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Find and state a definition of parametric and non-parametric methods that distinguishes between the two. In your own words, explain the difference between parametric and non-parametric methods.

Parametric and non-parametric statistical methods denote two general classifications of statistical procedures. Parametric tests are grounded in the assumptions about the distribution of the fundamental population, which provided the sample. The most widely spread parametric assumption implies that data are divided in an approximately normal manner. Non-parametric tests are not...

Explain which types of data require parametric statistics to be used and which types of data require non-parametric statistics to be used and why.

The parametric statistical method is used with continuous, interval data, demonstrating equality or differences of intervals. Non-parametric tests relate to ordinal data, including “Likert scale data,” which involves data ranking. Statistical methods are responsible for the primary tasks applied to various types of data in terms of data collection, presentation...

Compare the advantages and disadvantages of using parametric and non-parametric statistics.

Statistical analysis encompasses multiple ways of its application to determine a confidence interval about a mean. Non-parametric statistics Advantages: No need for models Can define and localize changes Provides options for signal analysis Appropriate for long-term application to early detect cases requiring model-based interpretation Disadvantages: The complexity of physical interpretation...

How do I interpret measures of central tendency as well as measures of dispersion when dealing with various variables that have continuous data in SPSS, and how do these measures affect my results?

Measures of central tendency and dispersion attempt to describe data that is currently available in the SPSS dataset, with the most commonly used ones being the mean, median, and mode for measures of central tendency, and the standard deviation, variance, and range for measures of dispersion. Owing to the fact...

Propose a Specific Observational Research Design to Investigate a Causal Theory

Discuss the substantive importance of your research question: e.g., why is it important to study your dependent variable? Discuss your observational research design to test your theory. Address whether there is any potential reverse causality in your theory and if you claim that there is a potential reverse causality, you...

Create a Monthly Budget for Your Future Self

Think about your future self, and realistically consider what your middle adult life will be like. Your career? Your salary? Your lifestyle? With all of this in mind, create a monthly budget. A budget should include the following: mortgage or rent, phone bill, utilities, Internet, cable, car payment, insurance (life,...

Would Be Lady Young Road As a Steep As Paramin in Maraval a Success?

If the Lady Young Road was steep as Paramin in Maraval, would it be a major roadway to get into Port-of-Spain? What does the gradient or slope have to do with the Lady Young Road and getting to the top of Paramin? What will make it impossible for a vehicle...

Define and give examples for key terms related to math experiences for young children.

According to Jean Piaget, even at an early age, children have to face different forms of math experiences. The first one is physical knowledge, meaning learning objects and their characteristics, for example, color and size. Logico-mathematical knowledge involves obtaining more detailed information, such as comparing and counting, in order to...

What is the purpose of a post-hoc test with an analysis of variance?

Post-hoc tests in the Analysis of Variance (ANOVA) are meant for situations where the researcher has found a significant omnibus F-test together with another factor consisting of three or more means. Therefore, the need for additional exploration is necessary to get specific information that has contributed to the significant differences...

Discuss specific ways to incorporate diversity into math experiences.

As games involving some mathematical concepts are played all over the world, the diversity issues have to be prevented. Not only does that regard cultural and national aspects, but also possible disabilities. Some of them may be connected to difficulties arising during the process of learning Maths. In order to...

What is probabilistic equivalence? Why is it important?

Probabilistic equivalence is a concept in experimental design methodology, which implies that the researcher is perfectly aware of the odds that he or she will find come across a pretest difference between the two groups under investigation. However, it does not necessarily mean that the two groups being studied will...

Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?

A parametric test is used when the researcher understands the population parameters. They include statistics such as t-test, ANOVA, and z-test. On the other hand, if the population parameters are not available a researcher uses nonparametric statistics to test the hypothesis. They include Mann-Whitney and Kruskal-Wallis tests, among others. According...

If you were doing a study to see if a treatment causes a significant effect, what would it mean if, within groups, the variance was higher than between groups variance? If between groups variance was higher than within groups variance?

There are two main sources of variance namely, between groups and within groups. The 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. Variability within groups is a result of several factors...

