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This document provides an overview of hypothesis testing. It begins with an outline of the key topics to be covered, including the logic of hypothesis testing, types of errors, specific hypothesis tests, effect size, and statistical power. The body of the document then defines these concepts in more detail through examples and explanations. It discusses how to state hypotheses, set decision criteria, collect and analyze data, and make conclusions regarding whether to reject the null hypothesis. Factors that influence hypothesis tests like sample characteristics and test assumptions are also outlined.

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Lund 2009

This document discusses statistical principles for writing scientific manuscripts, including how to describe sampling uncertainty, present results using measures of central tendency and variability, and report findings using confidence intervals and p-values. It emphasizes quantifying and conveying measurement uncertainty and effect sizes rather than relying solely on hypothesis testing. Guidelines are proposed for systematically reporting the design, methods, results and interpretation of laboratory experiments to improve transparency and enable verification.

Hypothesis Testing

BMI (kg/m2)
22.1
23.4
24.8
26.2
27.6
28.9
30.3
31.6
32.9
34.2
35.5
36.8
38.1
39.4
The sample mean is 29.1 kg/m2 and the sample standard
deviation is 4.2 kg/m2. Test the hypothesis that the
population mean BMI is 30 kg/m2 at 5% level of
significance.

What So Funny About Proportion Testv3

The document discusses hypothesis testing and proportion tests. It provides an overview of hypothesis testing terminology and steps. It also gives examples of using one-proportion and two-proportion tests to analyze business data on regulatory compliance documentation and workload balance between regions. The null hypothesis is tested in each example to determine if there are statistically significant differences between the proportions.

Testing of hypothesis

This document discusses the process of testing hypotheses. It begins by defining hypothesis testing as a way to make decisions about population characteristics based on sample data, which involves some risk of error. The key steps are outlined as:
1) Formulating the null and alternative hypotheses, with the null hypothesis stating no difference or relationship.
2) Computing a test statistic based on the sample data and selecting a significance level, usually 5%.
3) Comparing the test statistic to critical values to either reject or fail to reject the null hypothesis.
Examples are provided to demonstrate hypothesis testing for a single mean, comparing two means, and testing a claim about population characteristics using sample data and statistics.

Hypothesis testing

This document discusses hypothesis testing, which involves drawing inferences about a population based on a sample from that population. It outlines the key elements of a hypothesis test, including the null and alternative hypotheses, test statistics, critical regions, significance levels, critical values, and p-values. Type I and Type II errors are explained, where a Type I error involves rejecting the null hypothesis when it is true, and a Type II error involves failing to reject the null when it is false. The power of a hypothesis test is defined as the probability of correctly rejecting the null hypothesis when it is false. Controlling type I and II errors involves considering the significance level, sample size, and population parameters in the null and alternative hypotheses.

Lesson05_Static11

The document discusses hypothesis testing methodology and steps. It defines key terms like the null hypothesis, alternative hypothesis, type I and type II errors, and level of significance. It then covers the z-test for the mean when the population standard deviation is known, including the steps to conduct the test and examples comparing means and proportions from independent samples.

Ch5 Hypothesis Testing

1) Hypothesis testing involves specifying a null hypothesis (H0) and an alternative hypothesis (H1). The null hypothesis states that there is no difference or relationship, while the alternative hypothesis specifies a difference or relationship.
2) A statistical test is used to determine whether to reject the null hypothesis based on sample data. There is a risk of making Type I or Type II errors.
3) The p-value represents the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.

10. sampling and hypotehsis

The document discusses sampling and hypothesis testing. It defines key concepts like population, sample, parameter, statistic, sampling distribution, null hypothesis, alternative hypothesis, type I and type II errors. It explains different sampling methods and how to test hypotheses about population means using z-tests. Examples are provided to illustrate hypothesis testing for single and two population means. The summary tests hypotheses about population means using z-scores and critical values at given significance levels.

