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This report focuses on the data analysis of various factors and effects of United Kingdom. The researcher analysed the data with the help of SPSS-20 software. The analysis would help to find out and highlight the equality and diversity in mentality and behaviours among the people of countries of UK. The report includes descriptive statistics, inferential statistics, paired two-sample t-test, independent sample t-test, parametric and non-parametric analysis.

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Running head: QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Quantitative Data Analysis Assignments

Name of the Student:

Name of the University:

Author’s Note:

Quantitative Data Analysis Assignments

Name of the Student:

Name of the University:

Author’s Note:

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1QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Table of Contents

Introduction:...............................................................................................................................2

Data Analysis:............................................................................................................................2

Descriptive Statistics:.............................................................................................................2

Box-plot:................................................................................................................................3

Paired two-sample t-test:........................................................................................................5

Independent sample t-test:......................................................................................................7

Parametric:...........................................................................................................................10

Pearson’s correlation coefficient:.....................................................................................10

Non-Parametric:...................................................................................................................10

Chi-square test:.................................................................................................................10

One-way ANOVA:...............................................................................................................12

MANOVA:...........................................................................................................................14

Multiple Regression Model:.................................................................................................18

Conclusion and Limitations:....................................................................................................22

Reference:................................................................................................................................23

Table of Contents

Introduction:...............................................................................................................................2

Data Analysis:............................................................................................................................2

Descriptive Statistics:.............................................................................................................2

Box-plot:................................................................................................................................3

Paired two-sample t-test:........................................................................................................5

Independent sample t-test:......................................................................................................7

Parametric:...........................................................................................................................10

Pearson’s correlation coefficient:.....................................................................................10

Non-Parametric:...................................................................................................................10

Chi-square test:.................................................................................................................10

One-way ANOVA:...............................................................................................................12

MANOVA:...........................................................................................................................14

Multiple Regression Model:.................................................................................................18

Conclusion and Limitations:....................................................................................................22

Reference:................................................................................................................................23

2QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Table of Tables

Table 1: Table of descriptive statistics.......................................................................................3

Table 2: Tables of paired two-sample t-test...............................................................................6

Table 3: Table of independent sample t-test..............................................................................8

Table 4: Table of Pearson’s correlation coefficient.................................................................11

Table 5: The One-way ANOVA table.....................................................................................13

Table 6: The table of multiple comparisons.............................................................................14

Table 7: Table of Homogeneous subsets.................................................................................15

Table 8: Table of descriptive analysis of MANOVA analysis................................................16

Table 9: Fixed and random effect of multivariate tests of MANOVA analysis......................16

Table 10: Table of testing between-subject effects..................................................................16

Table 11: Table of comparison of Person’s age last birthday with respect to Person 1 sex for

“Males”....................................................................................................................................18

Table 12: Table of Multivariate test of homogeneity...............................................................18

Table 13: Table of Univariate Tests.........................................................................................18

Table 14: Table of Multiple R-square......................................................................................19

Table 15: ANOVA table of multiple regression model...........................................................20

Table 16: Table of intercept and slopes of multiple regression model....................................20

Table of Figures

Figure 1: Distribution of the variable “Respondent’s Socio-Economic Group (pre-SOC2000)

best estimate”.............................................................................................................................5

Figure 2: Distribution of the variable “Respondent’s Social Class (pre-SOC2000) best

estimate”.....................................................................................................................................5

Table of Tables

Table 1: Table of descriptive statistics.......................................................................................3

Table 2: Tables of paired two-sample t-test...............................................................................6

Table 3: Table of independent sample t-test..............................................................................8

Table 4: Table of Pearson’s correlation coefficient.................................................................11

Table 5: The One-way ANOVA table.....................................................................................13

Table 6: The table of multiple comparisons.............................................................................14

Table 7: Table of Homogeneous subsets.................................................................................15

Table 8: Table of descriptive analysis of MANOVA analysis................................................16

Table 9: Fixed and random effect of multivariate tests of MANOVA analysis......................16

Table 10: Table of testing between-subject effects..................................................................16

Table 11: Table of comparison of Person’s age last birthday with respect to Person 1 sex for

“Males”....................................................................................................................................18

Table 12: Table of Multivariate test of homogeneity...............................................................18

Table 13: Table of Univariate Tests.........................................................................................18

Table 14: Table of Multiple R-square......................................................................................19

Table 15: ANOVA table of multiple regression model...........................................................20

Table 16: Table of intercept and slopes of multiple regression model....................................20

Table of Figures

Figure 1: Distribution of the variable “Respondent’s Socio-Economic Group (pre-SOC2000)

best estimate”.............................................................................................................................5

Figure 2: Distribution of the variable “Respondent’s Social Class (pre-SOC2000) best

estimate”.....................................................................................................................................5

3QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Figure 3: Distribution of the variable “Respondent’s Occupational Class (7 categories)”........6

Figure 4: The distribution of “Respondent NS-SEC Socio-economic Class” at analytic class

level............................................................................................................................................6

Figure 5: The grouped bar plot of selected two variables........................................................14

Figure 6: The histogram plot of residual values of the multiple regression model..................23

Figure 7: The normal probability plot of standardized residual of multiple regression model23

Figure 3: Distribution of the variable “Respondent’s Occupational Class (7 categories)”........6

Figure 4: The distribution of “Respondent NS-SEC Socio-economic Class” at analytic class

level............................................................................................................................................6

Figure 5: The grouped bar plot of selected two variables........................................................14

Figure 6: The histogram plot of residual values of the multiple regression model..................23

Figure 7: The normal probability plot of standardized residual of multiple regression model23

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4QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Introduction:

The data analysis in this report and quantitative research highlights many surveyed

factors and effects of United Kingdom. Socio-economic conditions, study level, demographic

background, performance towards work, online activity, life styles and many more aspects of

life are present in the data set.

