M12L4 Review
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This document discusses hypothesis testing and provides examples. It explains that hypothesis testing allows determining if there is bias or if results are due to chance. The null hypothesis assumes no difference or effect. Data is then analyzed to see if it contradicts the null hypothesis. If a statistic is more than 1.96 standard deviations from the mean, the null hypothesis can be rejected, meaning the results are unlikely due to chance. Two examples applying these concepts to analyze claims are also provided.
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Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docx
Page 266
LEARNING OBJECTIVES
· Explain how researchers use inferential statistics to evaluate sample data.
· Distinguish between the null hypothesis and the research hypothesis.
· Discuss probability in statistical inference, including the meaning of statistical significance.
· Describe the t test and explain the difference between one-tailed and two-tailed tests.
· Describe the F test, including systematic variance and error variance.
· Describe what a confidence interval tells you about your data.
· Distinguish between Type I and Type II errors.
· Discuss the factors that influence the probability of a Type II error.
· Discuss the reasons a researcher may obtain nonsignificant results.
· Define power of a statistical test.
· Describe the criteria for selecting an appropriate statistical test.
Page 267IN THE PREVIOUS CHAPTER, WE EXAMINED WAYS OF DESCRIBING THE RESULTS OF A STUDY USING DESCRIPTIVE STATISTICS AND A VARIETY OF GRAPHING TECHNIQUES. In addition to descriptive statistics, researchers use inferential statistics to draw more general conclusions about their data. In short, inferential statistics allow researchers to (a) assess just how confident they are that their results reflect what is true in the larger population and (b) assess the likelihood that their findings would still occur if their study was repeated over and over. In this chapter, we examine methods for doing so.
SAMPLES AND POPULATIONS
Inferential statistics are necessary because the results of a given study are based only on data obtained from a single sample of research participants. Researchers rarely, if ever, study entire populations; their findings are based on sample data. In addition to describing the sample data, we want to make statements about populations. Would the results hold up if the experiment were conducted repeatedly, each time with a new sample?
In the hypothetical experiment described in Chapter 12 (see Table 12.1), mean aggression scores were obtained in model and no-model conditions. These means are different: Children who observe an aggressive model subsequently behave more aggressively than children who do not see the model. Inferential statistics are used to determine whether the results match what would happen if we were to conduct the experiment again and again with multiple samples. In essence, we are asking whether we can infer that the difference in the sample means shown in Table 12.1 reflects a true difference in the population means.
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Review Z Test Ci 1
1. The document discusses hypothesis testing using the z-test. It outlines the steps of hypothesis testing including stating hypotheses, setting the criterion, computing test statistics, comparing to the criterion, and making a decision.
2. Examples are provided to demonstrate a non-directional and directional z-test, including stating hypotheses, computing test statistics, comparing to criteria, and interpreting results.
3. Key concepts reviewed are the central limit theorem, type I and II errors, significance levels, rejection regions, p-values, and confidence intervals in hypothesis testing.
Example of a one-sample Z-test The previous lecture in P.docx
Example of a one-sample Z-test
The previous lecture in Powerpoint explained the general procedure for conducting a hypothesis
test. Now let’s go through an example of a hypothesis test to see how it actually works.
Say you’ve developed a new drug that you think might influence people’s cognitive ability,
although you aren’t really sure what it will do. (Yes, this is a really bad study!) You give the
drug to a sample of N = 49 people and then test their IQ. Say their IQ turns out to be X = 106.
Based on decades of test development, we know that in the general U.S. population, the mean IQ
is = 100 with a standard deviation of = 15. So the research question that we want to address
is whether the people who take the “IQ Pill” will have IQ scores that are different from the
general population (suggesting that the pill had some effect), or whether they basically look the
same as everybody else in the country (suggesting that the pill didn’t do anything).
Let’s test this question by using the formal steps of hypothesis testing:
1.Generate H0 and HA
2.Select statistical procedure
3.Select
4.Calculate observed statistic for your data
5.Determine critical statistic
6.Compare (4) and (5)
7.If (4) exceeds (5), reject H0
8.Otherwise, fail to reject H0
1. Generate H0 and HA
So what are H0 and HA? We don’t know whether the drug will make people’s IQs get higher or
lower, so we need to use a 2-tailed or non-directional hypothesis test. Since the mean in the
general population is 100, we will test whether the mean in our test group is equal to 100.
H0: = 100 HA: 100
In this case, refers to the mean of the population that our treatment group represents. This is a
theoretical population of people who have taken our IQ pill. Obviously, this population doesn’t
exist in reality, because the only people who have ever taken our pill are the 49 people who were
in our study. But IN THEORY, a whole lot of other people could also take this drug, and IN
THEORY, they should respond to it in the same way that our 49 participants respond. So we are
making an inference from our 49 participants to that very large group of people who in theory
could also have taken this drug.
