Power Analysis as a Useful Tool - Coursework Example

Power Analysis Power analysis is a tool that has the capability to locate statistically significant differences when the null hypothesis is false. The power of a study is established by three aspects: The samples size, the alpha level and the effect of the size (Wisconsin, n.d.). Incorporating power analysis and size sample estimation is a significant factor of experimental design. Without the said calculations, the sample size of a study or research could be too high or too low (StatSoft, 1984). Descriptive Correlation Designs Correlation is a measure of degree of relationship between paired data. All statistical research aim to establish relationship between paired variables to enable the researcher to predict one variable in terms of the other variable. It should be understood that correlation does not determine the cause and effect of the relationship, but rather it focuses on the strength of the relationship between the paired variables (Zulueta et al, 2003).. The term correlation refers to the association which occurs between two or more statistical series of values. The coefficient of correlation which represents correlation value shows the extent to which two variables are related and to what extent variations in one group of data do to the variation in the other. Coefficient of correlation is a single number that tells us to what extent two variables are related. It could vary from a value of 1.00 which means perfect positive correlation through (0), which means no correlation at all; and -1.00 which means perfect correlation (AllPsychOnlineResearch Methods, 2004). Perfect correlation refers to direct relationship between any two sets of data in that any increase in the values of the first set of data will correspondingly generate in a corresponding increase in the second set of data, respectively. When correlation is negative, an inverse behavior of data is observed in that; a decrease in values of a first set of data will result in an increase in the second set by being compared or vice versa. When there is minimal or even zero change at one time or another between two sets of data being correlated, there is little or no correlation at all. The coefficient of correlation does not give directly anything like a percentage of relationship. It cannot be concluded that a correlation value of 0.50 indicates twice the relationship that is indicated by a correlation value of 0.25. A coefficient of relationship is an index number, not a measurement of interval. Moreover, we cannot compute a coefficient of correlation from just two measurements on one person alone (Zulueta et al, 2003). Quasi Experimental Research Designs The quasi experimental research designs were intended to identify variables and are commonly used when randomization is probable. Moreover, using quasi-experimental designs lessens the demands on external validity. Since quasi-experiments are natural experiments, findings in one set of study may be applied to settings, allowing for some conclusions to be made about an identified group of respondents. The treatment of the x-variable could lead to unusual conditions. The need for a random assignment in the quasi-experimental design method could permit studies and experiments to be more realistic, although it could post a risk for the researcher. Insufficiency in randomization makes it harder to rule new threats to internal validity. And since randomization is nonexistent, related data could be estimated. However, the cause and effect of the deductions made will be quite hard to determine. And since the researcher does not have total control over the variables the cause of the experiments cannot be confirmed (PPA 696 Research Methods, n.d.). True Experimental Designs In a true experimental design, the proper test of a hypotheses is the comparison of the test made before hand between the treatment group and the control group (Abrahams, n.d.). This design makes use of a control group, using random assignment to even out the comparison groups. This eliminates the threats to internal validity excluding mortality (Abrahams, n.d.). Thus, confidence is established that whatever differences there are between the treatment group and control group are due to the treatment involved in the study or research. In connection to regression, the classic experimental design could direct regression through random selection of subjects with excessive charateristics. This guarentees that whenever regression does take place, both groups of respondents will evenly experience its effect. Regression with regards to the mean should not account for any differences between the groups on the posttest. “Randomization also controls for selection threat to internal validity by making sure that the comparison groups are equivalent (Abrahams, n.d.).” T-Test The t-test assesses the means of two groups that are statistically different from each other. And this analysis is appropriate whenever there is a need to compare the means of two groups (Trochim, 2006). The t-test shows the differences between the spread and variance of the scores of the two groups being currenlty studied. T-test is likewsie used to compare a smaple mean vs. A population mean. If the sample size is less thatn 30 and the population standard deviation is unknown the assumpption of normality cannot be taken for granted. The student t or t-distribution is the appropriate test statistics for this type of situation. The t-distribution was developed and published by William S. Gosset in 1908. He was concerend with the discrapancy in the standard deviation and population standard deviation when standard deviation was used to estimate ppopulation standard deviation for sample sizes less than 30. The following characteristics of the t-distribution are based on the assumption that the population of interest is normal or nearly normal (Trochim, 2006). Properties of the t-distribution: 1. It is a continuous distribution. 