Focusing mainly descriptive statistics and inferential statistics, the researcher analysed

the data with the help of SPSS-20 software. The analysis would help to find out and highlight

the equality and diversity in mentality and behaviours among the people of countries of UK.

Data Analysis:

Descriptive Statistics:

Table 1: Table of descriptive statistics

Descriptive Statistics

N Range Minimum Maximum Mean Std.

Deviation

Variance

Respondent's Socio-

Economic Group

(pre-SOC2000) best

estimate

4134 18.00 2.00 20.00 8.9485 3.70671 13.740

Respondent: Social

class (pre-

SOC2000) best

estimate dv

4134 7.00 1.00 8.00 3.2121 1.39950 1.959

Respondent's

occupational class

(7 categories) dv

4184 7.00 1.00 8.00 3.7990 2.06574 4.267

Respondent NS-

SEC Socio-

economic Class

(analytic class

level): dv

4311 6.90 1.10 8.00 3.9452 2.12574 4.519

The descriptive statistics of the selected four variables displays that-

Out of 4134 samples, the values of the best estimate of socio-economic group (pre-

SOC2000) varies in the interval of 2 to 20. The average and standard deviation of

these values are 8.9485 and 3.70671 respectively (Altman and Bland 1996).

Introduction:

The data analysis in this report and quantitative research highlights many surveyed

factors and effects of United Kingdom. Socio-economic conditions, study level, demographic

background, performance towards work, online activity, life styles and many more aspects of

life are present in the data set.

Focusing mainly descriptive statistics and inferential statistics, the researcher analysed

the data with the help of SPSS-20 software. The analysis would help to find out and highlight

the equality and diversity in mentality and behaviours among the people of countries of UK.

Data Analysis:

Descriptive Statistics:

Table 1: Table of descriptive statistics

Descriptive Statistics

N Range Minimum Maximum Mean Std.

Deviation

Variance

Respondent's Socio-

Economic Group

(pre-SOC2000) best

estimate

4134 18.00 2.00 20.00 8.9485 3.70671 13.740

Respondent: Social

class (pre-

SOC2000) best

estimate dv

4134 7.00 1.00 8.00 3.2121 1.39950 1.959

Respondent's

occupational class

(7 categories) dv

4184 7.00 1.00 8.00 3.7990 2.06574 4.267

Respondent NS-

SEC Socio-

economic Class

(analytic class

level): dv

4311 6.90 1.10 8.00 3.9452 2.12574 4.519

The descriptive statistics of the selected four variables displays that-

Out of 4134 samples, the values of the best estimate of socio-economic group (pre-

SOC2000) varies in the interval of 2 to 20. The average and standard deviation of

these values are 8.9485 and 3.70671 respectively (Altman and Bland 1996).

5QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Out of chosen 4134 samples, the values of the best estimate of social class of

respondents varies in the interval of 1 to 8 with range 7. The mean and standard

deviation of these values are 3.2121 and 1.39950.

Respondent’s occupational class for 4184 samples displays that the highest and lowest

values are 1 and 8 respectively with range 7. The average and standard deviation of

the values of these variables are respectively 3.7990 and 2.06574.

Respondent NS-SEC Socio-economic class for 4311 samples indicates that the

highest and lowest values are respectively 1.1 and 8. The mean value and standard

deviation of the variable is calculated as 3.9452 and 2.12574.

Box-plot:

Figure 1: Distribution of the variable “Respondent’s Socio-Economic Group (pre-SOC2000) best estimate”

Most of values of the variable (75%) lie in the range of 12 to 7 (Wonnacott and Wonnacott

1990). The median value of the samples is 9. The outliers are the values equal to 20. The

outliers are 716, 900, 897 and 1013th samples (George and Mallery 2016).

Figure 2: Distribution of the variable “Respondent’s Social Class (pre-SOC2000) best estimate”

Out of chosen 4134 samples, the values of the best estimate of social class of

respondents varies in the interval of 1 to 8 with range 7. The mean and standard

deviation of these values are 3.2121 and 1.39950.

Respondent’s occupational class for 4184 samples displays that the highest and lowest

values are 1 and 8 respectively with range 7. The average and standard deviation of

the values of these variables are respectively 3.7990 and 2.06574.

Respondent NS-SEC Socio-economic class for 4311 samples indicates that the

highest and lowest values are respectively 1.1 and 8. The mean value and standard

deviation of the variable is calculated as 3.9452 and 2.12574.

Box-plot:

Figure 1: Distribution of the variable “Respondent’s Socio-Economic Group (pre-SOC2000) best estimate”

Most of values of the variable (75%) lie in the range of 12 to 7 (Wonnacott and Wonnacott

1990). The median value of the samples is 9. The outliers are the values equal to 20. The

outliers are 716, 900, 897 and 1013th samples (George and Mallery 2016).

Figure 2: Distribution of the variable “Respondent’s Social Class (pre-SOC2000) best estimate”

6QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Most of values of the variable (75%) lie in the range of 2 to 4. Median is calculated as 3. The

outliers are the values equal to 8. The outliers are 716, 900, 897 and 1013th samples.

Figure 3: Distribution of the variable “Respondent’s Occupational Class (7 categories)”

Most of the values of the variable (75%) lie in the interval of 2 to 6. The median value is

calculated as 3. No outlier is observed in the distribution of the undertaken variable.

Figure 4: The distribution of “Respondent NS-SEC Socio-economic Class” at analytic class level.

Most of values of the variable (75%) lie in the range of 2 to 4. Median is calculated as 3. The

outliers are the values equal to 8. The outliers are 716, 900, 897 and 1013th samples.

Figure 3: Distribution of the variable “Respondent’s Occupational Class (7 categories)”

Most of the values of the variable (75%) lie in the interval of 2 to 6. The median value is

calculated as 3. No outlier is observed in the distribution of the undertaken variable.

Figure 4: The distribution of “Respondent NS-SEC Socio-economic Class” at analytic class level.