2.Select statistical procedure
At this point, I’m just going to tell you that the statistical procedure that you will use is
something called the Z-test. This is a test that is appropriate for testing whether one sample is
different from some specified value when the value of the population standard deviation () is
known. Over the next few days, we will be introduced to some other statistical procedures that
are appropriate for different kinds of situations than this, and you will need to choose which one
is the best to use.
3.Select
In many cases, I will just tell you what level to use. But you should understand why a
researcher might choose one level compared to a.
Example of a one-sample Z-test The previous lecture in P.docx
Example of a one-sample Z-test
The previous lecture in Powerpoint explained the general procedure for conducting a hypothesis
test. Now let’s go through an example of a hypothesis test to see how it actually works.
Say you’ve developed a new drug that you think might influence people’s cognitive ability,
although you aren’t really sure what it will do. (Yes, this is a really bad study!) You give the
drug to a sample of N = 49 people and then test their IQ. Say their IQ turns out to be X = 106.
Based on decades of test development, we know that in the general U.S. population, the mean IQ
is = 100 with a standard deviation of = 15. So the research question that we want to address
is whether the people who take the “IQ Pill” will have IQ scores that are different from the
general population (suggesting that the pill had some effect), or whether they basically look the
same as everybody else in the country (suggesting that the pill didn’t do anything).
Let’s test this question by using the formal steps of hypothesis testing:
1.Generate H0 and HA
2.Select statistical procedure
3.Select
4.Calculate observed statistic for your data
5.Determine critical statistic
6.Compare (4) and (5)
7.If (4) exceeds (5), reject H0
8.Otherwise, fail to reject H0
1. Generate H0 and HA
So what are H0 and HA? We don’t know whether the drug will make people’s IQs get higher or
lower, so we need to use a 2-tailed or non-directional hypothesis test. Since the mean in the
general population is 100, we will test whether the mean in our test group is equal to 100.
H0: = 100 HA: 100
In this case, refers to the mean of the population that our treatment group represents. This is a
theoretical population of people who have taken our IQ pill. Obviously, this population doesn’t
exist in reality, because the only people who have ever taken our pill are the 49 people who were
in our study. But IN THEORY, a whole lot of other people could also take this drug, and IN
THEORY, they should respond to it in the same way that our 49 participants respond. So we are
making an inference from our 49 participants to that very large group of people who in theory
could also have taken this drug.
2.Select statistical procedure
At this point, I’m just going to tell you that the statistical procedure that you will use is
something called the Z-test. This is a test that is appropriate for testing whether one sample is
different from some specified value when the value of the population standard deviation () is
known. Over the next few days, we will be introduced to some other statistical procedures that
are appropriate for different kinds of situations than this, and you will need to choose which one
is the best to use.
3.Select
In many cases, I will just tell you what level to use. But you should understand why a
researcher might choose one level compared to a ...
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Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docx
Page 266
LEARNING OBJECTIVES
· Explain how researchers use inferential statistics to evaluate sample data.
· Distinguish between the null hypothesis and the research hypothesis.
· Discuss probability in statistical inference, including the meaning of statistical significance.
· Describe the t test and explain the difference between one-tailed and two-tailed tests.
· Describe the F test, including systematic variance and error variance.
· Describe what a confidence interval tells you about your data.
· Distinguish between Type I and Type II errors.
· Discuss the factors that influence the probability of a Type II error.
· Discuss the reasons a researcher may obtain nonsignificant results.
· Define power of a statistical test.
· Describe the criteria for selecting an appropriate statistical test.
Page 267IN THE PREVIOUS CHAPTER, WE EXAMINED WAYS OF DESCRIBING THE RESULTS OF A STUDY USING DESCRIPTIVE STATISTICS AND A VARIETY OF GRAPHING TECHNIQUES. In addition to descriptive statistics, researchers use inferential statistics to draw more general conclusions about their data. In short, inferential statistics allow researchers to (a) assess just how confident they are that their results reflect what is true in the larger population and (b) assess the likelihood that their findings would still occur if their study was repeated over and over. In this chapter, we examine methods for doing so.
SAMPLES AND POPULATIONS
Inferential statistics are necessary because the results of a given study are based only on data obtained from a single sample of research participants. Researchers rarely, if ever, study entire populations; their findings are based on sample data. In addition to describing the sample data, we want to make statements about populations. Would the results hold up if the experiment were conducted repeatedly, each time with a new sample?