Why would anyone ever want more than two levels of an independent variable?

Independent variable is that element of experimental research, which is manipulated or changed by the research in order to cause changes in other elements being studied. Therefore, the independent variable is one of the core or major components of experimental research. It is the variable that is altered or manipulated...

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. In more specific terms, error variance is the variability that cannot be accounted for in experimental research using the systematic differences that the researcher is...

What is an F-ratio? Define all the technical terms in your answer.

F-ratio is a statistical concept in experimental research design, which helps to assess whether variance in two different samples is equal. It is also used to determine the variance within groups of sample data as well as the variance between two groups of data. The F-ration is mostly applied in...

Why is it important to pay attention to the assumptions of the statistical test? What are your options if your dependent variable scores are not normally distributed?

Assumptions in a study related to the population parameters and measures. A statistical test ascertains the validity of the assumptions made by the researcher. Thus, statistical measures test the validity of the assumptions. If they are valid, then the study’s procedures are correct and thus, its findings are significant. However,...

What does p = .05 mean? What are some misconceptions about the meaning of p =.05? Why are they wrong? Should all research adhere to the p = .05 standard for significance? Why or why not?

The p-value in research describes the probability that the H0 is true at a given level of significance. Thus, p = .05 means that, assuming a correct H0, the probability that the data (dependent variable) are significant is 0.05. If p < 0.05 (at 95% confidence), the H0 is rejected....

What is the difference between a statistically significant result and a clinically or “real world” significant result?

Statistical significance estimates the probability that the differential outcomes between the control and experimental conditions are caused by the independent variable. Researchers use p-value and levels of confidence (CI) to estimate significance. CI measures the limits within which the results of a study would fall even with repeated measurements while...

What is NHST in statistics? Describe the assumptions of the model.

The NHST model is a statistic, such as a t-test, for determining whether a given variable causes the effect being tested. NHST tests often make certain assumptions. The NHST model (z-test and t-test) makes assumptions regarding the distribution of the tested variable. One such assumption relates to the normal distribution...

What are three criticisms of Null Hypothesis Significance Testing?

One of the NHST model criticisms relates to the rejection of the H0 based solely on the p-value. Markus argues that the decision to reject or fail to reject the H0 using p values is flawed because it creates a converse inequality error. NHST estimates the test statistic within a...

What is the General Linear Model? Why does it matter?

Peck, Olsen, and Devore define the GLM as a “multiple regression analysis” approach that includes both qualitative and quantitative variables. It is applied in parametric statistics involving single dependent and multiple qualitative and quantitative variables. It is used in covariance analysis or ANCOVA. GLM is important in statistics because it...

What do inferential statistics allow you to infer?

Inferential statistics allow a researcher to draw conclusions regarding the population based on the sample data. Thus, they enable the researcher to generalize the study’s findings to other populations. Inferential statistics determine the characteristics of the population based on the sample as well as the cause-and-effect relationship between the IV...

What is a prior probability?

Prior probability is the estimated probability of the state of affairs before a practical survey is conducted to acquire relevant details. This is usually a conclusion based on past events. For instance, Peter passed the test (A) last year; therefore, the probability P (Pc) he will pass test C is...

What is modal logic?

Modal logic is an extension of formal logic that allows reasoning about certainties and possibilities. In comparison with classical logic, modal one considers that things may not always be as they are at that moment. For example, one may use modal logic by saying, “although the sun is usually yellow,...

What are De Morgan’s Laws?

De Morgan’s Laws are a pair of transformation logical rules and are an example of mathematical duality. They can be expressed as: the negation of a disjunction is the conjunction of the negations while the negation of a conjunction is the disjunction of the negations.

We want to find the average height of adult men in America. We choose a SRS of 36 adult American men and perform a 95% confidence interval. Using this procedure, we find that their average height is 71 in. +/- 0.52 inches. What is the margin of error of this confidence interval?

The margin of error shows how accurate one expects the value of the unknown parameter to be. The margin of error of the given confidence interval is equal to ± 0.52 inches. This means that the value of ± 0.52 inches is the maximum amount by which the sample results...