Lund 2009

This document discusses statistical principles for writing scientific manuscripts, including how to describe sampling uncertainty, present results using measures of central tendency and variability, and report findings using confidence intervals and p-values. It emphasizes quantifying and conveying measurement uncertainty and effect sizes rather than relying solely on hypothesis testing. Guidelines are proposed for systematically reporting the design, methods, results and interpretation of laboratory experiments to improve transparency and enable verification.

Hypothesis Testing

BMI (kg/m2)
22.1
23.4
24.8
26.2
27.6
28.9
30.3
31.6
32.9
34.2
35.5
36.8
38.1
39.4
The sample mean is 29.1 kg/m2 and the sample standard
deviation is 4.2 kg/m2. Test the hypothesis that the
population mean BMI is 30 kg/m2 at 5% level of
significance.

What So Funny About Proportion Testv3

The document discusses hypothesis testing and proportion tests. It provides an overview of hypothesis testing terminology and steps. It also gives examples of using one-proportion and two-proportion tests to analyze business data on regulatory compliance documentation and workload balance between regions. The null hypothesis is tested in each example to determine if there are statistically significant differences between the proportions.

Testing of hypothesis

This document discusses the process of testing hypotheses. It begins by defining hypothesis testing as a way to make decisions about population characteristics based on sample data, which involves some risk of error. The key steps are outlined as:
1) Formulating the null and alternative hypotheses, with the null hypothesis stating no difference or relationship.
2) Computing a test statistic based on the sample data and selecting a significance level, usually 5%.
3) Comparing the test statistic to critical values to either reject or fail to reject the null hypothesis.
Examples are provided to demonstrate hypothesis testing for a single mean, comparing two means, and testing a claim about population characteristics using sample data and statistics.

Hypothesis testing

This document discusses hypothesis testing, which involves drawing inferences about a population based on a sample from that population. It outlines the key elements of a hypothesis test, including the null and alternative hypotheses, test statistics, critical regions, significance levels, critical values, and p-values. Type I and Type II errors are explained, where a Type I error involves rejecting the null hypothesis when it is true, and a Type II error involves failing to reject the null when it is false. The power of a hypothesis test is defined as the probability of correctly rejecting the null hypothesis when it is false. Controlling type I and II errors involves considering the significance level, sample size, and population parameters in the null and alternative hypotheses.

Lesson05_Static11

The document discusses hypothesis testing methodology and steps. It defines key terms like the null hypothesis, alternative hypothesis, type I and type II errors, and level of significance. It then covers the z-test for the mean when the population standard deviation is known, including the steps to conduct the test and examples comparing means and proportions from independent samples.

Ch5 Hypothesis Testing

1) Hypothesis testing involves specifying a null hypothesis (H0) and an alternative hypothesis (H1). The null hypothesis states that there is no difference or relationship, while the alternative hypothesis specifies a difference or relationship.
2) A statistical test is used to determine whether to reject the null hypothesis based on sample data. There is a risk of making Type I or Type II errors.
3) The p-value represents the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.

10. sampling and hypotehsis

The document discusses sampling and hypothesis testing. It defines key concepts like population, sample, parameter, statistic, sampling distribution, null hypothesis, alternative hypothesis, type I and type II errors. It explains different sampling methods and how to test hypotheses about population means using z-tests. Examples are provided to illustrate hypothesis testing for single and two population means. The summary tests hypotheses about population means using z-scores and critical values at given significance levels.

312320.pptx

The document discusses hypothesis testing and outlines the key steps in the hypothesis testing process:
1) Formulating the null and alternative hypotheses about a population parameter. The null hypothesis is tested while the alternative is accepted if the null is rejected.
2) Determining the significance level and critical value based on this level which establishes the boundary for rejecting the null hypothesis.
3) Selecting a sample, calculating the test statistic and comparing it to the critical value to determine whether to reject or fail to reject the null hypothesis.
4) Hypothesis tests can be one-tailed, focusing rejection in one tail, or two-tailed, splitting rejection between both tails. Steps are generally the same but null and alternatives differ.