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7QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Most of the values of the variable (75%) lie in the interval of 2 to 6. The median value is

calculated as 4. No outlier is observed in the distribution of the chosen variable.

Paired two-sample t-test:

Hypothesis:

Null hypothesis (H0): The average values of two variables “Which news website do you visit

more often” and “Which news website do you visit next more often” are equal to each other.

Alternative hypothesis (HA): The difference of average values of two variables “Which news

website do you visit more often” and “Which news website do you visit more often” is not

equal to 0.

Table 2: Tables of paired two-sample t-test

Most of the values of the variable (75%) lie in the interval of 2 to 6. The median value is

calculated as 4. No outlier is observed in the distribution of the chosen variable.

Paired two-sample t-test:

Hypothesis:

Null hypothesis (H0): The average values of two variables “Which news website do you visit

more often” and “Which news website do you visit next more often” are equal to each other.

Alternative hypothesis (HA): The difference of average values of two variables “Which news

website do you visit more often” and “Which news website do you visit more often” is not

equal to 0.

Table 2: Tables of paired two-sample t-test

8QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

The average value of the first variable “Which news website do you visit most often”

is 15.01 for 2268 samples. The average value of the second variable “Which news website do

you visit next most often” is 15.16 for 2268 samples.

Test applied: Paired two-sample t-test.

Correlation coefficient: 0.49 with significant p-value 0.019.

Level of significance: 0.05.

Degrees of freedom: 2267

Calculated t-statistic: (-0.172)

Significant p-value: 0.864.

Inference: The significant p-value 0.0864 is greater than 0.05. Therefore, the null

hypothesis is not rejected (Traitler Coleman and Burbidge 2017).

The average value of the first variable “Which news website do you visit most often”

is 15.01 for 2268 samples. The average value of the second variable “Which news website do

you visit next most often” is 15.16 for 2268 samples.

Test applied: Paired two-sample t-test.

Correlation coefficient: 0.49 with significant p-value 0.019.

Level of significance: 0.05.

Degrees of freedom: 2267

Calculated t-statistic: (-0.172)

Significant p-value: 0.864.

Inference: The significant p-value 0.0864 is greater than 0.05. Therefore, the null

hypothesis is not rejected (Traitler Coleman and Burbidge 2017).

9QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Interpretation: As the null hypothesis is failed to reject, therefore, it could be

interpreted that the average values of two variables “Which news website do you visit

most often?” and “Which news website do you visit next most often?” are unequal.

Decision-making: According to the average, the two variables are almost equal to

each other. Therefore, no change would occur significantly in future days in case of

visiting news website (De Winter 2013).

Independent sample t-test:

Null hypothesis (H0): The average values of dependent variable “Which forms of transport

do you think contribute most to climate change: cars: Versions B, C, D” for number of trips 0

or 1 are equal.

Alternative hypothesis (HA): The average values of dependent variable “Which forms of

transport do you think contribute most to climate change: cars: Versions B, C, D” for number

of trips 0 or 1 are unequal.

Table 3: Table of independent sample t-test

Group Statistics

How many trips did you

make by plane during the

last 12 months?: Versions

B, C, D

N Mean Std.

Deviation

Std. Error

Mean

Which forms of

transport do you think

contribute most to

climate change: cars:

Versions B, C, D

0 1639 .78 1.202 .030

1 616 .82 1.096 .044

Which forms of

transport do you think

contribute most to

climate change: buses:

Versions B, C, D

0 1639 .69 1.221 .030

1 616 .63 1.134 .046

Which forms of

transport do you think

contribute most to

climate change: vans:

Versions B, C, D

0 1639 .93 1.159 .029

1 616 .91 1.064 .043

Which forms of

transport do you think

contribute most to

climate change:

planes: Versions B, C,

D

0 1639 .67 1.223 .030

1 616 .68 1.128 .045

Which forms of 0 1639 .21 1.201 .030

Interpretation: As the null hypothesis is failed to reject, therefore, it could be

interpreted that the average values of two variables “Which news website do you visit

most often?” and “Which news website do you visit next most often?” are unequal.

Decision-making: According to the average, the two variables are almost equal to

each other. Therefore, no change would occur significantly in future days in case of

visiting news website (De Winter 2013).

Independent sample t-test:

Null hypothesis (H0): The average values of dependent variable “Which forms of transport

do you think contribute most to climate change: cars: Versions B, C, D” for number of trips 0

or 1 are equal.

Alternative hypothesis (HA): The average values of dependent variable “Which forms of

transport do you think contribute most to climate change: cars: Versions B, C, D” for number

of trips 0 or 1 are unequal.

Table 3: Table of independent sample t-test

Group Statistics

How many trips did you

make by plane during the

last 12 months?: Versions

B, C, D

N Mean Std.

Deviation

Std. Error

Mean

Which forms of

transport do you think

contribute most to

climate change: cars:

Versions B, C, D

0 1639 .78 1.202 .030

1 616 .82 1.096 .044

Which forms of

transport do you think

contribute most to

climate change: buses:

Versions B, C, D

0 1639 .69 1.221 .030

1 616 .63 1.134 .046

Which forms of

transport do you think

contribute most to

climate change: vans:

Versions B, C, D

0 1639 .93 1.159 .029

1 616 .91 1.064 .043

Which forms of

transport do you think

contribute most to

climate change:

planes: Versions B, C,

D

0 1639 .67 1.223 .030

1 616 .68 1.128 .045

Which forms of 0 1639 .21 1.201 .030

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10QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

transport do you think

contribute most to

climate change: trains:

Versions B, C, D

1 616 .20 1.101 .044

Which forms of

transport do you think

contribute most to

climate change: ships:

Versions B, C, D

0 1639 .24 1.207 .030

1 616 .24 1.111 .045

Which forms of

transport do you think

contribute most to

climate change:

motorbikes: Versions

B, C, D

0 1639 .25 1.210 .030

1 616 .21 1.106 .045

Which forms of

transport do you think

contribute most to

climate change: none

of these: Versions B,

C, D

0 1639 .17 1.191 .029

1 616 .14 1.082 .044

Which forms of

transport do you think

contribute most to

climate change: don't

believe/happen

anyway: Versions B,

C, D

0 1639 .17 1.191 .029

1 616 .14 1.084 .044

transport do you think

contribute most to

climate change: trains:

Versions B, C, D

1 616 .20 1.101 .044

Which forms of

transport do you think

contribute most to

climate change: ships:

Versions B, C, D

0 1639 .24 1.207 .030

1 616 .24 1.111 .045

Which forms of

transport do you think

contribute most to

climate change:

motorbikes: Versions

B, C, D

0 1639 .25 1.210 .030

1 616 .21 1.106 .045

Which forms of

transport do you think

contribute most to

climate change: none

of these: Versions B,

C, D

0 1639 .17 1.191 .029

1 616 .14 1.082 .044

Which forms of

transport do you think

contribute most to

climate change: don't

believe/happen

anyway: Versions B,

C, D

0 1639 .17 1.191 .029

1 616 .14 1.084 .044

11QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

(Panik 2012)

Test applied: One variable independent sample t-test.

Level of significance: 5%.

Degrees of freedom: 2253 (when equal variances are assumed) and 1207 (when

unequal variances are assumed).

For all the variables with respect to the factor variable “How many trips did you make by

plane during the last 12 months?: Versions B, C, D”, the significant p-values are greater than

5% (level of significance). Hence, all the variables with respect to mediator variable, have

equal averages in case of no trip and at least one trip (Abbott 2017). The means of various

observations of “Which forms of transport do you think contribute most to climate change:

don't believe/happen anyway: Versions B, C, D” with respect to number of yearly trips (0 or

1) are equal to each other.

(Panik 2012)

Test applied: One variable independent sample t-test.

Level of significance: 5%.

Degrees of freedom: 2253 (when equal variances are assumed) and 1207 (when

unequal variances are assumed).

For all the variables with respect to the factor variable “How many trips did you make by

plane during the last 12 months?: Versions B, C, D”, the significant p-values are greater than

5% (level of significance). Hence, all the variables with respect to mediator variable, have

equal averages in case of no trip and at least one trip (Abbott 2017). The means of various

observations of “Which forms of transport do you think contribute most to climate change:

don't believe/happen anyway: Versions B, C, D” with respect to number of yearly trips (0 or

1) are equal to each other.

12QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Parametric:

Pearson’s correlation coefficient:

Table 4: Table of Pearson’s correlation coefficient

The Pearson’s correlation coefficient between two scale variables are calculated here. These

are - “Urban/Rural Indicator 2011 (England and Wales)” and “Urban/Rural Indicator 2011

(Scotland)”.

Test statistic: (-0.719).

Significant p-value: 0.0.

Interpretation: As r = (-0.719), therefore, it could be interpreted that the correlation is strong

and negative (Mukaka 2012).

Conclusion: The value of correlation coefficient is negative and statistically significant.

Therefore, it could be interpreted that if the urban or rural indicator of England and Wales

increases, then urban or rural indicator of Scotland significantly decreases and vice-versa.

Non-Parametric:

Chi-square test:

Null hypothesis (H0): The two variables “Do you have internet access at

home/work/elsewhere or on smartphone/tablet/mobile device” and “Do you have a personal

Twitter account?” are independent to each other. That is, there exists no association between

these two variables.

Parametric:

Pearson’s correlation coefficient:

Table 4: Table of Pearson’s correlation coefficient

The Pearson’s correlation coefficient between two scale variables are calculated here. These

are - “Urban/Rural Indicator 2011 (England and Wales)” and “Urban/Rural Indicator 2011

(Scotland)”.

Test statistic: (-0.719).

Significant p-value: 0.0.

Interpretation: As r = (-0.719), therefore, it could be interpreted that the correlation is strong

and negative (Mukaka 2012).

Conclusion: The value of correlation coefficient is negative and statistically significant.

Therefore, it could be interpreted that if the urban or rural indicator of England and Wales

increases, then urban or rural indicator of Scotland significantly decreases and vice-versa.

Non-Parametric:

Chi-square test:

Null hypothesis (H0): The two variables “Do you have internet access at

home/work/elsewhere or on smartphone/tablet/mobile device” and “Do you have a personal

Twitter account?” are independent to each other. That is, there exists no association between

these two variables.

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13QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Alternative hypothesis (HA): The two variables “Do you have internet access at

home/work/elsewhere or on smartphone/tablet/mobile device” and “Do you have a personal

Twitter account?” are associated with each other.

Chi-square test is applied to find the association between two categorical variables.

The interpretation may also tend to find the independence of two variables too.

Out of 3539 samples who have internet access, 790 people has twitter amount and

2749 people do not have twitter amount. Out of 89 samples who do not have internet access,

only 4 people has twitter amount and 785 people do not have twitter amount (Field 2013).

Test applied: Chi-square t-test.

Level of significance: 0.05.

Degrees of freedom: 1

Alternative hypothesis (HA): The two variables “Do you have internet access at

home/work/elsewhere or on smartphone/tablet/mobile device” and “Do you have a personal

Twitter account?” are associated with each other.

Chi-square test is applied to find the association between two categorical variables.

The interpretation may also tend to find the independence of two variables too.

Out of 3539 samples who have internet access, 790 people has twitter amount and

2749 people do not have twitter amount. Out of 89 samples who do not have internet access,

only 4 people has twitter amount and 785 people do not have twitter amount (Field 2013).

Test applied: Chi-square t-test.

Level of significance: 0.05.

Degrees of freedom: 1

14QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Calculated Chi-square statistic: 204.973.

Significant p-value: 0.0.