You sample 100 apples from your farm’s harvest of over 200,000 apples. The mean weight of the sample is 112 grams. Let’s assume that you know the weight of all apples produced by your farm is normally distributed and the standard deviation of the weight is 40 grams. What is the 99% confidence interval for the mean weight of apples of your farm? If we want to shorten the length of the confidence interval by half while keeping the same confidence level at 99%, how many apples should we sample to begin with?

In order to shorten the length of the confidence interval by half without changing the confidence level, the value of (σ / (number of samples0.5)) should be halved. Given that σ is the constant value, the number of samples needs to be increased, so that (new number of samples0.5) /...

Suppose you buy a case of 36 cans of soda and carefully measure the volume of each. You average the results and determine that the sample mean is 12.1 oz. Let’s assume that you know that the canning facility outputs cans whose volumes are distributed normally with a standard deviation of 0.24 oz. What is the 80% confidence interval of the mean of the volume? Is it larger or smaller than the 90% confidence interval. Does this make sense?

Since z* is equal to 1.282 for the 80% confidence interval, the 80% confidence interval of the mean of the volume is 12.1 ± 1.282 × (0.24 / (36 0.5)) = 12.1 ± 0.05128. It can be stated that the calculated interval is smaller than the 90% confidence interval, with...

The mean income of households in Utica is $50,000 with a standard deviation of $10,000. Can we use Table A, the Standard Normal table, to estimate the probability that a single randomly chosen Utica household will have an income of less than $52,500? Why or why not?

Given that income distribution in Utica is normal, it is possible to use Table A to estimate the probability that a single randomly chosen Utica household will have an income of less than $52,500. This is because the value of $52,500 can be standardized, and the cumulative proportion for the...

The total amount of money spent by shoppers in one visit to Wainwright’s department store is normally distributed with a mean of $50 with a standard deviation of $10. Use the Standard Normal table to compute the following probability: What is the probability that a shopper chosen at random will spend less than $47 during their next visit to Wainwright’s?

In order to use Table A, a standardized amount of money spent by shoppers should be calculated. For a shopper who spends $47 during one visit to Wainwright’s, this standardized amount of money equals z = (47 – 50) / 10 = -0.3. The cumulative proportion for z is 0.3821....

View the Khan Academy video on the Central Limit Theorem and comment on it.

The Central Limit Theorem is a profound concept in statistics that makes statistically significant inferences about the general population based on samples. For example, a variable has a normal distribution (or any other type of distribution). One repeatedly takes samples from this general population and calculates the mean of each...

Give an example of a survey (real or invented) that is poorly designed because it contains one or more type of bias. State clearly what kinds of bias the survey has.

The name of the store and the following example of a survey were invented by the author. Kaufmann’s is a large department store that offers expensive clothing for high-income customers, both men and women. A limited collection of jewelry was launched for the first time, and a survey was designed...

Find an example in your environment (in a newspaper article, a TV news show, a political campaign, etc.) in which two variables are correlated and the author/presenter/speaker is implying that one of these variables causes the other. Comment on the strength of the evidence that causation is really present. Can you think of another factor (a confounding or lurking variable) that might be the underlying cause of both variables?

In order to demonstrate the example when correlation does not imply causation, the article discussing the link between soft drinks and aggression in children was chosen. It is stated that heavy soda drinkers are much prone to violent behavior than other children. For this particular research, the intake of soft...

Take a look at the career batting averages of four of the greatest baseball players of all time. When watching a game many people will say that a given player is “due” for a home run or a hit after a period of uncharacteristically low offense. Let’s say Willie Mays is in a slump – he has made an out the last 10 times at bat. What are his chances of getting a hit? Is he “due” for a hit? Why or why not?

The chance of a hit in ideal conditions is 0.5. The player can either hit the ball and make a hit or miss with equal probability. In this sense, it is wrong to say that he must make a hit, but he can make a hit with a chance of...

Take a look at the career batting averages of four of the greatest baseball players of all time. In terms of the law of large numbers, what can we assume about how accurately these career averages reflect the actual abilities of the players?

