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Study Guide Conceptual Take-Home-Test 2
Statistical Methods (PSY-205)
Marian University
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Study Guide Conceptual Take-Home-Test 2
Identifying What Analysis to Use: Given a description of a research question and dataset, you'll need to be able to indicate which type of statistical analysis you'd perform (e., correlation, regression, confidence intervals, one-sample NHST). Questions in the "What Would You Recommend?" section at the close of Chapter 6 are a good way to review for these type of questions. Complete the following questions from the end of Chapter 6 (pg. 125) your textbook to prepare (after you've answered each, check the back of the book). o B. Among a group of friends, one person is the best golfer. Another person in the group is the best at bowling. What statistical technique allows you to determine that one of the two is better than the other? I will recommend one-sample NHST o C. Tuition at Almamater U. has gone up each of the past 5 years. How can I predict what it will be in 25 years when my child enrolls? By using a linear regression relationship between the years and the tuition cost after collecting data. o F. Suppose you study some new, relatively meaningless material until you know it all. If you are tested 40 minutes later, you recall 85%; 4 hours later, 70%; 4 days later, 55%; and 4 weeks later, 40%. How can you express the relationship between time and memory? I will recommend regression analysis would produce a regression coefficient, which is a measure of the strength and direction of the relationship between the two variables. o H. For a class of 40 students, the study time for the first test ranged from 30 minutes to 6 hours. The grades ranged from a low of 48 to a high of 98. What statistic describes how the variable Study time is related to the variable Grade? Use the Pearson product-moment correlation coefficient to quantify the strength and direction of the relationship between these two variables. Chapter 6: Describe what each type of correlation (positive, negative, zero) represents (i., what does it mean about how the variables are related)? Ans: A positive correlation means two variables move in the same direction. There is a tendency for both variables to grow when one increases. A negative correlation means two variables move against each other. The tendency is for the other variable to decrease as one increases. A zero correlation means there is no linear relationship between two variables. Changes in one variable do not predict changes in the other variable.
How can you interpret a correlation coefficient to determine the strength of a correlation? Ans: The correlation coefficient shows the direction and degree of linear relationship between two variables. Using the effect size index for r Small (d = 0), Medium (d =0), Large (d = 0) Find a scatterplot on the Internet (not in your textbook). Copy and paste it into your study guide & then write a short paragraph interpreting the graph. Be sure to identify what variables are represented, what type of correlation the scatterplot depicts, and what this data means. Ans: The linear regression found a close positive correction among different ages of happiness and the married population. 35 to 55 years married population increase happiness. Discuss whether causal (i., cause & effect) relationships can be established using correlational analysis. Why or why not? Ans: Cause and effect relationships are measuring one variable (independent variable) and observing its effect on another variable (dependent variable) while controlling for other potential influences, it can be small (d = 0), medium (d = 0), and large (d = 0) effect size. Describe the difference between correlation and linear regression. Ans: Correlation is a statistical technique that describes the direction and degree of relationship between two variables, used to determine whether and how strongly two variables are related, while linear regression is a statistical method that produces a straight line that best fits a bivariate distribution, is used for prediction and understanding the nature of the relationship between variables. For linear regression, what do the variables X and Y stand for? X represents the known values of the independent variable(s).
A lottery where players choose numbers from 1 to 100. Assuming the lottery is fair and each number has an equal chance of being chosen, the distribution of selected numbers would follow a uniform distribution. Each number from 1 to 100 has an equal probability of being selected, resulting in a flat, rectangular shape on a graph. The uniform distribution indicates that each number is equally likely to occur, representing a square/rectangular distribution. Describe the similarities, differences, and relationships between empirical and theoretical distributions. What is each based on and what is each used for? Ans: Empirical Distributions are scores that come from observation on real data gathered from experiments, surveys, observations, or measurements. Theoretical distributions are hypothesized scores based on mathematical formulas and logic. Examples include the normal distribution, binomial distribution, and rectangular distribution. Similarities: Both Represent Probabilities: Both empirical and theoretical distributions can be used to calculate probabilities associated with specific events or values. Sum to 1: The total area under the probability density curve (for continuous distributions) or the sum of probabilities (for discrete distributions) is always 1 for both empirical and theoretical distributions. This reflects the certainty that some outcome will occur. Differences: Empirical distributions are derived directly from observed data, while theoretical distributions are based on mathematical formulations and assumptions. Empirical distributions are specific to the data set from which they are derived and are used for understanding the dataset, while theoretical distributions are general mathematical models that can be applied to a wide range of situations, even ones for which no empirical data exists. Relationship: Empirical distributions can be compared to theoretical distributions to assess how well the theoretical model fits the observed data. If the fit is good, the theoretical distribution can be used to make predictions and draw conclusions about the population from which the data were sampled. If the fit is poor, alternative theoretical models or modifications to the existing model may be considered. Empirical distributions are based on observed data and are used to describe the actual behavior of a dataset. Theoretical distributions are based on mathematical formulations derived from specific probability models and are used for modeling and prediction.
