Analysis of Fertility Statistics in Canada - Coursework Example

2021-07-15 18:59:05
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Harvey Mudd College
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Births 252 30111.59 2574.508 6628091.42 .064 .153 -.623 .306

Valid N (listwise) 252 Descriptive were carried out on the birth of persons in Canada between 1991 and 2011. Table 1 shows that the average number of persons born per month (M=30111.59, S.D = 2574.51). Within this period, there was a population variance of 6628091.42. The skewness of the data is greater than 0 (skewness=.064). A normal distribution of data is expected to have the skewness value of 0. Therefore, the present data is assymetric and its distribution is not normal with positive skewness. The dataset has a Kurtosis value of less than 3 implying that the dataset has lighter tails than a normal distribution (a dataset that has a Kurtosis value>0 is said to have heavier tails than the normal distribution) (Green & Salkind, 2010).

Further analysis of the data was carried out to determine the total number of children born in Canada for each of the years 1991 to 2011. Table 2 shows the number of children born each year over the twenty- year period. To show the childbirth trend, a bar chart was plotted as shown in Figure 1.

Table 2. The number of children born each year between 1991 and 2011

Year Total Births

1991 402533

1992 398643

1993 388394

1994 385114

1995 378016

1996 366200

1997 348598

1998 342418

1999 337249

2000 327882

2001 333744

2002 328802

2003 335202

2004 337072

2005 342176

2006 354617

2007 367864

2008 377886

2009 380863

2010 377213

2011 377636

 

Figure 1. Trends in childbirth in Canada between 1991 and 2011

Figure 1 shows that the annual number of children born in Canada fell between 1996 and 2006 to below 350,000 births before increasing again to >350,000 per year. The highest number of births was recorded in 1991 while the lowest was recorded in 2000.

Table 3. The average number of live births in each of the 12 months

Month Average Births by Month

1 28890.52

2 27378.81

3 31000.86

4 30681.29

4 30681.29

5 31954.19

6 30911.05

7 31888.38

8 31143.33

9 31255.48

10 30002.67

11 27991.86

12 28240.71

Table 3 shows the average number of live births in each of the 12 months. Figure 2 below shows a better representation of the number of births using a sample of the latest 12 months (2011). It can be seen that the highest number of births were recorded in the third quarter of 2011.

 

Figure 2. The number of live births in each of the 12 months of 2011

Table 4. Frequency distribution of Births between January and December (2011)

Frequency Relative Frequency

Valid 27993 1 8.3

29497 1 8.3

30235 1 8.3

30350 1 8.3

30761 1 8.3

31325 1 8.3

31884 1 8.3

32390 1 8.3

32527 1 8.3

33429 1 8.3

33564 1 8.3

33681 1 8.3

Total 12 100.0

A paired-samples t-test was performed to determine whether there is a statistically significant difference between the mean numbers of children born in the first quarter compared to the children born in the fourth quarter (1991 2011). Demsar (2006) suggests that paired samples tests are the most suitable tests of variance for two sets of group data. It is particularly important when testing the hypothesis that significant difference exists between two sets of similar data. Table 5 shows that there was no statistically significant difference between the mean number of children born in the first quarter (M = 29090.06, SD = 2488.79) and the children born in the fourth quarter (M = 28745.08, SD = 2226.92) in Canada; (t(62) = 1.307, p = .196.

Table 5. Paired Samples Test

Paired Samples Statistics

Mean N Std. Deviation Std. Error Mean

Pair 1 First 29090.06 63 2488.790 313.558

Fourth 28745.08 63 2226.922 280.566

Paired Samples Test

Paired Differences t df Sig. (2-tailed)

Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 First - Fourth 344.984 2094.836 263.924 -182.593 872.562 1.307 62 .196

Question 2: Reliability and Correlation Analysis

Before subjecting the data to any statistical analysis, it is important to determine the total score (summated scale) for the scales to be used in the analysis. SPSSs data Transform function is a useful tool through which variables of a scale can be computed (Meeker & Escobar, 2014). As a first step, however, there is need to reverse any negatively worded statement before summing the variables together. In the present analysis, People on the MBA often think about quitting, I frequently think of quitting the MBA and The MBA is very stressful were negatively worded and thus were subject to the reversing process.

Before applying further statistical analysis on the items of the research, it is important to test the reliability of the scale to understand the extent to which it produces a consistent result if measurements were to be repeated. In the present case, the reliability statistics were only carried out upon reversing the three items mentioned in the foregoing paragraph. The Cronbachs Alpha was used to determine the association between scores obtained from different attributes of the scale used. The scale produces consistent results if the relationship is high on a scale of 0 1. According to Cronbach (1951), the value has to be greater than 0.6 for the Likert scale to be seen as reliable. The reliability statistics below shows that Cronbach's Alpha is 0.696, implying that the scale is reliable (or 69.6% reliable).