In the hypothetical experiment described in Chapter 12 (see Table 12.1), mean aggression scores were obtained in model and no-model conditions. These means are different: Children who observe an aggressive model subsequently behave more aggressively than children who do not see the model. Inferential statistics are used to determine whether the results match what would happen if we were to conduct the experiment again and again with multiple samples. In essence, we are asking whether we can infer that the difference in the sample means shown in Table 12.1 reflects a true difference in the population means.
Recall our discussion of this issue in Chapter 7 on the topic of survey data. A sample of people in your state might tell you that 57% prefer the Democratic candidate for an office and that 43% favor the Republican candidate. The report then says that these results are accurate to within 3 percentage points, with a 95% confidence level. This means that the researchers are very (95%) confident that, if they were able to study the entire population rather than a sample, the actual percentage who preferred th ...
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This document discusses various probability distributions including the binomial, Poisson, and normal distributions. It provides definitions and formulas for calculating probabilities for each distribution. For the binomial distribution, it covers the binomial probability formula and using the binomial table. For the Poisson distribution, it discusses the Poisson probability formula and Poisson table. It also addresses calculating the mean, variance, and standard deviation for the binomial and Poisson distributions. Finally, it introduces the normal distribution as the most important continuous probability distribution.
Review Z Test Ci 1
1. The document discusses hypothesis testing using the z-test. It outlines the steps of hypothesis testing including stating hypotheses, setting the criterion, computing test statistics, comparing to the criterion, and making a decision.
2. Examples are provided to demonstrate a non-directional and directional z-test, including stating hypotheses, computing test statistics, comparing to criteria, and interpreting results.
3. Key concepts reviewed are the central limit theorem, type I and II errors, significance levels, rejection regions, p-values, and confidence intervals in hypothesis testing.
Example of a one-sample Z-test The previous lecture in P.docx
Example of a one-sample Z-test
The previous lecture in Powerpoint explained the general procedure for conducting a hypothesis
test. Now let’s go through an example of a hypothesis test to see how it actually works.
Say you’ve developed a new drug that you think might influence people’s cognitive ability,
although you aren’t really sure what it will do. (Yes, this is a really bad study!) You give the
drug to a sample of N = 49 people and then test their IQ. Say their IQ turns out to be X = 106.
Based on decades of test development, we know that in the general U.S. population, the mean IQ
is = 100 with a standard deviation of = 15. So the research question that we want to address
is whether the people who take the “IQ Pill” will have IQ scores that are different from the
general population (suggesting that the pill had some effect), or whether they basically look the
same as everybody else in the country (suggesting that the pill didn’t do anything).
Let’s test this question by using the formal steps of hypothesis testing:
1.Generate H0 and HA
2.Select statistical procedure
3.Select
4.Calculate observed statistic for your data
5.Determine critical statistic
6.Compare (4) and (5)
7.If (4) exceeds (5), reject H0
8.Otherwise, fail to reject H0
1. Generate H0 and HA
So what are H0 and HA? We don’t know whether the drug will make people’s IQs get higher or
lower, so we need to use a 2-tailed or non-directional hypothesis test. Since the mean in the
general population is 100, we will test whether the mean in our test group is equal to 100.
H0: = 100 HA: 100
In this case, refers to the mean of the population that our treatment group represents. This is a
theoretical population of people who have taken our IQ pill. Obviously, this population doesn’t
exist in reality, because the only people who have ever taken our pill are the 49 people who were
in our study. But IN THEORY, a whole lot of other people could also take this drug, and IN
THEORY, they should respond to it in the same way that our 49 participants respond. So we are
making an inference from our 49 participants to that very large group of people who in theory
could also have taken this drug.
2.Select statistical procedure
At this point, I’m just going to tell you that the statistical procedure that you will use is
something called the Z-test. This is a test that is appropriate for testing whether one sample is
different from some specified value when the value of the population standard deviation () is
known. Over the next few days, we will be introduced to some other statistical procedures that
are appropriate for different kinds of situations than this, and you will need to choose which one
is the best to use.
3.Select
In many cases, I will just tell you what level to use. But you should understand why a
researcher might choose one level compared to a.
Example of a one-sample Z-test The previous lecture in P.docx
Example of a one-sample Z-test
The previous lecture in Powerpoint explained the general procedure for conducting a hypothesis
test. Now let’s go through an example of a hypothesis test to see how it actually works.
Say you’ve developed a new drug that you think might influence people’s cognitive ability,
although you aren’t really sure what it will do. (Yes, this is a really bad study!) You give the
drug to a sample of N = 49 people and then test their IQ. Say their IQ turns out to be X = 106.