Malimu statistical significance testing.

This document provides an introduction to statistical significance testing. It discusses why significance tests are used, how they work, key terminology like p-values and hypotheses, and examples of one-sample and two-sample significance tests for means, proportions, and categorical data. Specific tests covered include the z-test, t-test, and chi-square test. The goal of significance testing is to determine whether observed differences in sample data could plausibly be due to chance or represent real effects in the underlying population.

inferentialstatistics-210411214248.pdf

This document provides an overview of inferential statistics. It defines inferential statistics as using data to make generalizations about a larger population beyond the available sample data. Key points include:
- Inferential statistics uses hypothesis testing and estimation to analyze data. It involves making inferences about a population from a sample.
- Hypothesis testing involves forming a null and alternative hypothesis, setting a significance level, choosing a statistical test, and making a decision to accept or reject the null hypothesis based on the p-value or critical value.
- Estimation provides point estimates and interval estimates like confidence intervals to describe population parameters based on sample data.
- Common inferential statistical tests covered are z-tests, t

Inferential statistics

The document provides an overview of inferential statistics. It defines inferential statistics as making generalizations about a larger population based on a sample. Key topics covered include hypothesis testing, types of hypotheses, significance tests, critical values, p-values, confidence intervals, z-tests, t-tests, ANOVA, chi-square tests, correlation, and linear regression. The document aims to explain these statistical concepts and techniques at a high level.

Nonparametric and Distribution- Free Statistics

This document summarizes several nonparametric statistical tests that do not rely on assumptions about the population distribution, including the sign test, Wilcoxon signed-rank test, median test, Mann-Whitney test, Kolmogorov-Smirnov goodness-of-fit test, and Kruskal-Wallis one-way analysis of variance. It provides details on the theoretical background, test statistics, assumptions, and procedures for the sign test for single samples and paired data. An example application of the paired sign test to a dental study is shown.

Hypothesis

This document provides an overview of hypothesis testing. It defines key terms like the null hypothesis (H0), alternative hypothesis (H1), type I and type II errors, significance level, p-values, and test statistics. It explains the basic steps in hypothesis testing as testing a claim about a population parameter by collecting a sample, determining the appropriate test statistic based on the sampling distribution, and comparing it to critical values to reject or fail to reject the null hypothesis. Examples are provided to demonstrate hypothesis tests for a mean when the population standard deviation is known or unknown.

Nonparametric and Distribution- Free Statistics _contd

This document summarizes the Wilcoxon signed-rank test, a nonparametric test used to test hypotheses about the median or location of a population when the assumptions of the t-test are not met. It provides an example applying the test to data on cardiac output measurements from 15 patients. The test calculates the differences between each observation and the hypothesized median, ranks the absolute values of the differences, and sums the ranks with positive and negative signs. The smaller of the two sums is the test statistic, which is compared to a critical value to determine if the null hypothesis that the population median equals the hypothesized value can be rejected.

Test of significance

The document discusses various statistical tests used for hypothesis testing, including parametric and non-parametric tests. It provides information on descriptive statistics, inferential statistics, and the Gaussian distribution. Key tests covered include the z-test, t-test, chi-square test, ANOVA, and their appropriate uses and calculations. Examples are given to illustrate how to apply and interpret each test.

Day-2_Presentation for SPSS parametric workshop.pptx

This document provides an overview of parametric statistical tests, including t-tests and analysis of variance (ANOVA). It discusses the concepts of statistical inference, hypothesis testing, null and alternative hypotheses, types of errors, critical regions, p-values, assumptions of t-tests, and procedures for one-sample t-tests, independent and paired t-tests, one-way ANOVA, and repeated measures ANOVA. The document is intended as part of an online workshop on using SPSS for advanced statistical data analysis.

Research methodology - Estimation Theory & Hypothesis Testing, Techniques of ...

