Guided Reading Ch 4, 5, 7, 11

pdf

School

California State University, Fullerton *

*We aren’t endorsed by this school

Course

MISC

Subject

Statistics

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by BrigadierKangaroo10846

Guided Reading Chapter 4, 5, 7, 11 Fill these in to the best of your ability and submit to canvas by the deadline, using Lane https://onlinestatbook.com/2/describing_bivariate_data/bivariate.html 1. Define "bivariate data" A set of data that includes two distinct variables is referred to as bivariate data. In bivariate data sets, every pair of values represents a measurement or observation made on two variables for every unit or study participant. 2. Define "scatter plot" Each data point in a scatter plot is represented by a dot or marker, and the values of the two variables under comparison dictate where the dot is placed on the graph. 3. Distinguish between a linear and a nonlinear relationship Linear relationships have a constant rate of change, while nonlinear relationships exhibit varying rates of change. 4. Identify positive and negative associations from a scatter plot On a scatter plot, a positive association is often observed as a general upward trend from left to right. A negative association is often observed as a general downward trend from left to right. 5. Describe what Pearson's correlation measures A statistical metric known as Pearson's correlation coefficient, or simply r, is used to express how strongly and in which direction a linear relationship is between two continuous variables. It evaluates the extent to which a change in one variable corresponds to a corresponding change in another. 6. Give the symbols for Pearson's correlation in the sample and in the population r is used for the sample correlation coefficient, and ρ is used for the population correlation coefficient 7. State the possible range for Pearson's correlation r=+1: Perfect positive correlation. It indicates a perfect linear relationship where an increase in one variable is associated with an exact proportional increase in the other. r=0: No correlation. There is no linear relationship between the two variables.

r=−1: Perfect negative correlation. It indicates a perfect linear relationship where an increase in one variable is associated with an exact proportional decrease in the other. 8. Identify a perfect linear relationship A consistent and precise proportionality in the correlation between two variables characterizes a perfect linear relationship. 9. Are Pearson’s r correlations affected by linear transformations? That is, would the correlation between height and weight be influenced by whether or not height is measured in inches, feet, or miles? No, Pearson's correlation coefficient (r) is not affected by linear transformations. This means that the correlation between two variables remains the same regardless of whether the variables are measured in different units or are subject to linear transformations. 10. This one is free – just remember that correlation does NOT imply causation. 11. This one is also free – Pearson r correlation only works with linear relationships 12. Define symmetrical outcomes Situations where the results or repercussions are equal, balanced, or mirror each other in some way are referred to as symmetrical outcomes. 13. Distinguish between frequentist and subjective approaches The frequentist approach emphasizes objective, frequency-based probabilities derived from empirical observations, while the subjective approach acknowledges the role of personal beliefs and subjective assessments of uncertainty in defining probabilities. 14. Describe the Gambler’s Fallacy Gambler's Fallacy is a cognitive bias that leads people to believe that past events influence future events in games of chance, despite the events being statistically independent. 15. Define permutations and combinations

An arrangement of a set's components in a certain sequence is called a permutation. A combination of a set is a choice of its components without taking the order into account. 16. Define binomial outcomes When there are just two possible outcomes for every trial or experiment, these circumstances are referred to as binomial outcomes. These are usually labeled as "success" or "failure," and the experiences are unrelated to one another. 17. Define independent events in terms of probability According to probability theory, two occurrences are independent if the chance of one event happening or not depends on the outcome of the other. 18. Describe the shape of normal distributions A normal distribution has a bell-shaped, symmetric shape. 19. State 7 features of normal distributions Symmetry, bell-shaped curve, mean/median/mode equality, tails extend indefinitely, empirical rule, parameters, standard normal distribution 20. What is the purpose of standardizing a distribution using Z scores with a mean of zero and a standard deviation of 1? Why would someone standardize a distribution? Bringing a distribution to par Z scores are a helpful statistical approach that can be used to prepare data for statistical analyses, identify outliers, make data more similar, and facilitate interpretation. It is a standard step in many statistical techniques and ensures that variables are comparable enough to allow for meaningful comparisons. 21. State the relationship between sample size and the accuracy of normal approximation of the binomial distribution. The Central Limit Theorem describes the link between sample size and the accuracy of the normal approximation of the binomial distribution.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

