Quantitative Methods PDF

QUANTITATIVE METHODS The primary purpose of defining a research problem is to guide the research process by identifying a specific issue The primary goal of inferential statistics is to make predictions about populations based on samples The primary purpose of confidence interval i...

QUANTITATIVE METHODS The primary purpose of defining a research problem is to guide the research process by identifying a specific issue The primary goal of inferential statistics is to make predictions about populations based on samples The primary purpose of confidence interval in inferential statistics is to estimate the population parameter with a range of values. The purpose of random sampling in a research study is to ensure every individual has an equal chance of being selected The purpose of conducting a hypothesis test for two populations is to assess if there is a statistically difference between the means of the two populations. The difference between descriptive and inferential statistics is to descriptive statistics summarize data, while inferential statistics make predictions about population. The difference between a research problem and a research question, a research problem is a statement, while a research question is a inquiry Standard deviation used to describe the spread or dispersion of a dataset. The potential consequences of an impractical or irrelevant research problem is the feasibility that ensures the research problem is achievable, and relevance ensures its significance. In the concept of “narrowing down” a research problem means focusing on a specific aspect or dimension of the problem. The role of the literature review play on the analyzing the components of a well-defined research problem is focusing on specific aspect or dimensions of the problem. Normal distribution is use to describe a symmetric bell-shaped distribution often observed in nature and social sciences. Sample is the subset of of a population from which data is collected in a research study If dataset has a positively skewed distribution, majority of the data located in relation to the right mean of the mean A skewed distribution from a symmetric distribution in terms of shape means that the skewed distributions have equal frequencies on either side of the means. In a research study, it is important for researchers to consider the extreme events are more likely in heavy-tailed distributions of the data collected exhibits a heavy-tailed distribution. In the presentation of histogram showing a bimodal distribution, it imply that there are two distinct groups within the data. Systematic sampling is a sampling method that can be used to estimate the average income of households in a city and divide to survey every 10th household on a randomly selected street. A cluster that are randomly selected for inclusion in the study in cluster sampling is the geographical proximity of the clusters. The main advantage of using a convenience sampling method in a preliminary study or exploratory research is to quick and easy data collection. Cluster sampling can be applied a researcher wants to study the opinions of university students and decides to survey students from three randomly selected departments. Stratified sampling can be applied in designing a sampling strategy for a nationwide survey to estimate the average satisfaction level of customers regarding a new product. In reviewing the results of a survey that employed quota sampling, the potential limitation should be considered to limited generalized to the entire population  The null hypothesis (Ho) in a hypothesis-testing context is a statement of equality or no effect. If the test statistic for a hypothesis test falls in the critical region, the decision is to reject the null hypothesis. In a significant test, the P-value indicates the strength of the evidence against the null hypothesis. When conducting hypothesis testing, it is essential to choose an appropriate significance level (o) in order to set the threshold for statistical significance In conducting one sample mean t-test to compare the mean of a sample to known population mean represent in Ho: μ = µ𝑜 The primary distinction between a z-score and a t-score in statistical analysis is that z-scores are standardized, while t-scores are not. A researcher wants to test whether the average IQ f a sample of students is significantly different from the population mean of 100 Is an example of z-test. If a t-test yields a p-value of 0.07, the decision should be fail to reject the null hypothesis. It is appropriate in a two-sample t-test when comparing the means of two independent groups. The z-test can be more appropriate than a t-test, when the population standard deviation is known. Use 95% confidence level to reject6 or fail to reject the null hypothesis (Ho: μ = 1125) represents: z-test: Reject Ho In a paired sample t-test, if the sample size is increased while keeping the standard deviation of the differences constant, the effect on the t-statistics is that the t-statistic will increase. A paired sample t-test is appropriate when there are two dependent samples In a paired sample test, if the p-value is calculated to be 0.029, the decision at 0.05 level of significance is to reject the null hypothesis (because α =0.05 is greater than 0.029) In a paired samples t-test for two populations, the positive t-statistic indicate that the paired differences are positively correlated Remember: - Reject the null hypothesis, as the t-statistic is less than the critical value - Accept the null hypothesis, as the t-statistic is greater than the critical Value Apply the appropriate statistical test: - Use the Analysis of Variance (ANOVA) when comparing the means of three independent groups. - Use z-test if the sample size is large (n ≥ 30) - Use t-test if the sample size is small (n ≤ 30)