Inference: The significant p-value 0.0 is lesser than 0.05. Therefore, the null

hypothesis is rejected at 5% level of significant.

Interpretation: As the null hypothesis is rejected, therefore, the alternative

hypothesis is not rejected. It could be interpreted that the two variables “Do you

personally have internet access at home or other places on mobile or other gadgets?”

and “Do you have a personal twitter account?” are associated with each other.

Decision-making: These two variables are significantly associated with each other.

Figure 5: The grouped bar plot of selected two variables

One-way ANOVA:

Null hypothesis (H0): The means of expected retired ages from main job in all the three

countries alike England, Scotland and Wales are equal.

Alternative hypothesis (HA): There exists at least one inequality in the means of expected

retired ages from main job in all the three countries alike England, Scotland and Wales.

One-way ANOVA (analysis of variance) test examines the equality averages of the

chosen variables within a certain statistical significant level (Leech, Barrett and Morgan

2013).

Table 5: The One-way ANOVA table

Calculated Chi-square statistic: 204.973.

Significant p-value: 0.0.

Inference: The significant p-value 0.0 is lesser than 0.05. Therefore, the null

hypothesis is rejected at 5% level of significant.

Interpretation: As the null hypothesis is rejected, therefore, the alternative

hypothesis is not rejected. It could be interpreted that the two variables “Do you

personally have internet access at home or other places on mobile or other gadgets?”

and “Do you have a personal twitter account?” are associated with each other.

Decision-making: These two variables are significantly associated with each other.

Figure 5: The grouped bar plot of selected two variables

One-way ANOVA:

Null hypothesis (H0): The means of expected retired ages from main job in all the three

countries alike England, Scotland and Wales are equal.

Alternative hypothesis (HA): There exists at least one inequality in the means of expected

retired ages from main job in all the three countries alike England, Scotland and Wales.

One-way ANOVA (analysis of variance) test examines the equality averages of the

chosen variables within a certain statistical significant level (Leech, Barrett and Morgan

2013).

Table 5: The One-way ANOVA table

15QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

The values of the variable “At what age do you expect to retire from your main job?” are

separated according to the three countries that are “England”, “Scotland” and “Wales”. The

average estimated age of retirement for all the three countries are 66.88 years, 68.27 years

and 67.22 years respectively.

(Norusis 2008.)

Test applied: One-way ANOVA test.

Level of significance: 0.05.

Degrees of freedom: 1208

Calculated F-statistic: 0.884.

Significant p-value: 0.413.

Inference: The significant p-value 0.413 is lesser than 0.05. Therefore, the null

hypothesis is not rejected at 5% level of significant.

Interpretation: The null hypothesis is accepted with 5% level of significance. It

could be interpreted that the average ages of expectation of retirement in “England”,

“Scotland” and “Wales” are equal to each other with 95% probability.

Decision-making: As the mean expected ages of the responders from “England”,

“Scotland” and “Wales” are same, therefore, it could be concluded that the peoples of

all the three counties regard the same consideration about the age of retirement.

Post Hoc Tests

Table 6: The table of multiple comparisons

The values of the variable “At what age do you expect to retire from your main job?” are

separated according to the three countries that are “England”, “Scotland” and “Wales”. The

average estimated age of retirement for all the three countries are 66.88 years, 68.27 years

and 67.22 years respectively.

(Norusis 2008.)

Test applied: One-way ANOVA test.

Level of significance: 0.05.

Degrees of freedom: 1208

Calculated F-statistic: 0.884.

Significant p-value: 0.413.

Inference: The significant p-value 0.413 is lesser than 0.05. Therefore, the null

hypothesis is not rejected at 5% level of significant.

Interpretation: The null hypothesis is accepted with 5% level of significance. It

could be interpreted that the average ages of expectation of retirement in “England”,

“Scotland” and “Wales” are equal to each other with 95% probability.

Decision-making: As the mean expected ages of the responders from “England”,

“Scotland” and “Wales” are same, therefore, it could be concluded that the peoples of

all the three counties regard the same consideration about the age of retirement.

Post Hoc Tests

Table 6: The table of multiple comparisons

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16QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Table 7: Table of Homogeneous subsets

The significant p-value of the expected ages of retirement responded from chosen three

counties found to be 0.530. Hence, these average responses are equal to each other.

MANOVA:

One-way multivariate analysis (One-way MANOVA) determines whether there are

any differences between independent groups on at least two continuous dependent variables.

Actually, one-way MANOVA is an omnibus test statistic and fails to refer which specific

groups were significantly different from each other (Montgomery, Runger and Hubele 2009).

Null hypothesis (H0): The means of ages of the persons in all the nine observations are equal

when phone 1 sex relation is assumed male.

Alternative hypothesis (HA): There exists at least one inequality in the means of ages of the

persons in all the nine observations when phone 1 sex relation is assumed male.

Table 7: Table of Homogeneous subsets

The significant p-value of the expected ages of retirement responded from chosen three

counties found to be 0.530. Hence, these average responses are equal to each other.

MANOVA:

One-way multivariate analysis (One-way MANOVA) determines whether there are

any differences between independent groups on at least two continuous dependent variables.

Actually, one-way MANOVA is an omnibus test statistic and fails to refer which specific

groups were significantly different from each other (Montgomery, Runger and Hubele 2009).

Null hypothesis (H0): The means of ages of the persons in all the nine observations are equal

when phone 1 sex relation is assumed male.

Alternative hypothesis (HA): There exists at least one inequality in the means of ages of the

persons in all the nine observations when phone 1 sex relation is assumed male.

17QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Table 8: Table of descriptive analysis of MANOVA analysis

Table 9: Fixed and random effect of multivariate tests of MANOVA analysis

The calculated F (2, 1) = 27.672. Here, p-value is 0.133 which is greater than 0.05.

Wilk’s ᴧ = 0.018, partial ղ2 = 0.982.

