Statistics Project - Research Paper Example

Running Head: SPSS - STATISTICS PROJECT Statistics Project [The [The of the SPSS - Statistics Project Research Study 1 Once the decision is made that the best way to answer the research problem is by means of quantitative research, there are a number of important aspects, specific to quantitative research, that need to be considered. These aspects include some basic terms, method of data collection, data capturing and editing, statistical analysis, interpretation and report writing. These aspects will now be discussed. Stating the hypothesis We have a two-tailed test and an alpha level of .05. Notice the research hypothesis is framed in the direction that we should expect, an improvement in scoring. Nevertheless we will assess the hypothesis using a two-tailed test. So aaccording to given conditions we state that null hypothesis and alternative hypothesis will be Null Hypothesis: There is no significant linear association between level of popularity and math test score, or Ho: = 0 Alternative Hypothesis: There is some significant linear association between level of popularity and math test score, or Ha: 0 = 0.05 We try to observe the association between the levels of popularity verses math test score. Is there any evidence to show the association between these two variables Data Analysis There are various statistical packages designed to carry out quantitative data analysis, the most widely used package is SPSS. SPSS enables the researcher to input raw data modify or reorganize the data once inputted and then perform a wide selection of analytical techniques (Blaxter, Hughes & Tight 2001). The scales utilized within the test instruments will be designed to denote the use of detailed statistical algorithms on collected data. Preliminary data analysis will include descriptive statistics, which will encompass univariate analytic techniques such as means, modes and standard deviations, and exploratory descriptive statistics, which will ascertain if the data collected, is normally distributed. Statistical Method Under the assumption that the random variables level of popularity and math test scores are each normally distributed, a test of the null hypothesis = 0 can be based on the equation t = , which is a value of t distribution with degree of freedom = n-2. According to SPSS result: Correlations Popularity Level Math Test Score Popularity Level 1 -.368 Math Test Score -.368 1 * Correlation is significant at the 0.05 level (2-tailed). So the Pearson correlation (r) of popularity and math scores is equal to -0.368. So according to this small value of correlation coefficient we conclude that there is a week negative association between these variables. This may imply as popularity level increases, math test scores decreases and vice versa. We use correlation method to determine whether some variable that's not under our control is associated - correlated - with another variable of our interest. Correlational studies aim at identifying relationships between variables. Test Statistic By using formula t = , = = = -1.1194 Scatter Plot Critical Region: t 2.048 Do not reject Ho, because the calculated value is not fall in the critical region. Conclusion: Do not reject null hypothesis so we conclude that there is no significant linear association/relationship between level of popularity and math test score. So in the relationship between children's level of popularity with their peers and their performance in academic tests they respond that there is no significant relationship between these popularity level and their maths scores. Descriptive Statistics The Descriptive procedure displays univariate summary statistics for several variables in a single table and calculates standardized values (z scores). Variables can be ordered by the size of their means (in ascending or descending order), alphabetically, or by the order in which we select the variables. Simple it is a useful procedure for obtaining summary comparisons of approximately normally distributed scale variables and for easily identifying unusual cases across those variables by computing z scores (Kinner, 2006, p.152). We can conclude that the mean for "popularity level" of 9-year old primary school children is higher then their "math test scores". The popularity level is between the intervals of 1-30; on the other hand the math scores are in the range of 10-50. The standard error for this parameter shows to be not too small. Means plots show the graphical representation of both variables. Means Plots Psychologist say statistically significant means a statistical test has been applied to the data and the observed difference is unlikely to have arisen by chance or because of few extreme cases. Research Study 2 According to descriptive results we can say that throughout the evolutionary theory IQ level of husband's gives higher average results with mean 110.24 and standard deviation 11.256. On the other hand IQ level of wives are slightly low that is 109.12 averages with 10.963 of standard deviation as compare to husband's case. So overall the husband's IQ level is higher then their wives IQ level. Pearson 'R' Correlation The Pearson R correlation notifies us the magnitude and direction of the association between two variables that are on an interval or ratio scale. So in this case we are investigating the relationship between the husband and their wives IQ level. Pearson correlation coefficient is a number between +1 and -1. It tells us regarding the magnitude and direction of the relationship/ association between IQ levels of couples. According to given SPSS output we can say that as r = 0.662 closer to +1, so there is a stronger positive the correlation between the IQ levels of husband and their wives. As in terms of direction of the correlation we observe that it's a positive correlation, so these two variables having a positive relationship (as one increases, the other also increases). In conclusion as husband's IQ level having increases, their wife's also having increasing IQ levels. Hypotheses: Null: There is no association between the husband and their wives IQ level. Alternate: There is an association between the husband and their wives IQ level Spearman's Rank Correlation It is equivalent of Pearson's correlation coefficient, but used for non-parametric data. The observations are ranked and the product moment correlation is calculated for the ranks. The statistic is called rho (). According to the next SPSS output we can observe that spearman's rho = 0.596 closer to +1, so it also shows that there is a stronger positive the correlation between the IQ levels of husband and their wives. As in terms of direction of the correlation we observe that it's a positive correlation, so these two variables having a positive relationship (as one increases, the other also increases). Scatter plot shows the trend of linearity, this plot indicates that data is linear (as the data seem to be moving in a straight line, that's a good indication that our data is linear). In conclusion as husband's IQ level increases, their