Team B-Statistics Project Amal Andersen Jessica Bogunovich Jocelyn Cuff Zachary Ramoz PSYCH 625 Mary Sue Farmer April 13, 2015 1 Introduction Key Terms Degrees of Freedom Descriptive Statistics Interval ratio variables Pearson Product-Movement Correlation Positive correlation Significance Level 1. Degrees of Freedom is a value, which is different for different statistical tests, that approximates the sample size of number of individual cells in an experimental design. Descriptive statistics are values that organize and describe the characteristics of a collection of data, sometimes called a data set. Interval variables are those that measure a variable by giving a numerical value in steps Pearson Product-Movement correlations show the strength of a relationship using summations of values from each axis, the summation of the squares of the data points for each axis, and takes the sample number all into a neat equation. Positive correlations show a relationship between variables and a trend moving in the same direction be it small to great or great to small. Significance level is the risk set by the researcher for rejecting a null hypothesis when it is true. 3 Independent T-Test Another analysis we decided to run on the data set was an independent t-test comparing the means of reading, math, and total test scores between males and females. The independent t-test was used because this analysis deals with two groups and the participants were not being tested more than once (per topic over time). 4 Independent T-Test Results Degrees of freedom = 48 for all three tests (math, reading and total score) Math t value = -.487 Significance = .628 Reading t value = -1.250 Significance = .217 Total t value = -.956 Significance = .344 The SPSS output for the independent t-test on the previous slide demonstrates the t value of reading scores, math scores and total test scores, as well as the degrees of freedom (48 for all three computations). If one were to analyze the math scores only, they would find the t value to be -.487 and the significance to be .628. Analyzing the reading scores only we find the t value to be 1.250 and the significance to be .217. Analyzing the total score only one would find the obtained value, or t value, to be -.956 and find the significance to be .344 (p=.344). 5 Pearson Product-Movement Correlation Correlations TESTPREP MATHSCORE TESTPREP Pearson Correlation 1 .653** Sig. (1-tailed) .000 N 50 50 MATHSCORE Pearson Correlation .653** 1 Sig. (1-tailed) .000 N 50 50 **. Correlation is significant at the 0.01 level (1-tailed). The Pearson Product-Movement was run through SPSS to show a bivariate correlation between test preparation and how well the participants scored on the math portion of the test. The chart displays the numbers in a more readable, decipherable fashion with test prep as the x-axis and math score as the y-axis. The two varaibles, test prep and math score, are interval/ratio varaibles, thus the easy conversion to a correlation. 6 Pearson Product-Movement Correlation Results Positive Correlation = .653 As test prep number increases, so does the math score An up slope The visual representation shows the relationship Significance Shoes a relationship Not very strong Meaningful? The results of the correlation show a positive relationship. As the number of hours of test prep, the x-axis, increases so do does the score on the math test, y-axis. The direction of this positive relationship goes up. The scatterplot helps to being a visual representation to the chart for more discernable visuals. Although there is a decent correlation number, at .653, it seems the relationship is not very strong. This is due to the median time of 2 having many points. Also, the outliers also bring down the significance level as well. These results do show there is a relationship between the two varibles and one could argue that more test prep may yield a higher test score; However, it should be noted the realtionship is not high on significance thus making meaningfulness come to question. 7 Descriptive Statistics Descriptive statistics are used to describe the common data from a study (Salkind, 2014). These deliver summaries about the sample used in the study, as well as the types of measures that were used. The descriptive statistics combined with analytical visuals provide a quantitative analysis of the data. Descriptive statistics describe what the data is and illustrates. These are useful when trying to present and describe quantitative data descriptions in manageable pieces (Salkind, 2014). Researchers are able to simplify huge amounts of data in a meaningful way, as each descriptive statistics reduces the large amounts of data into a smaller summary. 8 Descriptive Statistics Summary 50 total participants 26 males 24 females Ages ranged from 25-40 Average age=32 Reading Test Scores ranged from 45-9 Average reading score=75.58 Math Test Scores ranged from 45 to 92 Average math score=75 Total Test Scores ranged from 95 to 186 Average total test score=150.78 Analytical data from a test group of 50 people was collected and studied. There were 26 males and 24 females in the test group. The participants were surveyed on age, sex, years of college experience, caffeine consumption, test prep, as well as math, reading and comprehensive test scores. This analysis focuses on descriptive statistics and uses the age, math score, reading score and total test score variables. The descriptive statistics demonstrate that the age of the participants ranges from 25 to 40 and the participants have an average age of 32. Math scores range from 45 to 92, and the average math score was 75. Reading scores range from 45 to 96 and the average reading score was 75.78. Total scores ranged from 95 to 186 and the average total score was 150.78. 9 Conclusion References Salkind, N. (2014). Statistics for people who think they hate statistics (5th ed.). Thousand Oaks, CA: Sage Publishing.

Please answer the following in 60 or more words per topic.

When would a researcher use a t test of independent means? Provide an example.

When would a researcher use a t test of dependent means? Provide an example.

What is an analysis of variance (ANOVA)? Describe the theory underlying it.

When would a researcher use ANOVA for data analysis? Provide an example