Therefore, there is statistically significant difference in ages of males based on observations

of males (Van Aelst and Willems 2011).

Table 10: Table of testing between-subject effects

Table 8: Table of descriptive analysis of MANOVA analysis

Table 9: Fixed and random effect of multivariate tests of MANOVA analysis

The calculated F (2, 1) = 27.672. Here, p-value is 0.133 which is greater than 0.05.

Wilk’s ᴧ = 0.018, partial ղ2 = 0.982.

Therefore, there is statistically significant difference in ages of males based on observations

of males (Van Aelst and Willems 2011).

Table 10: Table of testing between-subject effects

18QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

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19QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

It could be observed that p-value of observed F-statistics is 0.0. As p-value < 0.05, therefore,

the presence of statistical significance is accepted at 5% level of significance.

Estimated Marginal Means

Table 11: Table of comparison of Person’s age last birthday with respect to Person 1 sex for “Males”

Estimates

Dependent Variable Person 1 sex Mean Std. Error 95% Confidence Interval

Lower Bound Upper Bound

Person 1 age last

birthday Male 25.333 7.333 -6.219 56.886

Person 2 age last

birthday Male 55.000 10.149 11.333 98.667

Person 3 age last

birthday Male 52.667 11.348 3.840 101.493

Person 4 age last

birthday Male 28.000 6.928 -1.810 57.810

Person 5 age last

birthday Male 26.333 7.796 -7.210 59.877

Person 6 age last

birthday Male 23.667 6.438 -4.033 51.366

Person 7 age last

birthday Male 13.000 2.517 2.172 23.828

Person 8 age last

birthday Male 10.000 2.000 1.395 18.605

Person 9 age last

birthday Male 4.000 1.000 -.303 8.303

Table 12: Table of Multivariate test of homogeneity

Multivariate Tests

Value F Hypothesis

df

Error dfSig. Partial Eta

Squared

Noncent.

Parameter

Observed

Powera

Pillai's trace .000 . .000 .000 . . . .

Wilks'

lambda 1.000 . .000 1.500 . . . .

Hotelling's

trace .000 . .000 2.000 . . . .

Roy's largest

root .000 .000 2.000 .000 . .000 .000 .

Each F tests the multivariate effect of Person 1 sex. These tests are based on the linearly

independent pairwise comparisons among the estimated marginal means.

a. Computed using alpha = .05

It could be observed that p-value of observed F-statistics is 0.0. As p-value < 0.05, therefore,

the presence of statistical significance is accepted at 5% level of significance.

Estimated Marginal Means

Table 11: Table of comparison of Person’s age last birthday with respect to Person 1 sex for “Males”

Estimates

Dependent Variable Person 1 sex Mean Std. Error 95% Confidence Interval

Lower Bound Upper Bound

Person 1 age last

birthday Male 25.333 7.333 -6.219 56.886

Person 2 age last

birthday Male 55.000 10.149 11.333 98.667

Person 3 age last

birthday Male 52.667 11.348 3.840 101.493

Person 4 age last

birthday Male 28.000 6.928 -1.810 57.810

Person 5 age last

birthday Male 26.333 7.796 -7.210 59.877

Person 6 age last

birthday Male 23.667 6.438 -4.033 51.366

Person 7 age last

birthday Male 13.000 2.517 2.172 23.828

Person 8 age last

birthday Male 10.000 2.000 1.395 18.605

Person 9 age last

birthday Male 4.000 1.000 -.303 8.303

Table 12: Table of Multivariate test of homogeneity

Multivariate Tests

Value F Hypothesis

df

Error dfSig. Partial Eta

Squared

Noncent.

Parameter

Observed

Powera

Pillai's trace .000 . .000 .000 . . . .

Wilks'

lambda 1.000 . .000 1.500 . . . .

Hotelling's

trace .000 . .000 2.000 . . . .

Roy's largest

root .000 .000 2.000 .000 . .000 .000 .

Each F tests the multivariate effect of Person 1 sex. These tests are based on the linearly

independent pairwise comparisons among the estimated marginal means.

a. Computed using alpha = .05

20QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Table 13: Table of Univariate Tests

(Leech, Barrett and Morgan 2013)

Multiple Regression Model:

The multiple regression model refers the linear statistical significance between

dependent variable and independent variables. Here, the response variable is “Importance of

job involving personal contacts with others: Versions B, D”. The dependent variables are-

How important in a job: deciding own times or days of work (observed in 8 periods).

Null hypothesis (H0): There exists any statistically significant linear association between the

variables “Importance of job involving personal contact with others” and the eight different

observations of “How important in a job”.

Alternative hypothesis (HA): There does not exist a statistically significant linear association

between the variables “Importance of job involving personal contact with others” and the

eight different observations of “How important in a job”.

Table 14: Table of Multiple R-square

Table 13: Table of Univariate Tests

(Leech, Barrett and Morgan 2013)

Multiple Regression Model:

The multiple regression model refers the linear statistical significance between

dependent variable and independent variables. Here, the response variable is “Importance of

job involving personal contacts with others: Versions B, D”. The dependent variables are-

How important in a job: deciding own times or days of work (observed in 8 periods).

Null hypothesis (H0): There exists any statistically significant linear association between the

variables “Importance of job involving personal contact with others” and the eight different

observations of “How important in a job”.

Alternative hypothesis (HA): There does not exist a statistically significant linear association

between the variables “Importance of job involving personal contact with others” and the

eight different observations of “How important in a job”.

Table 14: Table of Multiple R-square

21QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

The value of multiple R2 in multiple regression model is 0.637. It is also known as the

“coefficient of variation” (Konasani and Kadre 2015). Therefore, the predictor variables can

explain 63.7% variability of the response variable.

Table 15: ANOVA table of multiple regression model

The ANOVA regression model displays that the value of F-statistic is 390.768. The

significant p-value is calculated as 0.0. The calculated p-value is less than 5% level of

significance. Therefore, the null hypothesis of linear significant association between

dependent variable and independent variables is accepted (Data and Bartz 1988).

