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# Descriptive & Inferential Statistics

University: Imperial College London

• Unit No: 8
• Level: High school
• Pages: 21 / Words 5188
• Paper Type: Assignment
• Course Code: CR2030
Question :

This sample will let you know about-

• What is Inferential Statistics?
• Explain difference between descriptive & inferential statistics.
• Explain the assumptions of parametric.
Organization Selected : N/A

## INTRODUCTION

Statistical analysis involves organizing data and generating results that assist in further analysis and strategy formulation (Cooper and Sommer, 2018). Various tools and techniques are employed to obtain precise results and modify data according to specific needs. This project explores different statistical methodologies and conducts various tests based on the data requirements.

## Explain the difference between descriptive & inferential statistics along with a suitable examples and explain why they constitute descriptive/inferential statistics

Descriptive statistics: In this method, data is used to summarise the graph and this process allow to understand the set of observation. It describes the data such as samples that is very common and they do not have uncertainly because large population data is not used. There are some common tools which is used in descriptive statistics such as central tendency, dispersion, skewness etc. Get Assignment ExamplesTalk to our Experts!

For example: We collect 30 sample that is test score of students and calculate the summary statistics to produce graph.

As per the results, mean of the total score class is 79.18, range 66.21 to 96.53 and test accepting more than 70 score (Example of Descriptive Statistics, 2020). Data show that 86.7 % of students have acceptable scores because they secure more than 70 marks in the test.

statistics: This data collected from huge sample such as larger population because the aim of inferential statistics is to draw conclusions from sample of large population. There is various methodology used to calculate inferential statistics such as hypothesis tests, confidence intervals, and regression analysis (Galli, 2018).

For example: Assume that we collecting test score 100 students but they are not from the same class and they randomly collect sample. After that calculate all the required information such as mean, median, range etc. In this method, data is collected from large sample and provides final conclusion on the basis of random selection of sample.

It is very difficult to say that which statistical method is better because use of both methodologies based on the types of data. Descriptive statistics is the most suitable approach because it provides accuracy and the other hand, in order to solve complex data that, affect large population than use inferential statistics.

## Explain the assumption of sphericity and evaluate their own research scenario for the assumption, also identify that how these assumption is similar or different from the homogeneity of variance assumption

Sphericity is the assumption of repetitive measures of ANOVA but there are various conditions such as:

• All the independent variables should be equal
• Difference between combinations of the conditions are equal.
• If sphericity is desecrated, then variance calculations may be distorted.

Sphericity refer to the equality of variances that is repeated measures ANOVA and it also measure the homogeneity of the variances. It is quite similar to the homogeneity of variant among the groups where ANOVA is univariate. This is denoted with this â€œÎµâ€ symbol refer to the â€œcircularityâ€.

Homogeneity of variance assumption implicit F test or T test from the population variances where more than two sample consider equal. There is some assumption which mentioned below:

T-test and ANOVA required independent samples where each group comparison will be done with the same variance (Kerzner, 2018).

• T- test and ANOVA use the independent samples as per the t- test or F -test statistics.

## Explain the differences between one-way and two-way experimental designs along with suitable example and also define the two-way design advantages

One-way experimental design means one-way ANOVA and it is the statistical test which is used to compare variance within sample and include the independent factor or variance. It is a hypothesis based test and its aims to measure the multiple reciprocally exclusive theories regarding collected data.

For example: Group of randomly selected individual data divide into multiple small groups and perform different task. So in this case, individual learn the effect of tea and how it helps in weight loss such as green tea, black tea or no tea.Want to get Assignment help? Talk Our Expert Now!

Two-way experimental design called two-way ANOVA, where in one-way independent variable affecting dependent variable. In the tow way, there are two independent variable affect the other factors. If any research has quantitative results than two collection instructive variables available than implement two-way ANOVA.

For example If individual wanted to find interaction among income and gender for emotion level at job interviews. So emotional level of an individual is the actual outcome and the other side factor can be measured. There are two factors identified such as income & gender and consider as variables. Both factors are independent variables and it can say that Two Way ANOVA.

Some of the advantage of two-way ANOVA:
• Two-way experimental design is more cost effective in comparison to one-way design.
• It helps in analysing the interaction among two factors.
• It helps in understanding the combination of different factors and how they influence the behaviour.
• Two-way ANOVA allow to analyse synergistic effects among two different independent variables on dependent variable.

## Explain the assumptions of parametric and provide a suitable example for this

Parametric term refers to the statistics which is the procedure of hypothesis testing and this test based on the various assumptions which is collected with the help of observations of data. At the time of conduction parametric test, research need to ensure that all the assumptions should be fulfilled such as:

• Normal distribution of data where value of p depends upon normal sampling distribution.

