July 27, 2015
Reflection Summary Introduction In this summary, Team A discusses the steps in testing a research hypothesis, how to compare the means between two or more groups, how to calculate the correlation between two variables, as well as discussing the topics struggled with and how these topics relate in our field of work. The concepts covered in this discussion are the basic core of statistics and thus, are ones it is crucial to understand and apply in any statistical research.
Steps in Testing a Research Hypothesis
Research is an important tool for collecting data. Without data, there is no form of measurement. A research hypothesis is a tentative answer to a research question. Researchers form hypotheses because the hypothesis will influence how the research study is conducted. A research hypothesis must refer to concepts that can be studied scientifically. Testing a research hypothesis involves many things. The purpose of testing a research hypothesis is to prove or disprove the research question. The first step in testing a research hypothesis is to state the problem in the form of a question. The second step is to state the research question as it relates to the null hypothesis and alternative hypothesis. Then the parameters must be set to test the null hypothesis. The fourth step is to calculate the probability of the test statistics or rejection region. Finally, the findings from the tests must be stated.
Comparing the Means of Two or More Groups Confidence intervals and tests of hypothesis are used to compare the means of two or more groups. There are several methods which focus on confidence intervals. Three popular techniques include Tukey, Bonferroni and Scheffe methods which are available in the ANOVA program. The Tukey method is used when sample sizes are equal, where it is not the case for the Bonferroni procedure. The Scheffe technique compares all possible linear combinations of treatment means (called contrasts) which will produce wider confidence intervals as compared to Tukey or Bonferroni confidence intervals (McClave, Benson & Sincich, 2011). “In general, if there are k treatment means, there are
pairs of means that can be compared (McClave, Benson & Sincich, 2011).”
Another method used to compare means of two of more groups will focus on hypothesis testing. Two of the most popular techniques are the T-test and the Z-test. The T-test is used for limited sample sizes with unknown population variances. The Z-test is used for large samples greater than 30 with known variances such as standard deviations. Both the T and Z tests are used to test the hypothesis by comparison.
The formula for calculating T scores is given below:
Where, x1¯ = Mean of first set of values x2¯ = Mean of second set of values
S1 = Standard deviation of first set of values
S2 = Standard deviation of second set of values n1 = Total number of values in first set n2 = Total number of values in second set.
The formula for standard deviation is given by:
Where, x = Values given x¯ = Mean n = Total number of values.
("T-Test Formula", 2015)
The formula for calculating Z score is given below:
Where, x = Standardized random variable x¯ = Mean of the data σ = Population standard deviation.
The formula for population standard deviation is given below:
Where, σ = Population standard deviation xi = Numbers given in the data x¯ = Mean of the data n = Total number of items.
("Z-Test Formula", 2015)
Calculating the Correlation between Two Variables “Correlation is a closely related measure” (Anderson, para 3). The relationship can be positive or negative and between -1 and 1 (Anderson, 2013). If the correlation result is zero, the variables are considered unrelated or independent (Anderson, 2013). The correlation is used to measure the linear relationship between two numerical variables x and y (McClave, Bensen, and Sincich, 2011). Correlation is