Fundamentals, Standard Error, Estimation, Interval Estimation, Hypothesis, Characteristics of Hypothesis, Testing The Hypothesis, Type I & Type II error, One tailed & Two tailed test, Tabulated Values, Chi-square (2) Test, Analysis of variance (ANOVA)Introduction, The Sign Test, The rank sum test or The Mann-Whitney U test, Determination of Sample Size

hypothesis.pptx

Hypothesis testing involves setting up a null hypothesis and alternative hypothesis, determining a significance level, calculating a test statistic, identifying the critical region, computing the test statistic value based on a sample, and making a decision to reject or fail to reject the null hypothesis. The z-test is used when the sample size is large and the population standard deviation is known, while the t-test is used for small samples when the population standard deviation is unknown. Both tests involve calculating a test statistic and comparing it to critical values to determine if there is sufficient evidence to reject the null hypothesis. Limitations include that the tests only indicate differences and not the reasons for them, and inferences are based on probabilities rather than certainty.

Statistics for Lab Scientists

Statistics and experimental design are important for drawing valid conclusions from research. Well-designed experiments produce unbiased comparisons, precise estimates, and account for variability. Hypothesis tests answer yes/no questions about population values and aim to reject false null hypotheses. P-values indicate the likelihood of obtaining extreme data if the null is true. Multiple testing increases chances of false positives, requiring adjustments. Sample size impacts power to detect effects and precision of estimates. Both statistical and practical significance must be considered.

Basics of Hypothesis testing for Pharmacy

This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data

Unit 3

This document discusses hypothesis testing and the t-test. It covers:
1) The basics of hypothesis testing including null and alternative hypotheses, types of hypotheses, and types of errors.
2) The t-test, which is used for small samples from a normally distributed population. It relies on the t-distribution and the degree of freedom.
3) Applications of the t-test including testing the significance of a single mean, difference between two means, and paired t-tests.
4) When sample sizes are large, the normal distribution can be used instead in Z-tests for similar applications.

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.

Topic 7 stat inference

The document discusses statistical hypothesis testing. It defines key terms like the null hypothesis, alternative hypothesis, test statistic, rejection region, Type I and Type II errors, significance level, and p-value. It also describes the steps to conduct a hypothesis test including stating the hypotheses, choosing a test statistic, determining critical values, and interpreting the conclusions. Specific hypothesis tests for a population mean are also covered, including tests when the population variance is known versus unknown.

K.A.Sindhura-t,z,f tests

This document provides information about statistical hypothesis testing procedures including t-tests, z-tests, and F-tests. It defines key terms like the null hypothesis, alternative hypothesis, and level of significance. It explains the steps to conduct hypothesis tests including setting the hypotheses, fixing the significance level, choosing a test criterion, performing calculations, and making a conclusion. Specifically, it discusses one-sample and two-sample z-tests for large samples and one-sample and two-sample t-tests for small samples. The assumptions, conditions, and procedures for each test are outlined in detail over multiple pages.

Hypothesis testing

The document provides an overview of hypothesis testing. It begins by defining a hypothesis test and its purpose of ruling out chance as an explanation for research study results. It then outlines the logic and steps of a hypothesis test: 1) stating hypotheses, 2) setting decision criteria, 3) collecting data, 4) making a decision. Key concepts discussed include type I and type II errors, statistical significance, test statistics like the z-score, and assumptions of hypothesis testing. Factors that can influence a hypothesis test like effect size, sample size, and alpha level are also covered.

Inferential statistics

This document discusses inferential statistics and provides examples to illustrate key concepts. Inferential statistics involves drawing conclusions about populations from sample data using probability and statistical testing. Common situations where inferential statistics are used include comparing differences between two or more samples, estimating population parameters from samples, and assessing correlations. Key steps involve defining a null hypothesis, choosing an appropriate statistical test based on the type of variable (qualitative or quantitative) and sample size, calculating a test statistic, determining the probability, and interpreting results to either reject or fail to reject the null hypothesis. Examples are provided to demonstrate applying concepts like hypothesis testing, choosing between tests, and interpreting outcomes.