Table 16: Table of intercept and slopes of multiple regression model

The value of multiple R2 in multiple regression model is 0.637. It is also known as the

“coefficient of variation” (Konasani and Kadre 2015). Therefore, the predictor variables can

explain 63.7% variability of the response variable.

Table 15: ANOVA table of multiple regression model

The ANOVA regression model displays that the value of F-statistic is 390.768. The

significant p-value is calculated as 0.0. The calculated p-value is less than 5% level of

significance. Therefore, the null hypothesis of linear significant association between

dependent variable and independent variables is accepted (Data and Bartz 1988).

Table 16: Table of intercept and slopes of multiple regression model

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22QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Coefficientsa

Model Unstandardized

Coefficients

Standardized

Coefficients

t Sig.

B Std. Error Beta

1

(Constant) .351 .049 7.115 .000

How important in a job:

job security: Versions

B, D

.052 .023 .050 2.328 .020

How important in a job:

high income: Versions

B, D

-.042 .025 -.042 -1.706 .088

How important in a job:

good opportunities for

advancement: Versions

B, D

.017 .025 .018 .688 .491

How important in a job:

an interesting job:

Versions B, D

.230 .025 .218 9.129 .000

How important in a job:

working independently:

Versions B, D

.046 .024 .048 1.897 .058

How important in a job:

helping other people:

Versions B, D

.237 .027 .241 8.931 .000

How important in a job:

useful to society:

Versions B, D

.205 .024 .213 8.539 .000

How important in a job:

deciding own times or

days of work: Versions

B, D

.166 .021 .171 7.829 .000

a. Dependent Variable: Importance of job involving personal contact with others: Versions B,

D

The multiple regression model is calculated as-

“Importance of job involving personal contacts with others: Versions B, D” = 0.351 +

∑ β i∗(How important in a job: job security: Versions B, D)i .

The p-values of are less than 0.05 for the 4th, 6th, 7th and 8th observation of “Importance of job

involving personal contacts with others: Versions B, D”. Hence, these observations of the

predictor variables are statistically and significantly related to the response variable. The

significant variables are “job security”, “an interesting job”, “helping other people”, “useful

to society” and “deciding own times or days of work”. The insignificant factors of the model

are “high income”, “good opportunities for advancement” and “working independently”. All

the predictors except “high income” is positively associated with the dependent variable.

Therefore, it the values of predictors (except “high income”) increase, the value of response

also increases and vice versa (Brandt 2014).

Coefficientsa

Model Unstandardized

Coefficients

Standardized

Coefficients

t Sig.

B Std. Error Beta

1

(Constant) .351 .049 7.115 .000

How important in a job:

job security: Versions

B, D

.052 .023 .050 2.328 .020

How important in a job:

high income: Versions

B, D

-.042 .025 -.042 -1.706 .088

How important in a job:

good opportunities for

advancement: Versions

B, D

.017 .025 .018 .688 .491

How important in a job:

an interesting job:

Versions B, D

.230 .025 .218 9.129 .000

How important in a job:

working independently:

Versions B, D

.046 .024 .048 1.897 .058

How important in a job:

helping other people:

Versions B, D

.237 .027 .241 8.931 .000

How important in a job:

useful to society:

Versions B, D

.205 .024 .213 8.539 .000

How important in a job:

deciding own times or

days of work: Versions

B, D

.166 .021 .171 7.829 .000

a. Dependent Variable: Importance of job involving personal contact with others: Versions B,

D

The multiple regression model is calculated as-

“Importance of job involving personal contacts with others: Versions B, D” = 0.351 +

∑ β i∗(How important in a job: job security: Versions B, D)i .

The p-values of are less than 0.05 for the 4th, 6th, 7th and 8th observation of “Importance of job

involving personal contacts with others: Versions B, D”. Hence, these observations of the

predictor variables are statistically and significantly related to the response variable. The

significant variables are “job security”, “an interesting job”, “helping other people”, “useful

to society” and “deciding own times or days of work”. The insignificant factors of the model

are “high income”, “good opportunities for advancement” and “working independently”. All

the predictors except “high income” is positively associated with the dependent variable.

Therefore, it the values of predictors (except “high income”) increase, the value of response

also increases and vice versa (Brandt 2014).

23QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Figure 6: The histogram plot of residual values of the multiple regression model

The residual plot as a histogram indicates that the residuals a normally distributed.

Figure 7: The normal probability plot of standardized residual of multiple regression model

The normal probability plot displays that the fitting is not bad.

Figure 6: The histogram plot of residual values of the multiple regression model

The residual plot as a histogram indicates that the residuals a normally distributed.

Figure 7: The normal probability plot of standardized residual of multiple regression model

The normal probability plot displays that the fitting is not bad.

24QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Conclusion and Limitations:

The analysis displays that the economic conditions of the households of UK

inhabitants are overall prospered (Lindley 1996). They informed that their TV news channels

are enough satisfactory. Therefore, they would like to continue watching the similar TV

channels in near future. The internet facility is available is available to most of the inhabitants

and a significant number of the inhabitants have thereby Twitter account. The males among

the sampled people equally prefer bus, cars and all other vehicles as the modes of

transportation at the time of tour. Note that, the numbers of tours are very lower in count such

as either once in a year or never in a year.

Surprisingly the significant negative correlation indicates that urban or rural

development indexes for the “Scotland” and “England & Wales” are against to each other.

However, the expected mean age of retirement from permanent job according to all the three

provinces are almost same. Age levels according to the last birthday of the male candidates

are unequal to each other. In those sampled data, the significant association among

importance of job in case of communication and different types of factors such as high

income, job security and other factors are found.