Based on decades of test development, we know that in the general U.S. population, the mean IQ
is = 100 with a standard deviation of = 15. So the research question that we want to address
is whether the people who take the “IQ Pill” will have IQ scores that are different from the
general population (suggesting that the pill had some effect), or whether they basically look the
same as everybody else in the country (suggesting that the pill didn’t do anything).
Let’s test this question by using the formal steps of hypothesis testing:
1.Generate H0 and HA
2.Select statistical procedure
3.Select
4.Calculate observed statistic for your data
5.Determine critical statistic
6.Compare (4) and (5)
7.If (4) exceeds (5), reject H0
8.Otherwise, fail to reject H0
1. Generate H0 and HA
So what are H0 and HA? We don’t know whether the drug will make people’s IQs get higher or
lower, so we need to use a 2-tailed or non-directional hypothesis test. Since the mean in the
general population is 100, we will test whether the mean in our test group is equal to 100.
H0: = 100 HA: 100
In this case, refers to the mean of the population that our treatment group represents. This is a
theoretical population of people who have taken our IQ pill. Obviously, this population doesn’t
exist in reality, because the only people who have ever taken our pill are the 49 people who were
in our study. But IN THEORY, a whole lot of other people could also take this drug, and IN
THEORY, they should respond to it in the same way that our 49 participants respond. So we are
making an inference from our 49 participants to that very large group of people who in theory
could also have taken this drug.
2.Select statistical procedure
At this point, I’m just going to tell you that the statistical procedure that you will use is
something called the Z-test. This is a test that is appropriate for testing whether one sample is
different from some specified value when the value of the population standard deviation () is
known. Over the next few days, we will be introduced to some other statistical procedures that
are appropriate for different kinds of situations than this, and you will need to choose which one
is the best to use.
3.Select
In many cases, I will just tell you what level to use. But you should understand why a
researcher might choose one level compared to a ...
13-statistics.pptx
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What is a Single Sample Z Test?
A one-sample z-test is used to compare a sample proportion to a population proportion. The document provides an example where a survey claims 90% of doctors recommend aspirin, and a sample of 100 doctors found 82% recommend aspirin. The z-test is calculated to determine if this difference is statistically significant. The null hypothesis is the sample and population proportions are the same. If the calculated z-statistic falls outside the critical values of -1.96 and 1.96, the null will be rejected, meaning the proportions are significantly different.
How to do the maths
This document provides an introduction to hypothesis testing and summarizes key concepts such as the null and alternative hypotheses, outcome measures, effect sizes, confidence intervals, statistical significance, and p-values. It explains how to state the research question, assumptions, and hypotheses. It also outlines the steps to choosing a statistical test, calculating test statistics, and forming conclusions based on p-values and significance levels. Various effect sizes are defined, including risk ratio, risk difference, and odds ratio. Interpretation of confidence intervals and limitations of significance testing are also briefly covered.
Statistik Chapter 5
This document discusses various discrete probability distributions including the binomial and Poisson distributions. It provides examples and formulas for calculating probabilities using these distributions. The key points covered are:
- The binomial distribution describes the probability of successes in a fixed number of yes/no trials where the probability of success is constant. It requires the trials to be independent and have two possible outcomes.
- The Poisson distribution describes the probability of events occurring randomly in time, space or volume. It applies when the number of events is large but the probability of any one event is small.
- Formulas are provided for calculating probabilities using the binomial and Poisson distributions, including the binomial probability formula and Poisson probability formula. Tables can also be used to find binomial and
Hypothesis Testing
The document discusses hypothesis testing and provides examples to illustrate the process. It explains how to state the research question and hypotheses, set the decision rule, calculate test statistics, decide if results are significant, and interpret the findings. An example tests if narcissistic individuals look in the mirror more often than others and finds they do based on a test statistic exceeding the critical value. A second example finds no significant difference in recovery time for patients with or without social support after surgery.
Lecture2 hypothesis testing
This document discusses key concepts in research methods and biostatistics, including hypothesis testing, random error, p-values, and confidence intervals. It explains that hypothesis testing involves determining if study findings reflect chance or a true effect. The p-value represents the probability of observing results as extreme or more extreme than what was observed by chance alone. A p-value less than 0.05 indicates statistical significance. Confidence intervals provide a range of values that are likely to contain the true population parameter.
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This document summarizes issues related to data-dependent selections and hypothesis testing. It discusses how preliminary inspection of data can influence test statistics and null hypotheses, potentially altering a test's ability to reliably detect discrepancies from the null. Two examples are provided:
1) "Hunting" through multiple independent tests and only reporting the most statistically significant result can incorrectly estimate the actual error rate as being much higher than the nominal rate of 5%.
