Quantitative Data Analysis and Computing With SPSS - Report Example

Quantitative Data Analysis and Computing With SPSS (Mohammed) 25/05 Quantitative Data Analysis and Computing With SPSS Introduction There are two types of statistics: descriptive statistics and inferential statistics. Descriptive statistics refers to the collection, organization, presentation, and summary of data by either using charts and graphs or using a numerical summary and inferential statistics refers to generalizing from a sample to a population, estimating unknown parameters, drawing conclusions, and making decisions (Doane & Seward, 2009). This paper will describe the nature of the population of England and Wales as it appears in the British Crime Survey Statistics 1984 (by selecting approximately six variables) using the appropriate statistical tests and graphs. Further, this paper will investigate whether any of variables are associated with the variable personal victimization and, if so, how. The main aim of this assessment is to use SPSS to analyse data and knowledge of statistics to interpret the output and demonstrate an understanding of both univariate and bivariate analysis. Question – 1 Describe the nature of the population of England and Wales as it appears in the British Crime Survey Statistics 1984 (bcsteac.sav file) using the appropriate statistical tests and graphs. The univariate statistical analysis presents the demographic and socio-economic profile of England and Wales for the year 1984. The univariate statistical analysis involves only one statistical variable. The variables taken to answer this part of question from the British Crime Survey Statistics 1984 are age, sex, marital status, age on leaving full time education, house structure, duration of stay at present address and working status (last week) of the respondents. 1.1) Age of Respondents To describe the demographic profile of the respondents, it is important to know the age of the respondents. Age is measured on ratio scale. Table 1 shows the summary statistics for the age of the respondents. Table 1 Summary Statistics for age of the respondents Age of respondent N Valid 1394 Missing 12 Mean 45.40 Median 44.00 Mode 25 Std. Deviation 18.817 Variance 354.065 Skewness .262 Kurtosis -1.000 Range 77 Minimum 16 Maximum 93 The mean is the arithmetic average of a distribution of scores and is determined by adding the scores and dividing this sum by the number of scores (Hinkle, Wiersma & Jurs, 1981). The average (mean) age of the respondents was about 45.4 years. The median represents the middle value of the data that divides the population into two equal parts. About half of the respondent’s age was equal to or less than 44 years. The mode is the value that occurs more frequently. Most of the respondent’s age was equal to 25 years. The minimum and maximum age of the respondents was 16 years and 93 years, respectively. The range gives us an idea of dispersion of the data and is the difference between the highest and lowest values (Harper, 1991). The range of the respondent’s age was 77 years. The minimum and maximum values could be outliers, which is why the range might exaggerate the extent of dispersion around the mean. Thus, with range, it is necessary to be very careful and it cannot be trusted because it depends upon two values only. The variance indicates the extent to which the data is dispersed and is defined as the ‘mean of the squared deviated scores (Hinkle, Wiersma & Jurs, 1981:44). The standard deviation is an ‘an index of the amount of variability of scores around the mean of the scores’ (Howitt & Cramer, 2003:54). Interpreting the standard deviation along with the mean tells us something about how much spread there is in the scores, and important properties of the distribution relate to how far away from the mean we move, in terms of standard deviation (see Punch, 2000). The larger the standard deviation, the more spread out is the distribution (Wright, 1998). The standard deviation for the age of the respondents was about 18.8 years. This indicates that the age of respondents was more dispersed. Skewness is defined as ‘an index of the asymmetry or lop-sidedness of the distribution of scores on a variable (Howitt & Cramer, 2003:47-8). If the value of skewness coefficient is positive ( > 0) than the distribution is right skewed and if the value of skewness coefficient is negative (< 0) than the distribution is left skewed. For normal distribution, the value of skewness coefficient is close to zero. The value of skewness coefficient for the age of respondents is 0.26, which is close to zero. This suggests that the distribution of age of the respondents is approximately normal. Kurtosis measures the degree of peakness of a distribution. In other words, Kurtosis refers to the relative length of the tails and the degree of concentration in the center. If a distribution has a relatively high peak, it is called ‘leptokurtic’ (Hawkins & Weber, 1980:38). According to Doane & Seward (2009), a normal bell-shaped population is called mesokurtic (kurtosis = 0) and serves as a benchmark. Further, a population that is flatter than a normal (i.e., has heavier tails) is called platykurtic (kurtosis < 0) while one that is more sharply peaked than a normal (i.e., has thinner tails) is leptokurtic (kurtosis > 0). The value of kurtosis coefficient for the age of the respondents is -1.00 that suggests heavier tails. Figure 1 shows the histogram of age of the respondents. The histogram suggests that the distribution of age of the respondents is approximately normal. Figure 1: Distribution (Histogram) of age of the respondent 1.2) Sex and Marital Status of Respondents Table 2 shows the cross-tabulation of martial status and gender of the respondent. Table 2 Crosstabulation of Marital Status and Sex of respondent Sex of respondent Male N (%) Female N (%) Total N (%) Marital Status