The all data is not utilized in this short report. It is one of the major drawback. Not

only that, the present of missing data and secondary responses may cause bias in the data set

as well as data analysis. The number of parameters of this big data is high. Therefore, the data

is not easy to handle and the analysis is not easy to carry out.

Conclusion and Limitations:

The analysis displays that the economic conditions of the households of UK

inhabitants are overall prospered (Lindley 1996). They informed that their TV news channels

are enough satisfactory. Therefore, they would like to continue watching the similar TV

channels in near future. The internet facility is available is available to most of the inhabitants

and a significant number of the inhabitants have thereby Twitter account. The males among

the sampled people equally prefer bus, cars and all other vehicles as the modes of

transportation at the time of tour. Note that, the numbers of tours are very lower in count such

as either once in a year or never in a year.

Surprisingly the significant negative correlation indicates that urban or rural

development indexes for the “Scotland” and “England & Wales” are against to each other.

However, the expected mean age of retirement from permanent job according to all the three

provinces are almost same. Age levels according to the last birthday of the male candidates

are unequal to each other. In those sampled data, the significant association among

importance of job in case of communication and different types of factors such as high

income, job security and other factors are found.

The all data is not utilized in this short report. It is one of the major drawback. Not

only that, the present of missing data and secondary responses may cause bias in the data set

as well as data analysis. The number of parameters of this big data is high. Therefore, the data

is not easy to handle and the analysis is not easy to carry out.

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25QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Reference:

Abbott, M.L., 2017. Independent Sample T Test.

Altman, D.G. and Bland, J.M., 1996. Detecting skewness from summary information. British

Medical Journal, 313(7066), pp.1200-1201.

Brandt, S., 2014. Testing Statistical Hypotheses. In Data Analysis (pp. 175-207). Springer,

Cham.

Data, S. and Using Descriptive Statistics Bartz, A.E., 1988. Basic statistical concepts. New

York: Macmillan. Devore, J., and Peck.

De Winter, J.C., 2013. Using the Student's t-test with extremely small sample sizes. Practical

Assessment, Research & Evaluation, 18(10).

Field, A., 2013. Discovering statistics using IBM SPSS statistics. sage.

George, D. and Mallery, P., 2016. IBM SPSS Statistics 23 step by step: A simple guide and

reference. Routledge.

Konasani, V.R. and Kadre, S., 2015. Multiple regression analysis. In Practical Business

Analytics Using SAS (pp. 351-399). Apress, Berkeley, CA.

Leech, N., Barrett, K. and Morgan, G.A., 2013. SPSS for intermediate statistics: Use and

interpretation. Routledge.

Lindley, R.M., 1996. The school-to-work transition in the United Kingdom. Int'l Lab.

Rev., 135, p.159.

Montgomery, D.C., Runger, G.C. and Hubele, N.F., 2009. Engineering statistics. John Wiley

& Sons.

Mukaka, M.M., 2012. A guide to appropriate use of correlation coefficient in medical

research. Malawi Medical Journal, 24(3), pp.69-71.

Norusis, M., 2008. SPSS Statistics 17.0: Guide to data analysis. Prentice-Hall.

Panik, M.J., 2012. Testing Statistical Hypotheses. Statistical Inference: A Short Course,

pp.184-216.

Traitler, H., Coleman, B. and Burbidge, A., 2017. Testing the hypotheses. Food Industry

R&D: A New Approach, pp.227-247.

Van Aelst, S. and Willems, G., 2011. Robust and efficient one-way MANOVA tests. Journal

of the American Statistical Association, 106(494), pp.706-718.

Reference:

Abbott, M.L., 2017. Independent Sample T Test.

Altman, D.G. and Bland, J.M., 1996. Detecting skewness from summary information. British

Medical Journal, 313(7066), pp.1200-1201.

Brandt, S., 2014. Testing Statistical Hypotheses. In Data Analysis (pp. 175-207). Springer,

Cham.

Data, S. and Using Descriptive Statistics Bartz, A.E., 1988. Basic statistical concepts. New

York: Macmillan. Devore, J., and Peck.

De Winter, J.C., 2013. Using the Student's t-test with extremely small sample sizes. Practical

Assessment, Research & Evaluation, 18(10).

Field, A., 2013. Discovering statistics using IBM SPSS statistics. sage.

George, D. and Mallery, P., 2016. IBM SPSS Statistics 23 step by step: A simple guide and

reference. Routledge.

Konasani, V.R. and Kadre, S., 2015. Multiple regression analysis. In Practical Business

Analytics Using SAS (pp. 351-399). Apress, Berkeley, CA.

Leech, N., Barrett, K. and Morgan, G.A., 2013. SPSS for intermediate statistics: Use and

interpretation. Routledge.

Lindley, R.M., 1996. The school-to-work transition in the United Kingdom. Int'l Lab.

Rev., 135, p.159.

Montgomery, D.C., Runger, G.C. and Hubele, N.F., 2009. Engineering statistics. John Wiley

& Sons.

Mukaka, M.M., 2012. A guide to appropriate use of correlation coefficient in medical

research. Malawi Medical Journal, 24(3), pp.69-71.

Norusis, M., 2008. SPSS Statistics 17.0: Guide to data analysis. Prentice-Hall.

Panik, M.J., 2012. Testing Statistical Hypotheses. Statistical Inference: A Short Course,

pp.184-216.

Traitler, H., Coleman, B. and Burbidge, A., 2017. Testing the hypotheses. Food Industry

R&D: A New Approach, pp.227-247.

Van Aelst, S. and Willems, G., 2011. Robust and efficient one-way MANOVA tests. Journal

of the American Statistical Association, 106(494), pp.706-718.

26QUANTITATIVE DATA ANALYSIS ASSIGNMENTS

Wonnacott, T.H. and Wonnacott, R.J., 1990. Introductory statistics (Vol. 5). New York:

Wiley.

Wonnacott, T.H. and Wonnacott, R.J., 1990. Introductory statistics (Vol. 5). New York:

Wiley.

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