Homogeneity of variance mean data need to be similar throughout the sample (Brookes, N., Butler, Dey and Clark, 2014).

• Data should be independent from each other's.

## Conduct a series of test or compare two groups of participants

(a) Levene's test is being used for testing of â€œKâ€ samples which have equal variances. In the aspect of comparison of cognitive ability score of two groups, this can be find out that Levene's test is 0.02. In these two groups' cognitive score data, this can be find out that there is no variability. It is so because for variability between the data set of two groups, the Levene's test should be of 0.05. For this purpose, T-test can be used in order to find out variables between these two groups of offender and non offender.

(b) The Kolmogorov-Smirnov test is used to find out distinction between the empirical distribution functioning of sample and cumulative distribution function of reference distribution of two different samples. In the sense of test of two groups, this can be find out that value is 0.3 which shows that there is no variability in the data set of neuroticism scores. Apart from the Kolmogorov-Smirnov test, there is an another alternative which may be used for finding variances. The another test can be Chi-square test that will be suitable.

(c) In order to find out association between gender of participants and crime history, the suitable test will be correlation test. It is a type of test which is applied in order to evaluate association between two or more variables. This test is done on the basis of two methods which are Pearson correlation and parametric correlation test. In regards to find out relation between gender and crime history, the parametric correlation test will be suitable. As well as interpretation of this correlation can be done in accordance of calculated value of data. The reason of applying this test is that it can make best relation between two set of variables. As well as there is not any other test that can be applied instead of correlation test.

(d) For making comparison between to data set, one of the best test is T - test which makes better outcome. In the context of making comparison of offenders' anxiety score pre and post counselling, this test will be suitable. As well as under descriptive statistics calculation of mean will be suitable.

(e) In order to do test of interaction between gender's with pre and post counselling depression score, best test will be linear regression. It is so because by help of this users can find out each variables relation with another group's variable (Brocke and Lippe, 2015).

(f) For finding impact of age on anxiety scores, the best suitable test is Chi-square test. In the case when test will produce value of 0.14 then it can be concluded that there will be a variable. In addition, age group of 26-40 will be variable.

## Calculation

Depression score of ten participants:

 Serial number Depression score 1 12 2 6 3 1 4 5 5 8 6 6 7 8 8 15 9 6 10 14
• Mean= Î£x/N
 Depression score 12 6 1 5 8 6 8 15 6 14 Total= 90

Mean= 90/10

Standard deviation= âˆ‘(xâˆ’xÂ¯)Â²/Nâˆ’1

 x xÂ¯ (x-xÂ¯) (xâˆ’xÂ¯)Â² 12 9 3 9 6 9 -3 9 1 9 -8 64 5 9 -4 16 8 9 -1 1 6 9 -3 9 8 9 -1 1 15 9 6 36 6 9 -3 9 14 9 5 25 179

Standard deviation= 179/(10-1)

= 179/9

= 19.88

• Range= Higher value-minimum value

Higher value= 15

Minimum value= 1

Range= 15-1

= 14

• Explanation of what result means:

Mean- On the basis of data of depression score of ten respondents, this can be find out that value of mean is of 9. This is so because total score of depression is of 90 and number of respondents are 10.

Standard deviation- As per the value of mean, further standard deviation is calculated that is of 19.88.

Range- The range is difference between higher and lower values. In the aspect of above data set, higher value is of 15 and lower value is of 1. Thus, the range is 14.

## Appropriate statistical test determines whether male or female participants are more depressed

In order to determine the relationship among the variable i.e gender and depression liner regression statistical test have been performed. The results are listed below:

 Descriptive Statistics Mean Std. Deviation N Gender 1.4625 .50174 80 Depression score (possible range 0-21) 8.7000 4.50148 80

 Model Summaryb Model R R Square Adjusted R Square Std. Error of the Estimate 1 .100a .010 -.003 .50240 a. Predictors: (Constant), Depression score (possible range 0-21) b. Dependent Variable: Gender

 ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression .200 1 .200 .793 .376b Residual 19.687 78 .252 Total 19.887 79 a. Dependent Variable: Gender b. Predictors: (Constant), Depression score (possible range 0-21)

 Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 1.560 .123 12.698 .000 Depression score (possible range 0-21) -.011 .013 -.100 -.891 .376 a. Dependent Variable: Gender

The first table shows the results of R and R2 in which r is simple correlation that is 0.100 and R2 display the total fluctuation in dependent variables which is 10% that is not very large. The next table is theANOVAtable, which reports how well the regression equation fits the data. this also support to discuss the prediction of dependent variable in meaningful manner. Thus, from the table p =0.376 which is greater that the standard value of 0.05. TheCoefficientstable provides the necessary information to predict the depression level from the gender variable and also display the gender contribution statistically significantly to the model by considering sig value which is 0.376. Take Management Assignment Help from professional experts!