wife's also increases IQ levels. Research Study 3 Memory Scores According to above SPSS output of descriptive results researcher administered the Eysenck Personality Inventory (EPI) can say that average extravert memory scores are higher then the introvert memory scores. For extraverts group the average memory score is 26.30 with 6.23 std. deviation and for introverts group its 20.60and 6.204 respectively. So overall the extravert group's memory scores are higher then introvert group's memory scores. Hypothesis The null hypothesis is that the median of the distribution is zero. Alternative hypothesis is that the median oft he distribution is not equal to zero. Non-Parametric Tests For this case we use runs test, because it is used to test for randomness in a sample. This will be a necessary but not sufficient test for random sampling. Overall by median test we conclude that the extravert group's memory scores are higher then introvert group's memory scores. Nonparametric statistics uses when we have tests with much more general null hypotheses, and so fewer assumptions. It often a good choice when normality of the data cannot be assumed as well as if we reject the null hypothesis with a nonparametric test, it is a robust conclusion. However, with small amounts of data, we can often not get significant conclusions. In case of SPSS, we only get p-values from non-parametric tests, more interesting to know the mean difference and confidence intervals. So this is recommended that in these types of tests we must try to apply the non- parametric test rather then parametric. Research Study 4 Number of Flyers on Ground Descriptive tables shows the overall basic statistics of the given data, see below: Chi-Square Test For this study we try to use Chi Square test, because if the observed frequencies are different from what we would expect to find (we expect to see equal numbers in each group within all three groups of variables). First we calculate the observed and expected frequency tables for all three stages of presence of flyers on ground, see below: Frequencies Hypotheses Null: There are approximately equal numbers of cases in each group Alternate: There are not equal numbers of cases in each group In contrast to the hypothesis result we say that there is a significant difference (our significance level is less than .05 for the case of zero flyer on ground). Therefore, we can say that zero number of flyers present on the ground is associated with the participant does not drop litter. But for the other two cases of 5 or 10 number of flyers we reject null hypothesis and conclude that there are not equal numbers of cases in each group. Research Study 5 First we start this study by using descriptive table, with frequency distribution, see tables below: Life Satisfaction Rating Frequency Distribution Life Satisfaction Rating Poshville Chavstown Extremely dissatisfied 2 5 Very dissatisfied 3 3 Quit dissatisfied 3 1 Neither satisfied nor dissatisfied 2 4 Quite satisfied 3 4 Very satisfied 4 2 Extremely satisfied 3 1 20 20 Bar diagram shows the overall trend of rating by two towns, in which we can observe that the majority responses are in favor of satisfaction by Chavstown as compare to Poshville. T-test for independent samples Purpose /Assumptions: The t-test is the most commonly used method to evaluate the differences in means between two groups. For example, the t-test can be used to test for a difference in life satisfaction rating of Chavstown and Poshville. Theoretically, the t-test can be used even if the sample sizes are very small (e.g., as small as 10 and as long as 30; some researchers claim that even smaller n's are possible), as long as the variables are normally distributed within each group and the variation of scores in the two groups is not reliably different (Kinner, 2006, p.135). The p-level reported with a t-test represents the probability of error involved in accepting our research hypothesis about the existence of a difference. Technically speaking, this is the probability of error associated with rejecting the hypothesis of no difference between the two categories of observations (corresponding to the groups) in the population when, in fact, the hypothesis is true. Some researchers suggest that if the difference is in the predicted direction, you can consider only one half (one "tail") of the probability distribution and thus divide the standard p-level reported with a t-test (a "two-tailed" probability) by two. Others, however, suggest that you should always report the standard, two-tailed t-test probability (Field, 2000, p.71). Hypothesis Ho: There is no significant difference in life satisfaction of Poshville and Chavstown. Ha: Respondents are more satisfied with their life in Poshville as compare to Chavstown Life Satisfaction Rating Poshville % Chavstown % Extremely dissatisfied 2 10 5 25 Very dissatisfied 3 15 3 15 Quit dissatisfied 3 15 1 5 Neither satisfied nor dissatisfied 2 10 4 20 Quite satisfied 3 15 4 20 Very satisfied 4 20 2 10 Extremely satisfied. 3 15 1 5 Total 20 100 20 100 According to this table we can observe that satisfactory percentages of Poshville respondents are about 50% and in case of Chavstown it is 35%, so it is less likely in case of Chavstown. So we examine that the statement is rejected and conclude that yes respondents are more satisfied with their life in Poshville as compare to Chavstown. Paired Sample T- Test We would like to use Paired Samples T Test to compare the means of two variables. It computes the difference between the Poshville and Chavstown life satisfaction rating and tests to see if the average difference is significantly different from zero. T-Test Correlation value r= 0.090 shows that there is a week positive association between both places. Further the significance value 0.199 is not less then 0.05 so we do not reject our null hypothesis and conclude that there is no significant difference in life satisfaction rating of Poshville and Chavstown. This study describes the main aspects of relativist quantitative research in psychology. Methods are quantitative and attempt to understand some reality by measuring hypothesized relationships between constructs via isolation of these entities into independent and dependent variables. Quantitative research believes findings are externally valid if they can be generalized and implemented to the real world. In addition, we provide recommendations on analyzing complex samples with structural equation models. In most statistical packages I've used (none as good as SPSS of course) it has been very easy to do post hoc tests such as Tukey HSD and Scheffi. References Blaxter, L, Hughes, C & Tight, M (2001), How to Research, 2nd Edition. Open University Press, Buckingham; p 29-47. Cohen, Jacob (1969). Statistical power analysis for the behavioural sciences. NY: Academic Press. Field, Andy (2000). Discovering Statistics, Sage Publications. Kinner, P. R. & Gray, C. D. (2006) SPSS Made Simple. Psychology Press, Hove. Moore, D. S. (1995). The basic practice of statistics. NY: Freeman and Co. Read More