Single 169 (12.1) 143 (10.2) 312 (22.3) Married 416 (29.7) 436 (31.1) 852 (60.8) Separated 8 (0.6) 12 (0.9) 20 (1.4) Divorced 23 (1.6) 43 (3.1) 66 (4.7) Widowed 35 (2.5) 116 (8.3) 151(10.8) Total 651 (46.5) 750 (53.5) 1401 (100.0) Majority (53.5%) of the respondents was female. Further, majority (60.8%) of the respondents were married. Figure 2 shows the cluster bar chart for marital status and sex of respondent. Except widowed, the other distribution for martial status for male and female are approximately same. Figure 2: Cluster bar chart for marital status and sex of respondent 1.3) Working status of respondents Figure 3 shows the pie chart for working status (last week) of the respondents. About half (48%) of the respondents were working more than 10 hours in a week. About 39% of the respondents were working more than 30 hours in a week. The percentage of unemployed, sick/disabled, retired and housewife was 9%, 3%, 17% and 19%, respectively. Figure 3: Pie chart for working status (last week) of respondents 1.4) Age on leaving full time education Figure 4 shows the bar graph for age on leaving full time education of respondent. Figure 4: Bar chart for age on leaving full time education of respondent The figure suggests a poor picture of the educational background of the respondents. More than three-fourth (83%) of the respondents had left full time education at the age of 16 years. Only a small percentage (6%) of the respondents continued in education more than 20 years. Further, about 2% of the respondents were still engage in studies. Thus, it can be said that the educational level of the respondents were very low. 1.5) Stay duration at present address One cannot stay at the same place because of many reasons. Figure 5 shows the pie chart for stay duration at present address. Figure 5: Pie chart for stay duration at present address About half (49%) of the respondents were living at their present address for more than a decade. About 18% of the respondents were living at their present address from 5 to 10 years. Only about 8% of the respondents stay duration at present address was less than 12 months. 1.6) Type of House (Structurally) Figure 6 shows the bar chart for type of house of respondents. About 39% of the respondents were living in semi-detached type of house. About 29% of the respondents were living in mid-terrace type of house. Figure 6: Bar chart for type of house of respondents Question – 2 Investigate whether any of your variables from part 1 are associated with the variable personal victimization (‘incpers’) and, if so, how? Make personal victimization a dependent variable. This part of the paper will analyze the association between respondent’s age and personal victimization (if any) using the inferential statistical technique of correlation and regression and Chi-square test of Independence (association). Personal Victimization Table 3 shows the summary statistics for the number of personal victimizations. Table 3 Summary Statistics for the number of personal victimizations Number of personal victimizations N Valid 1405 Missing 1 Mean .34 Median .00 Mode 0 Std. Deviation 2.748 Variance 7.549 Skewness 16.023 Kurtosis 313.471 Range 67 Minimum 0 Maximum 67 Figure 7: Distribution (Histogram) of number of personal victimizations The average number of personal victimizations for respondents was about 0.34 (SD = 2.75). About half of the respondents had 0 number of personal victimization. The range of the personal victimization was 67 with minimum and maximum being 0 and 67, respectively. The distribution of number of personal victimizations for respondents is heavily positively skewed (Skew = 16.02). This is also confirmed by the histogram of the number of personal victimizations for respondents (figure 7). Correlation and Regression Analysis Regression analysis is used to develop a predictive model to predict values of dependent variable based on one or more independent variables. A simple linear regression involves drawing a straight line through the data when they are presented as a scatter plot (Wright, 1998). Figure 8 shows the scatterplot of respondent’s age and number of personal victimization. The scatterplot suggest very weak direct linear relationship between respondent’s age and number of personal victimization. Figure 8: Scatterplot of number of personal victimization vs. age of respondents The strength of the relationship is measured using correlation coefficient, which is a numerical measure or index of the amount of association between two sets of scores. The range of correlation coefficient is between -1 to +1. According to Howitt & Cramer (2003), the ‘+’ sign indicates a positive correlation, i.e. the scores on one variable increase as the scores on the other variable increase and a ‘-’ sign indicates a negative correlation, i.e. as the scores on one variable increase, the scores on the other variable decreases. A correlation coefficient value of |1| indicates a perfect association between the two variables and a value of 0 indicates no association between the two variables. A correlation of |0.5| would indicate a moderate (negative or positive) relationship between the two variables (Howitt & Cramer, 2003). Although a scatterplot revealed very weak positive relationship between respondent’s age and number of personal victimization. Let us check whether this relationship is statistically significant or not. The null and alternate hypotheses are (There is no significant relationship between age and personal victimization.) (There is a significant relationship between age and personal victimization.) The selected level of significance, α is .05 and the selected test is test for Zero Correlation. Table 4 shows the correlation matrix. Table 4 Correlations Matrix Number of personal victimizations Population of area Population of area -.023 Age of respondent -.106** -.016 * p < .05, **P Read More