2) Searching a DNA database and declaring a match with the first individual is different, as each non-match strengthens evidence for the inferred match. Adjusting is not needed as in the statistical "hunting" case.
Selection of cut-offs or model
Single sample z test - explain (final)
This document describes how to perform a one-sample z-test to compare a sample proportion to a population proportion. It provides an example where a survey claims 90% of doctors recommend aspirin, and a sample of 100 doctors found 82% recommend aspirin. It outlines calculating the z-statistic to determine if this difference is statistically significant using a 95% confidence level. The z-statistic is calculated to be -1.08, which falls within the acceptable range so the null hypothesis that the population and sample proportions are the same is retained.
Res 341 final exams
This document contains 57 multiple choice questions about statistical concepts such as probability distributions, sampling methods, confidence intervals, and hypothesis testing. The questions cover topics like parameters versus statistics, statistical inference, binomial and Poisson distributions, the central limit theorem, control charts, and sampling.
Telesidang 4 bab_8_9_10stst
The document discusses confidence interval estimation and hypothesis testing. It introduces key concepts such as point estimates, interval estimates, confidence intervals, null and alternative hypotheses, significance levels, test statistics, decision rules, and p-values. Examples are provided to illustrate how to construct confidence intervals for means and proportions, determine sample sizes, and conduct hypothesis tests for single means using z-tests and t-tests.
Hypothesis
Hypothesis testing involves developing a null hypothesis (H0) and an alternative hypothesis (Ha) to test a given situation. H0 states there is no difference, while Ha states there is a difference. Tests can be one-tailed or two-tailed. A two-tailed test rejects H0 if the sample mean is significantly different in either direction, while a one-tailed test only rejects if the difference is in the direction specified by Ha. When conducting a test, there is a risk of making a Type I error by rejecting a true H0, or a Type II error by failing to reject a false H0. The significance level determines the probability of a Type I error.
4_5875144622430228750.docx
The four steps of hypothesis testing are:
1. State the null and alternative hypotheses. The null hypothesis assumes the claim is true while the alternative contradicts it.
2. Set the significance level, typically 5%, which is the probability of a Type I error of rejecting a true null hypothesis.
3. Compute the test statistic to determine how far the sample mean is from the population mean stated in the null hypothesis.
4. Make a decision by comparing the p-value to the significance level. If p < 0.05, reject the null hypothesis.
Sample Size Determination.23.11.2021.pdf
This document discusses determining sample size for research studies. It defines key terms like sample size, population, and discusses factors that affect sample size like desired accuracy and available resources. It describes common methods for calculating sample size like formulas, tables, and software. Formulas use specifications like confidence level, margin of error, and population proportion to determine the needed sample size. The document emphasizes that determining an appropriate sample size is essential for research validity and making inferences to the target population.
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M12L4 Review
- 1. M12L4 Review
- 2. Hypothesis Testing Is it chance that your best friend continues to roll doubles in a game every turn when you have only rolled doubles once? Or, are they cheating? If you flip a coin to decide who has to do the dishes each night and your sister continues to win with heads 18 times out of 20, is that possibly chance? Hypothesis testing will allow us to determine whether it is likely or unlikely that there is bias in a given situation.
- 3. Hypothesis Testing Continued We start with null hypothesis which is sometimes referred to as the hypothesis of "no difference" or "no effect“ We may really expect that our sister is cheating with the coin, but our null hypothesis would assume she is not. Then we can check the data to see if it contradicts our null hypothesis. In a randomized controlled experiment, the null hypothesis will always be that there is no difference in the value of the variable for the control group and the treatment group.
- 4. But how do we know what would be far enough away from the average to not be considered chance? When a statistic is not in the middle 95% of our sample, we can reject the null hypothesis. To correlate that to a z-score, that would mean our statistic’s z-score is either 1.96 standard deviations above or below the mean. If the absolute value of z is less than 1.96, then you do no have enough evidence to reject the null hypothesis. Pic adjusted from http://jukebox.esc13.net/
- 5. REMEMBER… If a sample contains at least 30 individuals, you can use a z-test to be more precise with your hypothesis testing. To find the z-value of a statistic for a sample with n individuals, a sample mean of x, a population mean of µ, and a standard deviation σ, we do:
- 6. Example 1 A wireless company claims that it will save new customers 25% of what they pay for their current plans with other carriers. In a random sample of 35 new customers, the average amount saved was 23% with a standard deviation of 1.5%.
- 8. Example 2 A pharmaceutical company claims the drug data set will be 1000. In a test of the claim, the mean among 30 trials is actual 1015, with a standard deviation of 47.