Experimental Designs (Other (Not Listed) Sample)

Experimental Designs
Name
Institution
Experimental Designs
Q1: Even number exercises in Jackson (2012) pp. 308-310
Repeated ANOVA, also known as ANOVA for correlated samples is used to measure only related groups as opposed to independent groups. This is an extension of the dependent T-tests in experimental research designs. On the other hand, Randomized ANOVA is a statistical tool that is used to separate variability found within a set of data in to two main components, systematic and random factors. The random factors do not have significant statistical impact on the set of data as opposed to the systematic factors which have a major influence on the data set.
Q2: What is an F-ratio?
F-ratio is a statistical concept in experimental research design, which helps to assess whether variance in two different samples is equal (Schmidt, 2010). It is also used to determine the variance within groups of sample data as well as variance between two groups of data. The F-ration is mostly applied in ANOVA calculations and is calculated using the following formula;
F-ratio = MSM / MSR
Where MS=ss/df and
SS= sum of squares
Df= degrees of freedom.
The subscripted M is used to indicate ‘model’ and shows the systematic variance expected. This is often measures as between-groups variance. On the other hand, R stands for ‘residual’, and represents the unsystematic and random variance. This is often measured as within-groups variance. Occasionally the superscript w is also used very often.
Similarly, F can also be calculated using the Pearson correlation coefficient, that is, the r, as shown below;
F = r2 / (1 - r2)(n - 2)
In some cases, the f-ratio may not bear any significance statistically. Consequently, in such situations, it is assumed that there is homogeneity of variance. As a result, it will be prudent to employ the standard statistical T-test to show the differences of means (Schmidt, 2010). In cases where the F-ratio is significant statistically, alternative computations for the T-test such as the Cochran and Cox methodology may be used. Generally, the T-tests are calculated by dividing the ratios for systematic and intended variance with the unexpected and unsystematic variance. The formula for the T-tests can be simplified as shown below;
T-tests= systematic variance/unsystematic variance.
Furthermore the T-tests are often measured as the total value or sum of SS (squares), hence;
Test statistic = SSM / SSR
However, in situations of multiple variables, the F-ratio if often derived from the mean of the available multiple variables (Schmidt, 2010).
Q3: What is error variance and how is it calculated?
Error variance is an important concept in experimental design methodology. It is used to describe the differences that exist between different variables in the study. Specifically, error variance refers to that variability, which cannot be accounted for or explained using existing systematic differences within the groups being investigated. Essentially, error variance indicates the extent to which variability could be expected in an experimental study if there were no identifiable differences between two groups being studied. The degrees of freedom in error variance are the sum of each sample size minus one.
Q4: Why would anyone want more than 2 levels of independent variable?
The independent or manipulated variable is a core part o9f experimental research designs in statistical studies. This is the variable that is altered or manipulated by the researcher to bring forth another variable, the dependent variable, in the course of a research study (Jackson, 2012). The independent variable is also known as the grouping variable, since each of its categories is made up of specific levels or values of the independent variable. Given this scenario, all members of each category or group participate in the same intervention, though, for different groups.
There are at least two levels of independent t variables, although some studies may have up to five levels. The levels of independent variable refer to the various amounts or types of the independent variable used in an experiment (Trochim & Donnelly, 2008). For instance, in an experiment seeking to find out the impact of different dosages of a specific drug on behavior of patients, the independent variable is the drugs. However, the levels of the independent variable are the varying dosages that each subject in the research may be subjected to as the researcher manipulates the independent variable.
Furthermore, is one experiment is used to compare and contrast between experimental and control treatment, then the independent variable will have two levels, control and experimental. For instance, if one experiment compares different diets and their impact on human health, the study is more likely to have diet as the independent variable, but with various levels, namely the different types of diets. Consequently, the levels of independent variables in as study depend on the number of experimental conditions that exist for the particular research experiment (Jackson, 2012). Therefore, some studies are bound to have two or more levels of independent variables.
There are several reasons as to why researchers use various levels of one independent variable. First, it is to address the different conditions that may affect the quality of the study. For instance, in the experiment of food diet stated above, it can be inconclusive if the study only bases its experiment and findings on one type or level of diet. This is because it would not provide answer all the issues relating to diet and health. Therefore, different levels of independent variables also clarify the scope of the study as well as making the study clearer in terms of the issues investigated (Jackson, 2012).
Q5: What would it mean if there was variance higher within groups than between groups?
There are two main sources of variance namely, between groups and within groups. Variance between groups indicates the differences that exist between two groups while the variance within groups relates to differences among members of a particular group or category (Trochim & Donnelly, 2008). Variability within groups is as a result of several factors including inherent dispersion, poor research design, and more frequently due to errors in measurement.
There are different implications for higher variance in between groups and within groups. In the first instance, if variance within groups is higher than that between groups, it would imply that there would be no clear cut comparison between the two groups. For instance, in a research study comparing the level of intelligence between humans and apes, where humans have an IQ of 200 and the apes have an IQ of 100; within group variability would imply that the mean difference between the two groups will not show...