Interpreting the standard deviation along with the mean tells us something about how much spread there is in the scores, and important properties of the distribution relate to how far away from the mean we move, in terms of standard deviation (see Punch, 2000). The larger the standard deviation, the more spread out is the distribution (Wright, 1998). The standard deviation for the age of the respondents was about 18.8 years. This indicates that the age of respondents was more dispersed. Skewness is defined as ‘an index of the asymmetry or lop-sidedness of the distribution of scores on a variable (Howitt & Cramer, 2003:47-8).

If the value of skewness coefficient is positive ( > 0) than the distribution is right skewed and if the value of skewness coefficient is negative (< 0) than the distribution is left skewed. For normal distribution, the value of skewness coefficient is close to zero. The value of skewness coefficient for the age of respondents is 0.26, which is close to zero. This suggests that the distribution of age of the respondents is approximately normal. Kurtosis measures the degree of peakness of a distribution.

In other words, Kurtosis refers to the relative length of the tails and the degree of concentration in the center. If a distribution has a relatively high peak, it is called ‘leptokurtic’ (Hawkins & Weber, 1980:38). According to Doane & Seward (2009), a normal bell-shaped population is called mesokurtic (kurtosis = 0) and serves as a benchmark. Further, a population that is flatter than a normal (i.e., has heavier tails) is called platykurtic (kurtosis < 0) while one that is more sharply peaked than a normal (i.e., has thinner tails) is leptokurtic (kurtosis > 0).

The value of kurtosis coefficient for the age of the respondents is -1.00 that suggests heavier tails. Figure 1 shows the histogram of age of the respondents. The histogram suggests that the distribution of age of the respondents is approximately normal. Figure 1: Distribution (Histogram) of age of the respondent 1.2) Sex and Marital Status of Respondents Table 2 shows the cross-tabulation of martial status and gender of the respondent. Table 2 Crosstabulation of Marital Status and Sex of respondent Sex of respondent Male N (%) Female N (%) Total N (%) Marital Status Single 169 (12.1) 143 (10.2) 312 (22.3) Married 416 (29.7) 436 (31.1) 852 (60.8) Separated 8 (0.6) 12 (0.9) 20 (1.4) Divorced 23 (1.6) 43 (3.1) 66 (4.7) Widowed 35 (2.5) 116 (8.3) 151(10.8) Total 651 (46.5) 750 (53.5) 1401 (100.0) Majority (53.5%) of the respondents was female.

Further, majority (60.8%) of the respondents were married. Figure 2 shows the cluster bar chart for marital status and sex of respondent. Except widowed, the other distribution for martial status for male and female are approximately same. Figure 2: Cluster bar chart for marital status and sex of respondent 1.3) Working status of respondents Figure 3 shows the pie chart for working status (last week) of the respondents. About half (48%) of the respondents were working more than 10 hours in a week.

About 39% of the respondents were working more than 30 hours in a week. The percentage of unemployed, sick/disabled, retired and housewife was 9%, 3%, 17% and 19%, respectively. Figure 3: Pie chart for working status (last week) of respondents 1.4) Age on leaving full time education Figure 4 shows the bar graph for age on leaving full time education of respondent. Figure 4: Bar chart for age on leaving full time education of respondent The figure suggests a poor picture of the educational background of the respondents.

More than three-fourth (83%) of the respondents had left full time education at the age of 16 years. Only a small percentage (6%) of the respondents continued in education more than 20 years. Further, about 2% of the respondents were still engage in studies. Thus, it can be said that the educational level of the respondents were very low. 1.5) Stay duration at present address One cannot stay at the same place because of many reasons.

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