The UK Cross-Sectional Data Analysis - Essay Example

Econometrics Project Introduction This project will use cross-sectional data obtained collected all over the UK and which has information on wages, health, smoking, drinking, education and other socio-demographic characteristics of individuals Analysis Plan The first part of the analysis will focus on exploratory analysis of the data provided. Under exploratory analyses, descriptive statistics will be computed and a relationship will also be hypothesized using summary statistics (mean and standard deviation). Tabulations will also be used to make observations on the data. The second phase of analysis will use in-depth statistical analysis processes to create models relating the different observations, particularly that between gross weekly earnings (grmain1) and other observations such as age, sex, race, years of education and number of years in employment, among others. Correlation analysis will also be used to investigate the strength of the relationship observed between the dependent variable (gross weekly earnings) and other independent variables. A residual plot will be used to confirm the presence or absence of outliers, the plot will also indicate whether there were any particular areas where the model greatly under or over-predicted the relationship between unemployed persons and persons seeking employment. Exploratory Data Analysis a. Gross weekly earnings from main job The first step in this analysis will explore descriptive statistics of the dependent variable. The output is as shown below: From the results, it is observed that othe sample consists of 7227 respondents. The mean income is obtained as 10.3 and this corresponds to an income category of £300-350 per week. The standard deviation is obtained as 4.5 and this corresponds to an income category of £100-125 per week. This implies that on average, the respondents’ salaries differ from the average earning by this amount. Tabulation of the various categories of incomes earned are as shown below: The STATA output shown indicates that the greatest proportion of respondents (20.23%) earn over £600 per week followed by those that earn £300 - 350 and £250-300 with 9.5% and 9.2% respectively. Apart from persosn that do not earn anything, the income category of £50-75 has the least number of respondents. b. Sex Tabulation of gender of the responndents is shown below: It is observed that out of the 7227 respondents, 47% were male while the remaining 53% were female. These percentages correspond to 3398 and 3829 persons respectively. Observing these percentages, it is seen that both sexes made up approximately 50% of the sample. Further analysis of the data on sex in later sections of the paper will give further findings. c. Ethnicity Tabulation of the ethnicity categories as as shown below: The greatest proportion of respondents have “white british” ethnicity followed by “any other white background”. The two ethnicities account for almost 95% of all persons surveyed. This proportion of ethnicities perhaps reflects the overall population structure of the UK. For easier analysis, the 14 ethnicities can be collapsed into just five: white, mixed, Asian, black and Chinese. The summary is as shown below: Whites make the highest proportion of respondents followed by Asians and blacks. d. Age The histogram for ages of respondents and summary statistics are shown. The histogram shows that most respondents are aged between approximately 35 and 60 years. The proportion of respondents drops sharply after 60 years. Summary statistics for age show that the average age of respondents is 41 years while the standard deviation is 12.5 years. It is also seen that the youngest persons surveyed was 16years while the oldest one was 83 years. e. Number of Years of continuous employment The value for number of years of continuous employment is obtained by subtracting empsty from 2006, the year the survey was conducted. This new variable is known as nemploy. The histogram is shown below: From the histogram, most respondents have been in continuous employment for an average of 8 years. The distribution for nemploy is skewed to the right, implying the number of people in continuous employment decreases with increase in years, i.e. number of years in employment has a negative correlation with time. It is also seen that the highest number of years in continuous employment is 60 years. CONFIRMATORY DATA ANALYSIS a. Correlation Tests Correlation is used to investigate the extent of linear relationship between any two variables (Cohen, Cohen, West, & Leona 48). A correlation test is the most preferred as it will reveal whether one variable increases in magnitude as the other variable increases or otherwise. This in turn helps in determining whether the two variables are related, or follow a similar trend. A positive correlation would imply that as one variable increases in magnitude, the second variable also increases correspondingly. The first test will examine the correlation between gross weekly earnings from main job and number of years in employment. As expected, the correlation between the two variables is positive although not very strong. Hence, a person’s income is expected to increase with additional years of employment. The relationship is not as strong as expected since there are a myriad of factors that affect a person’s income. These factors include education level, type of job, type of degree acquired, and race, among others. Regression methods will be used to examine further these relations. Correlation analysis between earnings and education level is shown below: This analysis shows that just like the relation between earnings and number of years in employment, the relation between earnings and education level is also positive at 0.27. This shows that a person with high qualifications is most likely to have higher earnings than one with lesser qualifications. It is expected that as a result of this positive correlation, people with higher education have the highest earnings while those with no qualifications have the lowest synthetic work life earnings. As one’s academic attainment improves, they become specialists in their own fields and are able to attract higher paying jobs. Besides, these highly learned individuals are more likely to get promotions resulting into salary hikes. Ultimately, persons with higher academic credentials not only earn more than their counterparts with fewer qualifications, but they are also more likely to get employed as well. This accounts for high synthetic work life earnings among the former. This relation is supported by numerous studies and is not due to chance. b. Chi-Square Tests and Fisher’s exact Test This statistical test is used to compute variations in the frequency distribution of certain events observed in a population with those of a specific distribution, or hypothesized values (Miller, 34; 1997). The events under consideration must be mutually exclusive, that is, they cannot happen at the same time, and have a sum probability of 1. This test can also show whether a relation exists between two categorical variables. However, the cell frequencies must be greater than 5. In case this condition is not achieved, then Fisher’s exact test can be used. The first test will examine whether the proportion of sexes used in the study were significantly different from the expected 50% representation of each gender in the study. The results are shown: Since the p-value is 0, we conclude that the composition of sex of respiondents differs significantly from the hypothesized values that we used (50% of each gender). This could imply that the proportions of genders used in the sample were not necessarily equal. A Fisher’s exact test will be used to test whether a relationship exists between sex and educational attainmemt since the cell frequency for persons who never attended school is less than 5. The test looks into whether one gender more likely to attain a specific level of education as compared to another. The results are shown: The variable edlev is defined as follows: 1 stands for never attended school, 2 for no qualification, 3 for other qualification and 4 for higher education. The results suggest that there is not a statistically significant relationship between sex and educational attainment (p-value= 0.515). This means each gender is equally likely to attain a specific level of education. Using a chi-square after eliminating the column for persons who never attended school, we have the following result: Just as was observed in Fisher’s exact test, the chi-square test also suggests that there is not a statistically significant relationship between sex and educational attainment (p-value= 0.618). Chi-square test will further be used to examine the relation between education lelev and ethinicity, i.e are some ethnicities more or less learned that others? Observation for chinese and persons who never attended school aredropped. The STATA output is shown below: The results show that a significant difference exists in educational attainment among races and implies some races are more likely to attain specific levels of education as compared to others (p-value= 0). c. Regression The regression results show that age and number of employment both contribute positively to one’s earnings while education level is not significant in explaining one’s earnings. Reference Miller, G. (1997). Beyond ANOVA: Basics of Applied Statistics. Boca Raton, FL: Chapman & Hall. Read More