22. Define "null hypothesis" The assertion or presumption that there is no discernible difference or effect is known as the null hypothesis. 23. Define "alternative hypothesis" A claim that disputes or contradicts the null hypothesis is known as the alternative hypothesis. 24. Define "statistically significant" The term "statistically significant" is used to describe a result that is unlikely to have occurred by chance alone. 25. Distinguish between statistical significance and practical significance Statistical significance refers to the likelihood that an observed effect or relationship in the data is not due to random chance. Practical significance refers to the real-world importance or meaningfulness of an observed effect. 26. Define Type I and Type II errors A Type I error occurs when the null hypothesis (Ho) is incorrectly rejected when it is actually true. A Type II error occurs when the null hypothesis (Ho) is incorrectly not rejected when it is actually false. 27. Explain why the null hypothesis should not be accepted when the effect is not significant Failing to reject the null hypothesis does not provide evidence in favor of the null hypothesis. 28. Why are Two-tailed tests more common than one-tailed tests? Positive and negative effects are more perceptible in two-tailed testing. It is possible for researchers to identify a wider variety of effects by taking into account departures from the null hypothesis in both directions. 29. Discuss whether rejection of the null hypothesis should be an all-or-none proposition The rejection of the null hypothesis in statistical hypothesis testing is not an all-or-none proposition; rather, it involves a nuanced interpretation based on statistical evidence and a predetermined significance level.

30. State what it means to accept the null hypothesis failing to reject the null hypothesis is a cautious interpretation that acknowledges the limitations of the study and the inherent uncertainty in statistical inference. 31. Explain why the null hypothesis should not be accepted This phrase highlights the need to interpret results with caution, recognizes the uncertainties associated with statistical inference, and captures the dynamic aspect of scientific research. It is crucial to keep in mind the larger context of the research topic and study design and to refrain from asserting with certainty that the null hypothesis is true. 32. Describe how a non-significant result can increase confidence that the null hypothesis is false A non-significant result implies that there is not enough evidence in the data to confidently reject the null hypothesis. It can increase confidence within the null hypothesis. 33. Discuss the problems of affirming a negative conclusion Affirming a negative conclusion implies proving the absence of an effect, relationship, or difference 34. State the four steps involved in significance testing The four steps involved in significance testing are formulating hypotheses, choosing significance levels, collecting and analyzing data, and making a decision. 35. The null hypothesis for a particular experiment is that the mean test score is 20. If the 99% confidence interval is (18, 24), can you reject the null hypothesis at the .01 level? We can’t reject the null hypothesis because the hypothesized value of 20 falls within the interval which means there is no sufficient evidence. 36. State why the probability value is not the probability the null hypothesis is false

While the p-value is needed in hypothesis testing, it is essential to interpret it correctly. It provides information about the compatibility of the observed data with the null hypothesis but does not directly provide the probability that the null hypothesis is true or false. 37. Explain why a low probability value does not necessarily mean there is a large effect In statistical hypothesis testing, a low probability value (p-value) denotes the likelihood that the observed data would not have happened if the null hypothesis were true. 38. Explain why a non-significant outcome does not mean the null hypothesis is probably true Non-significant outcome does not provide strong evidence for the truth of the null hypothesis. It suggests a lack of sufficient evidence against the null hypothesis in the specific study, but conclusions should be drawn cautiously, considering statistical power, effect size, and other contextual factors. I just want you to have the info below Z-score formula z = ( x - μ ) / σ Where: • z = Z-score • x = the value being evaluated • μ = the mean • σ = the standard deviation The z-score shows the number of standard deviations a given data point lies from the mean. So, standard deviation must be calculated first because the z- score uses it to communicate a data point's variability. The higher (or lower) a z-score is, the further away from the mean the point is. This isn't necessarily good or bad; it merely shows where the data lies in a

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

normally distributed sample. Z-scores can be negative (below mean) or positive (above mean).

Guided Reading Ch 4, 5, 7, 11

Related Documents