The AVG parameter shows the success of the batting during a baseball game. Having discarded all other factors, the probability of hitting the ball with a bat is 0.5. From the law of large numbers, this parameter does not say anything about the likelihood of a successful strike during the...

The probability of tossing a coin and getting heads is 0.5 or 50%. Try this several times by hand, or use the GeoGebra Simulation. Imagine the simulation below, and that you were going to flip the coin 100 more times. Will you get 50 more heads and 50 more tails? Why or why not?

In fact, according to Bernoulli’s law, the average result will tend to be 0.5, as the number of shots has increased, but the number of added goals and tails will not be the same. The intuitive answer that there will be 50 goals and 50 tails is wrong because it...

The probability of tossing a coin and getting heads is 0.5 or 50%. Try this several times by hand, or use the GeoGebra Simulation. Imagine the simulation below, and that you were going to flip the coin just one more time. What is the probability you will get heads? What is the probability you will get tails?

It is a mistake to assume that the probability of heads or tails falling out during a throw depends on previous results. Despite the last 108 throws, the likelihood of a head fall for a symmetrical coin will still be 0.5. But it is worth distinguishing the probability of a...

Suppose a large class at Utica College has just given an exam and I picked 20 students at random from the class and asked each person their score on the exam. Here are their replies: 100, 98, 94, 94, 93, 93, 92, 90, 86, 86, 85, 84, 84, 78, 77, 73, 72, 68, 55, 12. Calculate the median of this data set.

To find the median, the data should be arranged in order from least to greatest: 12, 55, 68, 72, 73, 77, 78, 84, 84, 85, 86, 86, 90, 92, 93, 93, 94, 94, 98, 100. Since there is an even number of items, the median is calculated as the arithmetical...

Define statistics.

Statistics deals with gathering, grouping, examining, and interpreting numerical values based on their measurable probability. Thus, large data can be analyzed using the measures of central tendency. The information collected can be categorized as quantitative and qualitative data.

Work with one other person to look at the NCTM website. Find another math concept or skill you think could be taught through music. Collaborate to develop a strategy, and test it on children to see if it works. Reflect on the success of your idea(s).

During the collaboration with another student, it was theorized that the concept of fractions could be taught with the help of music. The approach based on using rhythm as the method of explaining fractions was used on fourth graders. The students seemed to have acquired a better idea of fractions...

Explain and evaluate the views of Pythagoras regarding the nature of substance.

Pythagoras was another philosopher interested in discovering the nature of the substance. In his opinion, mathematics (more specifically numbers) is the answer to the question. Since numbers cannot be mistaken, understanding them would provide knowledge about the nature of the substance. He is widely known for his studies of geometry...

Dataset below gives a picture of the first 15 values in a dataset that contains information on students within a particular university. Which are the variables (or ‘fields’) and which are the cases? Suggest two questions that we could possibly answer through an analysis of the data in dataset.

From the data given, the age of the students would be the variables since variables represent data that cannot be measured empirically. The cases would be the qualification entry requirements to the university since it is the subject matter of the analysis, and unlike the age of the students, it...

Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is μ=350 and σ=35. The 100 students who completed the tutoring program had an average score of 385 points. Is the students’ average score of 385 points significant at the 5% and 1% levels to support Tutor O-Rama’s claim of at least a 50-point increase in the SAT score? Is the Tutor O-Rama students’ average score of 385 points significantly different at the 5% and 1% levels from the average score of 350 points on the math portion of the SAT? What conclusion can you make, based on your results, about the effectiveness of Tutor O-Rama’s tutoring?

a. The average score of 385 points should be compared to the score of 400 points, considering that the tutor claims that their services will increase the average score of 350 by at least 50. z = ((x-μ)/√(σ2/N)) = ((385-400)/√(352/100)) = -4.285 The p-value for the z-score is 0.000009, which...

Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not.

The z-score is equal to: z = (12-14)/1.9 = -1.05 Given that the right-tailed p-value for this z-score is equal to 0.85, 85% of babysitters are paid more than my babysitter, which is why it is feasible to give her a rise.

Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variations from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91. Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. b. Calculate the test statistic. c. Find the P-value. d. What is the conclusion?

a. H0: the mean volume of all the bottles is 6 ounces. Ha: the mean volume of all the bottles is not equal to 6 ounces. b. The z-score is equal to: z = ((x-μ)/√(σ2/N)) = 5.989-(6/√(0.09/10)) = -0.115 c. The p-value is equal to 0.907.d. The null hypothesis should...

Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you. a. Write the research hypothesis and the null hypothesis. b. Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II errors. c. Write a paragraph explaining which error would be more severe, and why.

a. Ha: the effectiveness of drug B is greater than the effectiveness of drug A; H0: the effectiveness of drug B is equal to the effectiveness of drug A.b. Table 1 presents the outcomes of type I and type II errors. – – Reality Reality – – Drug B is...

You want to investigate the workplace attitudes concerning new policies that were put into effect. You have funding and support to contact at most 100 people. Choose a design method and discuss the following: a. Describe the sample design method you will use and why. b. Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.? c. Discuss the bias, on the part of both the researcher and participants.

a. It is a good idea to choose stratified random sampling since it yields more accurate results, as compared to simple random sampling. Workers will be divided into groups by their position. Then, depending on the number of groups, a certain number of workers will be randomly chosen from each...

The manager of a company wants to investigate job satisfaction among its employees. One morning after a meeting, she talks to all 25 employees who attended. Does this sampling plan result in a random sample? What type of sample is it? Explain.

This is not a random sample since employees who did not attend the meeting did not have a chance to be selected. Instead, this is convenience sampling since subjects were chosen only because the manager could easily access them.

A phone company obtains an alphabetical list of names of homeowners in a city. They select every 25th person from the list until a sample of 100 is obtained. They then call these 100 people to advertise their services. Does this sampling plan result in a random sample? What type of sample is it? Explain.

This sampling plan does not result in a random sample since individuals do not have an equal chance to be chosen. In fact, individuals that are at the end of the list may be not even reached if there are more than 2,500 people living in the city. Since the...

Describe how you could use regression analysis to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, what would be the independent and dependent variables, and how data could ideally be collected to calculate the regression equation.

I could think of one way of using a simple linear regression model to help me make better health choices. Some time ago, I stumbled upon a piece of research that showed that regular exercise correlated with better sleep quality. While it is now pretty established that physical activity improves...

Describe how you could use confidence intervals to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, how the interval would impact the decision, and how data could ideally be collected to determine the interval.

Everyday use of the concept of confidence intervals that I can think of is buying clothes. It is common knowledge that sizing is often arbitrary and depends on the company. Sometimes, however, I think it is neither negligence nor malicious intent. People come in many shapes and sizes, and it...

Describe how you could use hypothesis testing to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, what would be the null and alternative hypotheses, and how data could ideally be collected to test the hypotheses.

When I waited tables a few years ago, I was often curious about the average number of restaurant visitors depending on the day of the week. The information was of value to me because I wanted to know what to expect from a shift, and some of them were really...

After several grueling months of data collection and statistical analysis, you finally were able to test the following hypothesis: Null hypothesis: There is no relationship between yearly changes in Gross Domestic Product (GDP) and yearly changes in the national deficit. Alternative hypothesis: There is a relationship between yearly changes in Gross Domestic Product (GDP) and yearly changes in the national deficit. Your results told you to reject the null hypothesis (Χ2(4) = 2.35, p = 0.012). However, what did the p-value tell you about the results of the hypothesis test?

Scholars emphasize the significance of the p-value in scientific research and statistics. P-value is the probability of receiving the result that is at least as extreme as the one mentioned in the sample data with the assumption that the null hypothesis is true. When the p-value is less than the...

a. Show how you can use numbers, tables and graphs to describe a single set of values. b. Show how you can use numbers, tables and graphs to describe an association between two sets of values.

Numbers, tables, and graphs are very useful when describing a single set of values or showing an association between two sets of values. A single set of values are used in everyday life. For instance, the teaching staff is fond of using single sets of values when evaluating the learners’...