Parametric and Non-Parametric Statistical Tests - Essay Example

?Part A. Parametric and Non-parametric statistical tests Parametric tests are based on highly restrictive assumptions about the type of data which are obtained in the experiments. First, it is assumed that each sample of scores has been drawn from a normal population. Second, these populations are assumed to have the same variance. Lastly, the variable is assumed to have been measured on an interval scale. On the other hand, non-parametric tests make few assumptions about the nature of the experimental data. Most tests assume only an ordinal level of measurement. Also, as far as population distributions are concerned, non-parametric tests make no assumptions about the shape of these distributions, nor do they assume that the two populations have equal amounts of variability (Miller, 2006). Correlation and Regression A correlation is a numerical value that describes and measures the characteristics of the relationship between two variables. Typically, correlation measures the direction of the relationship, whether positive (direct) or negative (inverse); the type of the relationship, whether, linear, exponential, quadratic, etc.; and, the extent of relationship, that is, correlation close to 1 or -1 indicates a strong relationship while correlation close to zero indicates the minimality of the relationship. If the relationship is linear, then regression gives the linear equation that best predicts the relationship between the independent and dependent variables (Gravetter & Wallnau, 2008). Measures of central tendency The mean, median and mode of a data set measure central tendency. The mean is typically the “average” value of the data set, taken by summing up all the data points and dividing the sum by the total sample size. The mean is used when the distribution is somehow evenly distributed, without the presence of extreme values. The mode is the most frequent value in the data set, and is most commonly used when the data is made up of categorical or nominal values. The median is the “middle value” or the score that divides the distribution in half so that 50% of the values lie below or at the median (Bluman, 2004). When a distribution is symmetrical, the right-hand side of the graph will be a mirror image of the left-hand side. In this case, there is only one mode and it is equal to the mean and the median. Skewed distributions, on the other hand, are lopsided towards one side. Positively skewed distributions peak at the left where the mode is, the median to the right of the mode and the mean to the right of the median. In negatively skewed distributions peaked to the right where the mode is, the median to the left of the mode, and the mean to the left of the median (Gravetter & Wallnau, 2008). The meaning of “Statistical Significance” Statistical significance is basically the level of risk that one is willing to take in rejecting a true null hypothesis. For example, when testing the equality of the means of two data sets at 1% or .01 level of significance, it means that on any test of the null hypothesis, there is a 1% chance of rejecting the null hypothesis and thus concluding that there is a difference in the means when there is no difference at all (Miller, 2006). Part B. The research topic The data set extracted from Brainmass.com was gathered to conduct research on the housing of a neighborhood that encompasses 5 townships. Using the data gathered from 100 housing properties, the researcher wants to find out the relationship of the characteristics of the real estate property to its market value. Furthermore, the researcher wants to find out which among the variables have the greatest effect on the market price in order to come up with a mathematical model that will forecast the market value of a property given the values of the independent variables. The research variables The following variables were used in this data set: Price The variable “Price” refers to the current price or market value of the housing property, measured in thousands of US dollars. This variable is treated as being a continuous, ratio-type variable (Black, 2010). Bedrooms The variable “Bedrooms” refers to the number of bedrooms that the housing property has. It is a discrete variable that is ordinal in nature (Black, 2010). Size The variable “Size” refers to the total lot size of the housing property, measured in square feet (sq. ft.). It is a continuous variable that is of interval type (Black, 2010). Distance The variable “Distance” refers to the distance of the homes from the center of the town, measured in kilometers (km). It is a ratio-level variable which is continuous in nature (Black, 2010). Pool The variable “Pool” refers to the presence of a pool in a housing property. “Yes” means the housing property has a pool while “No” means the housing property does not