2. It is bell shaped and symmetrical. 3. There is a family of t-distributions depending on the sample size. 4. The t-distribution is more spread out and flatter that the standard deviation. However, as the sample size increases, the curve reperesenting the t-distribution approaches the standard normal distribution. 5. Since the population standard deviation is unknown, the sample standard deviation is used instead. This gives rise to n-1 degrees of freedom which means that there is one less degree of freedom for the variables that are free to vary. T-test for Comparing Two Sample Means T-test could also be used to compare two sample means by determining if the samples were obtained from normal populations with the same means. However, certain assumtptions are required and they are as follows (Zulueta, 2003): 1. The population must be at least approximately normally distributed. 2. The population must be indepedent. 3. The population variances must be equal. Test for quality of variances are taken up in advance. Standard Deviation Standard deviation is another measure of variability. The most commonly used indicator of the degree of dispersion and the most dependable measure to estimate the variability in a total population from which the sample came. It is similar to an average deviation if it is affected by all individual observations in the set. It may be referred to as the root-mean – square of the deviations from the arithmetic means. The standard deviation is also the square root of variance (Pinkney, n.d.). When using the standard deviation from an ungrouped data, standard deviation uses two methods in computing ungrouped data. These methods are: 1) working formula and 2) machine formula. In the case of a standard deviation from grouped data, if the grouped data is a frequency distribution, two methods may be used in computing the standard deviation. The first method is the midpoint or long method and the second one is the class deviation or short method. The class derivation method of computing the standard deviation is similar to computing the variance. The only difference is that in the standard deviation there is an extraction of the square root. In the class derivation method, a temporary arbitrary origin is chosen in any of the class limits. Below are the steps to be followed (Zulueta, 2003): 1. Choose the temporary arbitrary origin by dividing always the toal frequency by 2. Whatever the quotient must be the position of the zero value. 2. Assign coded values to the class limits, starting from zero at the origin and with positive values above the zero deviation and negative value below it if class limits are arranged from highest to lowest. 3. Multiply the deviation (d) by the corresponding class frequencies (f) to get (fd). 4. Sum the fd products algebraically, (Σ fd). 5. Take the product of fd and d to get fd2. 6. Take the sum of the products, fd2, (Σ fd2). 7. Then compute, using the standard deviation formula. The most accepted interpretation of standard deviation is within the range from one standard deviation below the mean (+1SD) to one standard deviation above the mean (+1SD). Chi Square The chi-square distribution was discovered by Karl Pearson. The distritubition was introduced to determine whether or not discrepancies between theoretical counts were significant (Zulueta, 2003). The test was used to find out how ell an observed frequency distribution conforms to or fits to some theoretical frequency distribution. This is referred to as the “goodness of fit test.” Chi-square could likewise be used to test the normality of any distribution. Testing a hypothesis made about several population proportions are sometimes considered. Testing goodness of fit can be used to see how well an observed frequency fits some theoretical frequency distribution. Chi-square is used in the following (Zulueta, n.d.): 1. Descriptive research if the researcher wants to determine the significant difference between the observed and expected or theoretical frequencies from independent variables. 2. It is also used to test the hypothesis that the variance of a normal population is equal to a given value. 3. It is used to test the goodness of fit where a theoretical value distribution is fitted to some date (the fitting of a normal curve) 4. It is also used for the construction of confidence interval for variances. 5. It is used to compare two uncorrelated and correlated proportions. Moreover, chi-square is one way of classifying what is applicable when the researcher is interested in determining the number of subjects, objects or responses which fall in various categories. References Abrahams, David. (n.d.). True Experimental Designs. Retrieved October 12, 2008 from http://www.socialresearchmethods.net/tutorial/Abrahams/true.htm AllPsychOnlineResearch Methods. March 21, 2004. Chapter 8: Descriptive Statistics. Retrieved on October 11, 2008 from http://allpsych.com/researchmethods/correlation.html Pinkey, Matthew (n.d.). The Chi-Square Statistic. Retrieved on October 12, 2008 from http://math.hws.edu/javamath/ryan/ChiSquare.html PPA 696 Research Methods. (n.d.). Quasi Experimental Research Designs. Retrieved on October 11, 2008 from http://www.csulb.edu/~msaintg/ppa696/696quasi.htm Zulueta, Francisco M., Costales, Edilberto B. Jr. (2003) Methods of Research, Thesis Writing and Applied Statistics. National Bookstore, Quad Alpha Centrum Building, Mandaluyong City. StatSoft, Inc. (1984). Power Analysis. Retrieved on October 11, 2008 from http://www.statsoft.com/textbook/stpowan.html Trochim, William M. K. (2006). Research Methods, Knowledge Base. Retrieved on October 12, 2008 from http://www.socialresearchmethods.net/kb/stat_t.htm Read More