related to each other

**2.F R2**

The R2 value measured is 0.41, indicating that the coefficient of 41% with the dependent variable. The R2 value indicates that 41% of the total variations in physical readiness are explained by psychological readiness.

SUMMARY OUTPUT | ||||||||

Regression Statistics | ||||||||

Multiple R | 0.641478 | |||||||

R Square | 0.411494 | |||||||

Adjusted R Square | 0.399954 | |||||||

Standard Error | 11.03753 | |||||||

Observations | 53 | |||||||

ANOVA | ||||||||

| df | SS | MS | F | Significance F | |||

Regression | 1 | 4344.363 | 4344.363 | 35.66006 | 2.27E-07 | |||

Residual | 51 | 6213.184 | 121.8271 | |||||

Total | 52 | 10557.55 | ||||||

| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% |

Intercept | 5.359616 | 4.978836 | 1.07648 | 0.286779 | -4.63581 | 15.35505 | -4.63581 | 15.35505 |

physical readiness for transition | 0.813077 | 0.136157 | 5.971604 | 2.27E-07 | 0.53973 | 1.086424 | 0.53973 | 1.086424 |

**2.g Scatterplot**

**2.h Relationship between variables**

To get ready physically towards a medical procedure the psychology plays a vital role in preparing the patients. Therefore, psychological readiness is given some importance in the medical field. Physical readiness and psychological readiness is often intertwined before the medical procedure. If we look at the data presented we can see that the physical readiness and psychological readiness are moderately correlated. The R2 value indicates a 41% relationship between the variables. The f-value is 35 and the p-value is 0.00, which is lesser than the 0.05% the acceptable p-value level. Therefore, we must reject the null hypothesis which states that the physical readiness for transition is not a predictive of psychological readiness for transition and accept the alternate hypothesis which states the physical readiness for transition is predictive of psychological readiness for transition (Bates & Watts, 1988).

**Question-3**

**The research question is: **

Does the intervention, meditation classes, delivered daily for 1 week to patients with psychological readiness for transition scores of =/< 30, improve their psychological readiness for the transition?

**State the null hypothesis**

The psychological readiness for transition=/<30 premeditation scores is not equal to psychological readiness for transition=/<30 post-meditation scores

**State the research hypothesis. **

The psychological readiness for transition=/<30 premeditation scores is equal to psychological readiness for transition=/<30 post-meditation scores

**Identify the target population **

The target populations are the patients who receive medication classes and intervention

**Identify the sample population **

The total sample population from the database is identified as 53 and the samples are 23 after filtering the who received the meditation.

**Identify the independent variable or factor and level of measure**

The independent variable for the study here is if the patient is subject to the intervention and medication classes. The P-value considered is 0.05.

**Identify the dependent variable and the level of measure.**

The dependent variable for the study here is the psychological readiness after medication. The P-value considered is 0.05.

The T-test will be considered as a statistical technique for the scenario. The test will help us understand the mean differences and compare the averages (Ruxton, 2006).

**Step 2**

The level of significance that the study will consider is 0.05.

**Step 3**

The one-tailed test will only allow us to determine if the mean is higher or lesser than another mean, but not from both sides. So, two-sided will be considered

**Step 4**

t-Test: Paired Two Sample for Means | ||

| psychological readiness for transition=/<30 premeditation scores | psychological readiness for transition=/<30 post meditation scores |

Mean | 19.13043 | 26.52174 |

Variance | 56.02767 | 146.4427 |

Observations | 23 | 23 |

Pearson Correlation | 0.767993 | |

Hypothesized Mean Difference | 0 | |

df | 22 | |

t Stat | -4.45396 | |

P(T<=t) one-tail | 9.95E-05 | |

t Critical one-tail | 1.717144 | |

P(T<=t) two-tail | 0.000199 | |

t Critical two-tail | 2.073873 |

**Step 5**

The DF is calculated by Samples-1. The total number of samples is 23 and if we deduct one from it, the DF will be 22.

**Step 6**

The t Critical one-tail is 1.717144 and the t Critical two-tail value is 2.073873.

**Step 7**

The p-value is lesser than the 0.05 level. The t Critical one-tail is lesser than the t Critical two-tail value. Therefore, we must reject the null hypothesis and accept the alternative hypothesis. Therefore, we must reject the psychological readiness for transition=/<30 premeditation scores is not equal to psychological readiness for transition=/<30 post-meditation scores

**Part-B**

The mean psychological readiness for a transition during premeditation score is 19.13 and the psychological readiness for transition after the post-meditation score of 26.52. We can see a major improvement after the mediation. The results are also statistically significant. If we look at the numbers from the question-1, we can see people opt more for internal transitions. Therefore, the post-meditation results in having a positive impact also have a strong relationship with the transition type considered by the patient (Voss et al., 2011).

**Question-4**

**The research question is: **

Are patients who are =/>81 overall less ready for the transition, (as measured by their total readiness scores of physical plus psychological readiness), than patients in younger age groups?

**State the null hypothesis**

The mean difference between readiness for the transition between the patients who are over 80 is same as those who are below 80.

**State the research hypothesis. **

The mean difference between readiness for the transition between the patients who are over 80 is not as same as those who are below 80.

**Identify the target population **

The target population are the patients who are ready for the transition.

**Identify the sample population **

The total sample population from the database is identified as 53 and the samples are 45 after filtering the who received the meditation.

**Identify the independent variable or factor and level of measure**

The independent variable for the study here is if the patient is subject to the intervention and medication classes. The P-value considered is 0.05.

**Identify the dependent variable and the level of measure.**

The dependent variable for the study here is the psychological readiness after medication. The P-value considered is 0.05.

T-test with unequal variances will be considered as a statistical technique for the scenario. The test will help us understand the mean differences and compare the averages (Kim, 2015).

**Step 2**

The level of significance that the study will consider is 0.05.

**Step 3**

The one-tailed test will only allow us to determine if the mean is higher or lesser than the mean, but not from both sides. Here we are testing only one variable. So, one-sided will be considered

**Step 4**

t-Test: Two-Sample Assuming Unequal Variances | ||

| Readiness score over 81 | Readiness score for less than 80 |

Mean | 46.75 | 82.27273 |

Variance | 213.8816 | 270.4545 |

Observations | 20 | 33 |

Hypothesized Mean Difference | 0 | |

df | 44 | |

t Stat | -8.17324 | |

P(T<=t) one-tail | 1.14E-10 | |

t Critical one-tail | 1.68023 | |

P(T<=t) two-tail | 2.28E-10 | |

t Critical two-tail | 2.015368 |

**Step 5**

The DF is calculated by Samples-1. The total number of samples is 45 and if we deduct one from it, the DF will be 44.

**Step 6**

The t Critical one-tail is 1.68 and the t Critical two-tail value is 2.01.

**Step 7**

The p-value is lesser than the 0.05 level. The t Critical one-tail is lesser than the t Critical two-tail value. Therefore, we must reject the null hypothesis and accept the alternative hypothesis. Therefore, we must reject the hypothesis which states The mean difference between readiness for the transition between the patients who are over 80 is same as the those who are below 80.

**Part-B**

The mean total readiness for transition among those who are over 80 is 46 and the total readiness for transition for those who are below 80 is 85. We can see a major mean difference of readiness for those who are above and below 80+. The results are also statistically significant. If we look at the numbers from the question-1, we can see people opt more for internal transitions. Therefore, the age group and the total readiness among the samples deteriorate with age. We can see the pattern in our research conducted (Wilson & Robinson, 2002).

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