have a pool. It is a discrete and nominal type of variable (Black, 2010). Garage The variable “Garage” refers to the presence of a garage in a housing property. “Yes” means the housing property has a garage while “No” means the housing property does not have a garage. It is a discrete and nominal type of variable (Black, 2010). Township The variable “Township” refers to the town that the housing property belongs to. There are a total of 5 townships in the neighborhood and so the property is correspondingly labeled as 1, 2, 3, and so on, depending on the town that they are in. Township is a discrete and nominal type of variable (Black, 2010). The population and data sample Data was gathered from an unidentified US neighborhood which encompasses 5 townships. A total of 100 housing properties were chosen from the listed homes in the neighborhood’s real estate statistics taken from the Office of Housing Registration for the year 2005. Stratified sampling was conducted by randomly choosing 20 homes from each of the five townships of the neighborhood. Because data was taken from the local registry and random sampling was employed, the data possesses integrity in terms of its accuracy (Anderson, Sweeney, & Williams, 2009). Limitations Data gathered was limited to the neighborhood that is the subject of the research. The results cannot accurately represent the housing situation in other neighborhoods. Furthermore, the data available was for the year 2005 and may not be reflective of more current pricing trends. Summary Statistics Table 1. Summary of Descriptive Statistics of Price, Size and Distance. Descriptive Statistics Minimum Maximum Mean Std. Deviation Price 125.0 345.3 222.60 47.6 Size 1600 2900 2217.00 244.1 Distance 6 28 14.74 4.9 Table 2. Percentage Distribution of Homes’ Number of Bedrooms. Number of Bedrooms Frequency Percent 2 24 24.0 3 25 25.0 4 24 24.0 5 10 10.0 6 13 13.0 7 2 2.0 8 2 2.0 Total 100 100.0 Figure 1. Frequency Distribution of Homes’ Number of Bedrooms. Table 3. Percentage Distribution of Homes by Pool Ownership. Response Frequency Percent Yes 37 37.0 No 63 63.0 Total 100 100.0 Figure 2. Percentage Distribution of Homes by Pool Ownership. Table 4. Percentage Distribution of Homes by Garage Ownership. Response Frequency Percent Yes 67 67.0 No 33 33.0 Total 100 100.0 Figure 3. Percentage Distribution of Homes by Garage Ownership. Table 5. Percentage Distribution of Homes by Township. Township Frequency Percent 1 15 15.0 2 19 19.0 3 25 25.0 4 27 27.0 5 14 14.0 Total 100 100.0 Figure 4. Frequency Distribution of Homes by Township. Part C: Hypothesis testing 1. The hypothesis: There is a relationship between the distance of the homes from the center of the town and the homes’ market value. Null hypothesis: There is no relationship between the distance of the homes from the center of the town and the homes’ market value. The dependent variable in this hypothesis is “Price” while the independent variable is “Distance.” Figure 5. Scatterplot of Distance of Homes from the Town Center against their Price. Statistical test: Correlation A correlation is a numerical value that describes and measures the characteristics of the relationship between two variables. Typically, correlation measures the direction of the relationship, whether positive (direct) or negative (inverse); the type of the relationship, whether, linear, exponential, quadratic, etc.; and, the extent of relationship, that is, correlation close to 1 or -1 indicates a strong relationship while correlation close to zero indicates the minimality of the relationship. Correlation analysis is the appropriate test to use for the given data set because the strength of the relationship of price and distance are to be tested. Technically, there are no independent and dependent variables involved in correlation analysis because it is supposed to measure only relationship and not causation (Gravetter & Wallnau, 2008). But for the sake of this discussion the variables will be defined as described above. Table 6. Correlation Analysis of Price and Distance. Price Distance Price Pearson Correlation 1 -.393 Sig. (2-tailed)   .000 N 100 100 Distance Pearson Correlation -.393 1 Sig. (2-tailed) .000   N 100 100 The scatterplot in Fig. 5 shows a strong indication of a negative linear relationship and this will be formally examined using correlation analysis. Results in Table 6 indicate that price and distance indeed have a negative relationship, with Pearson Correlation r = -.393 significant at the .05 level. This is the same as saying that 39.3% of the values in home price can be accounted for by the distance of the housing property from the town center. The negative sign indicates that the relationship is negative which means that as the housing property’s distance from the town center increases, its market value decreases. This result is significant with p Read More