## Appropriate statistical test to determine whether participants' socioeconomic status impacts on their anxiety scores.

Chi square test is considering to be an effective statistical test which support to define the

socioeconomic status impacts on their anxiety scores.

 Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Low, medium or high socioeconomic status * Anxiety score (possible range 0-21) 80 100.0% 0 0.0% 80 100.0%

 Low, medium or high socioeconomic status * Anxiety score (possible range 0-21) Crosstabulation Anxiety score (possible range 0-21) Total 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 18.00 Low, medium or high socioeconomic status low Count 0 0 1 2 2 1 2 3 2 2 4 2 2 2 0 1 26 Expected Count .7 .7 .7 1.6 2.0 2.0 1.3 2.3 1.6 1.6 3.9 1.6 2.6 2.0 1.0 .7 26.0 medium Count 1 0 0 1 1 2 1 4 2 2 4 0 4 0 3 0 25 Expected Count .6 .6 .6 1.6 1.9 1.9 1.3 2.2 1.6 1.6 3.8 1.6 2.5 1.9 .9 .6 25.0 high Count 1 2 1 2 3 3 1 0 1 1 4 3 2 4 0 1 29 Expected Count .7 .7 .7 1.8 2.2 2.2 1.5 2.5 1.8 1.8 4.4 1.8 2.9 2.2 1.1 .7 29.0 Total Count 2 2 2 5 6 6 4 7 5 5 12 5 8 6 3 2 80 Expected Count 2.0 2.0 2.0 5.0 6.0 6.0 4.0 7.0 5.0 5.0 12.0 5.0 8.0 6.0 3.0 2.0 80.0

 Test Statistics Low, medium or high socioeconomic status Anxiety score (possible range 0-21) Chi-Square .325a 21.200b df 2 15 Asymp. Sig. .850 .131 a. 0 cells (.0%) have expected frequencies less than 5. The minimum expected cell frequency is 26.7. b. 0 cells (.0%) have expected frequencies less than 5. The minimum expected cell frequency is 5.0.

## Appropriate statistical test to determine whether participants' depression and anxiety scores significantly differ.

To determine the whether applicant's depression score and anxiety significantly differ from each other compare mean statistical test is used. The results are as follows:

 Case Processing Summary Cases Included Excluded Total N Percent N Percent N Percent Depression score (possible range 0-21) * Anxiety score (possible range 0-21) 80 100.0% 0 0.0% 80 100.0% ANOVA Table Sum of Squares df Mean Square F Sig. Depression score (possible range 0-21) * Anxiety score (possible range 0-21) Between Groups (Combined) 825.627 15 55.042 4.544 .000 Within Groups 775.173 64 12.112 Total 1600.800 79

 Measures of Association Eta Eta Squared Depression score (possible range 0-21) * Anxiety score (possible range 0-21) .718 .516

## Design of a question to the study

A) Research question

What is the relation between depression level and the Diagnosed with Chronic Pain?

This is important to determine that in what age mostly people suffer from these long lasting diagnosed pain.

B) Statistical tests

To figure out the relationship between the depression level and the level of Diagnosed with Chronic Pain correlation test is analysed which help to define the most significant values (Crawford, Langston, and Bajracharya, 2013). That can be seen from the results mention below:

 Descriptive Statistics Mean Std. Deviation N Diagnosed with a chronic pain disorder 1.5375 .50174 80 Depression score (possible range 0-21) 8.7000 4.50148 80

 Correlations Diagnosed with a chronic pain disorder Depression score (possible range 0-21) Diagnosed with a chronic pain disorder Pearson Correlation 1 -.292** Sig. (2-tailed) .009 N 80 80 Depression score (possible range 0-21) Pearson Correlation -.292** 1 Sig. (2-tailed) .009 N 80 80 **. Correlation is significant at the 0.01 level (2-tailed).

C) From the results above, it has been stated that value of diagnosed with pain disorder is of 1 and possible score for depression is of -292. The significance level the correlation between depression level and diagnosed with chronic pain is 0.09 which is lower than standard level.

D) The variable which is selected for the study is stress level of participants. The 2 * 2 factorial presentation is as follows:

 2*2 factorial IV1: Age below 25 IV1: Age over 25 Stress IV2: High stress dv: 15% dv: 85% IV2: Low stress dv: 85% dv: 15%

## CONCLUSION

On the basis of above project report this can be concluded that there are different types of tests under SPSS. In the project different sort of tests are applied such as T- test, chi-square test and many more. As well as descriptive analysis is also done including mean, standard deviation

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