Reliability Statistics

Cronbach's Alpha Cronbach's Alpha Based on Standardized Items N of Items

.696 .710 7

The new total social support scores (summated scale) were obtained by adding the scores of all the constructs of social support (including the reversed items). This summated scale was used in the analysis of the relationship between a students grade goal and self-efficacy at the outset of an MBA programme and their perceptions of social support and their actual average grade at the end of the programme.

Correlation analysis, also known as a bivariate statistic, is used to determine the degree of relationship between two variables (Norusis, 2006). The relationship between any two different variables can weak, null, or strong. A strong correlation strong enables us to use the score of one variable to predict the score of the second variable. However, a weak correlation implies that knowing the score of one variable does not help to predict the outcome of the second variable. The correlation coefficient ranges from 1.00 through 0 (no correlation) to +1.00 and any other value outside this range is not valid. It is also that values close to 1 show a strong relationship and those close to zero (0) represent weak relationships. The main types of correlation coefficients are Pearson's product moment correlation coefficient and Spearman's rank correlation coefficient. Kendalls correlation is seldom used. For purposes of this study, Pearson's product moment correlation coefficient was used to determine the relationship between five variables as follows;

Table 6 shows the relationship between the different variables explored in this analysis. Age was found to have a weak positive and statistically insignificant correlation with Gender (r(178) = .057, p> .05, two-tailed). The correlation between age and personal grade goal was found to be weak negative and statistically insignificant, r(178) = -.025, p> .05, two-tailed. The correlation between age and self-efficacy was found to be positive and statistically insignificant, r(175) = .097, p> .05, two-tailed. Likewise, the correlation between age and social support was found to be positive and statistically insignificant, r(169) = .059, p> .05, two-tailed. Gender was found to be positively correlated with personal grade goal but the relationship was statistically insignificant (r(178) = .056, p> .05, two-tailed). Additionally, the correlation between gender and self-efficacy was found to be positive and statistically insignificant, r(175) = .065, p> .05, two-tailed. However, the correlation between gender and social support was found to be positive (strong) and statistically significant, r(169) = .164, p< .05, two-tailed. Although the correlation between self efficacy and personal grade goal was positive (strong) and insignificant (r(175) = .119, p> .05, two-tailed), the correlation between personal grade goal and support was positive (strong) and significant, r(169) = .168, p< .05, two-tailed. These results show that gender, personal grade goal, and self-efficacy strongly correlated with social support.

Table 6. Correlation Statistics

Age Gender Personal grade goal General self efficacy Social support

Age Pearson Correlation 1 .057 -.025 .097 .059

Sig. (2-tailed) .449 .743 .204 .443

N 178 178 178 175 169

Gender Pearson Correlation .057 1 .056 .065 .164*

Sig. (2-tailed) .449 .462 .391 .033

N 178 178 178 175 169

Personal grade goal Pearson Correlation -.025 .056 1 .119 .168*

Sig. (2-tailed) .743 .462 .118 .029

N 178 178 178 175 169

General self efficacy Pearson Correlation .097 .065 .119 1 .400**

Sig. (2-tailed) .204 .391 .118 .000

N 175 175 175 175 167

Social support Pearson Correlation .059 .164* .168* .400** 1

Sig. (2-tailed) .443 .033 .029 .000 N 169 169 169 167 169

*. Correlation is significant at the 0.05 level (2-tailed). **. Correlation is significant at the 0.01 level (2-tailed). Question 3: Regression Analysis

Question 3: Regression Analysis

Before regression analysis was done, some variables were recoded in order to allow them to be run for regression statistics in SPSS. Specifically, some variables which were recorded as String values were recorded into Numeric values. Subsequently, the numeric numbers were assigned values. For example, participants from Canada were assigned a value of 1, those from the United States assigned the value of 2 and so forth.

A non-parametric test was conducted using recoded month of birth data to determine if the players born in the first quarter of the year (January, February and March) earn more than players born in the last quarter (October, November and December). The most appropriate test for this kind of analysis is the Mann-Whitney U test (Mayers, 2013). This test is based on four basic assumptions:

Assumption #1: The dependent variable is measured on a continuous (for example the salary of the players) or ordinal scale (in case the Likert scale is available).

Assumption #2: The independent variable consists of two categorical, independent groups. Our independent variable is a dichotomous variable divided into the first quarter and the fourth quarter.

Assumption #3: the third assumption is that the two groups of data to be analyzed are independent observations with no relationship between the observations or between the groups. For instance, the children born in the first quarter cannot be born again in the fourth quarter; the participants in each group are different.

Assumption #4: the distribution of scores for both groups of the predictor variable (e.g., the distribution of scores for participants born in the first quarter and the distribution of scores for participants born in the fourth quarter for the independent variable, MonthBirth) should be explored to determine whether they have the same shape or a different shape for purposes of interpretation of the Mann-Whitney U test.

Table 7 shows the results of the Mann-Whitney U test. The Mean Rank' column shows that the distribution of scores of the players born in the First quarter and Fourth quarter is not equal implying that the salaries of the respective groups of players are different. These resu...

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