Is the normal distribution preferable to other theoretical distributions? Why or why not? Normal distribution has proved to be extremely valuable than other theoretical distributions. Chapter 8: What is the expected value and standard error in terms of a sampling distribution? How are these similar to and different from the mean and standard deviation obtained from an empirical distribution? The expected value is the mean of the sampling distribution or the average value that would be obtained from a particular statistic. The standard error is the standard deviation of the sampling distribution. The sample standard deviation decreases as the sample size (n) increases. Similarities and Differences from the mean and standard deviation of an empirical distribution. Similarities: Both the expected value and the mean represent a measure of central tendency. The standard error and the standard deviation both quantify the spread or variability of the data. Differences: The expected value refers to the theoretical average obtained from infinite samples and is specific to the sampling distribution. Mean refers to the average calculated from a finite sample or a population. The standard error is related to the spread of the sampling distribution and indicates how much the sample mean is expected to vary from the true population mean due to random sampling. Standard deviation measures the variability of individual data points in a sample or a population. Come up with an example for each type of sample (random, biased, and research). Random Sample: Using a random number generator, a researcher studying public opinion on a new government policy chooses 500 people from a national database. Every person in the database has an equal probability of getting chosen. Every person has an equal chance of being included in this random sample, which makes it representative of the total population. Biased Sample: Only rally attendees are included in a poll a political party conducts regarding its policy. Because it solely consists of those who have
Confidence intervals provide a measure of confidence in the estimate, allowing businesses to make informed decisions. Chapter 9: What is null hypothesis significance testing (NHST) and what is it used for? Null hypothesis significance testing (NHST) is the process that produces probabilities that are accurate when the null hypothesis is true. NHST is used to test hypotheses about population parameters. Researchers use it to determine if the observed data provides enough evidence to reject the null hypothesis in favor of a specific claim or effect. Describe what a null hypothesis and alternative hypothesis are and provide an example of an alternative hypothesis you would be interested in studying. What would the null hypothesis be? Null Hypothesis (H 0 ) is a hypothesis about a population or the relationship among populations. The null hypothesis often states that a population parameter (such as a mean, proportion, or correlation) is equal to a specific value or follows a certain pattern. Alternative Hypothesis is a hypothesis about population parameters that is accepted if the null hypothesis is rejected. Alternative hypotheses can be directional (predicting a specific direction of change) or non-directional (predicting a change without specifying the direction). Example of an Alternative Hypothesis: A researcher is studying the effect of a new educational intervention on student test scores. They are interested in whether the intervention leads to an improvement in test scores. This hypothesis states that the mean test score of students who receive the intervention is different (either greater or lower) from the mean test score of students in the control group. The null hypothesis (H0) would state that there is no difference in the mean test scores between the intervention and control groups. This null hypothesis states that the mean test score of students who receive the intervention is equal to the mean test score of students in the control group, indicating no significant difference in test scores due to the intervention. Write a paragraph describing what alpha and beta are in relation to the concept of statistical significance. In your explanation, include significance levels, rejection regions, and critical values. Alpha is the probability of making a Type I error, which is incorrectly rejecting the null hypothesis when it is true. Beta is the probability of making a Type II
error, which is incorrectly failing to reject the null hypothesis when it is actually false. Significance levels, rejection regions, and critical values are all related to alpha and beta. The significance level is the probability of making a Type I error that a researcher is willing to accept. It is typically set to 0, which means that the researcher is willing to accept a 5% chance of making a Type I error. Concept Definition Alpha (α) Probability of making a Type I error Beta (β) Probability of making a Type II error Significance level Probability of making a Type I error that a researcher is willing to accept Rejection region Range of values of the test statistic that would lead to the rejection of the null hypothesis Critical value Value of the test statistic that separates the rejection region from the non-rejection region Example Since the p-value is less than the significance level, the researcher rejects the null hypothesis and concludes that the new drug is effective at reducing the risk of heart disease. Describe an example (not one provided in the book/lecture) of when you might use a one-sample t-test. Be specific about the means being compared and the hypothesis being tested. Example of when you might use a one-sample t-test Does a new drug reduce the average amount of time it takes for patients to recover from a certain illness? Hypothesis: Null hypothesis (H0): The average amount of time it takes for patients to recover from the illness is the same with and without the new drug. Alternative hypothesis (Ha): The average amount of time it takes for patients to recover from the illness is shorter with the new drug than without it. Data: A random sample of patients is recruited for a clinical trial. Half of the patients are randomly assigned to receive the new drug, and the other half are assigned to receive a placebo. The amount of time it takes for each patient to recover from the illness is recorded. A one-sample t-test is conducted to compare the mean recovery time of the patients who received the new drug to the hypothesized mean recovery time of the patients who received the placebo.
Study Guide Conceptual Take-Home-Test 2
Course: Statistical Methods (PSY-205)
University: Marian University
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