In this experiment, the main objective is to determine if there is a difference between the average total income and each of the highest populated provinces within Canada, using the data provided from Stats Canada. The data being used in this analysis are the 40 selected average income (CAD) in 40 different cities – there are 8 randomly selected average incomes per province in Canada during the year 2015. The 40-sample data are independently and randomly selected. Furthermore, the selection from the city’s average income of each province is independent of each other. The population of each province is assumed to be normally distributed and have a sample variance to meet the assumptions of the technique that will be used in this experiment (Levine et al., 2018, p.186). By selecting 8 random cities in 5 of the highest populated provinces and by collecting the average total income of each city, the correlation between the average total income and the provinces in Canada can be examined with the technique one-way ANOVA using SPSS (Statistical Package for the Social Sciences).
One-way ANOVA is the most appropriate technique to use to compare the average total income because it allows us to compare 3 or more populations with having one independent variable and one categorical variable (Levine et al., 2018, p.178). The independent variable would be the average income and the categorical variable would be the provinces. It would tell if the average total income would differ based on the provinces. Using the SPSS software, it would be easier to run the Tukey-Kramer procedure which determines which of the pairs of provinces are significantly different if there is a difference between the average total income (Levine et al., 2018, p.178). If there is not a significant difference in the average total income, then it would not be necessary to run the Tukey-Kramer (Levine et al., 2018, p.191).
As a group, we have chosen to research data on One-Way ANOVA. This term examines an analysis of variance to compare means of the groups. This data uses specific notations used in SPSS. We believe that utilizing the ANOVA technique would work out as it would provide us with significant findings to write about. We headed on over to the Statistics Canada website to get the information we need to perform-one-way ANOVA.
We came across a Census Profile of 2016 to analyze a value from a National Census. This profile presents information from the 2016 Census of Population for various levels of geography, including province and territories, census metropolitan areas, communities, and census tracts (Statistics Canada, 2020). By using the search or browse options below, users can search for an area of interest by simply typing the name of a place, postal code, or geographical code.
The basic steps to conduct an ANOVA is to perform a hypothesis testing for three or more population means. With this being said, we can have 4-5 groups from different provinces and 10 values within each group to form a data set. We decided to test the hypothesis from a 2015 data set about the average total of income in Canada. The provinces we chose are Ontario, Quebec, British Columbia, Alberta, and Manitoba. The SPSS program will help us to determine if there is evidence of a difference in the mean total income across the five provinces.
The SPSS program helps us to gain insight into large-scale data such as the census to perform sophisticated statistical analysis. This way we have a better understanding of the data we chose to analyze and to drive accurate conclusions.
It is critical that we set up the data in the SPSS program correctly. If it’s not set properly, the data will be analyzed improperly. For a simple one-way ANOVA, we need to have one variable that is dependent and the other to have a group measure.
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