RM U3 MGR Hypothesis Testing.ppt

Hypothesis testing is used to determine if a treatment has an effect by ruling out chance as an explanation for study results. It involves taking a sample from a population, administering a treatment, measuring outcomes, and comparing the sample to the original population. If the sample is noticeably different, it provides evidence the treatment had an effect. However, differences could also be due to sampling error. Hypothesis testing decides between two explanations: the difference is due to sampling error or the difference is too large to be due to chance and indicates a treatment effect.

sesion1.ppt

Este documento presenta una introducción a la econometría. Explica que la econometría ayuda a combinar la teoría económica y los datos económicos para tomar mejores decisiones económicas. También describe los modelos econométricos básicos, incluido el modelo de regresión lineal simple, y los supuestos subyacentes a estos modelos. Finalmente, introduce conceptos clave como el término de error y los mínimos cuadrados ordinarios.

312320.pptx

The document discusses hypothesis testing and outlines the key steps in the hypothesis testing process:
1) Formulating the null and alternative hypotheses about a population parameter. The null hypothesis is tested while the alternative is accepted if the null is rejected.
2) Determining the significance level and critical value based on this level which establishes the boundary for rejecting the null hypothesis.
3) Selecting a sample, calculating the test statistic and comparing it to the critical value to determine whether to reject or fail to reject the null hypothesis.
4) Hypothesis tests can be one-tailed, focusing rejection in one tail, or two-tailed, splitting rejection between both tails. Steps are generally the same but null and alternatives differ.

Malimu statistical significance testing.

This document provides an introduction to statistical significance testing. It discusses why significance tests are used, how they work, key terminology like p-values and hypotheses, and examples of one-sample and two-sample significance tests for means, proportions, and categorical data. Specific tests covered include the z-test, t-test, and chi-square test. The goal of significance testing is to determine whether observed differences in sample data could plausibly be due to chance or represent real effects in the underlying population.

inferentialstatistics-210411214248.pdf

This document provides an overview of inferential statistics. It defines inferential statistics as using data to make generalizations about a larger population beyond the available sample data. Key points include:
- Inferential statistics uses hypothesis testing and estimation to analyze data. It involves making inferences about a population from a sample.
- Hypothesis testing involves forming a null and alternative hypothesis, setting a significance level, choosing a statistical test, and making a decision to accept or reject the null hypothesis based on the p-value or critical value.
- Estimation provides point estimates and interval estimates like confidence intervals to describe population parameters based on sample data.
- Common inferential statistical tests covered are z-tests, t

Inferential statistics

The document provides an overview of inferential statistics. It defines inferential statistics as making generalizations about a larger population based on a sample. Key topics covered include hypothesis testing, types of hypotheses, significance tests, critical values, p-values, confidence intervals, z-tests, t-tests, ANOVA, chi-square tests, correlation, and linear regression. The document aims to explain these statistical concepts and techniques at a high level.

Nonparametric and Distribution- Free Statistics

This document summarizes several nonparametric statistical tests that do not rely on assumptions about the population distribution, including the sign test, Wilcoxon signed-rank test, median test, Mann-Whitney test, Kolmogorov-Smirnov goodness-of-fit test, and Kruskal-Wallis one-way analysis of variance. It provides details on the theoretical background, test statistics, assumptions, and procedures for the sign test for single samples and paired data. An example application of the paired sign test to a dental study is shown.

Hypothesis

This document provides an overview of hypothesis testing. It defines key terms like the null hypothesis (H0), alternative hypothesis (H1), type I and type II errors, significance level, p-values, and test statistics. It explains the basic steps in hypothesis testing as testing a claim about a population parameter by collecting a sample, determining the appropriate test statistic based on the sampling distribution, and comparing it to critical values to reject or fail to reject the null hypothesis. Examples are provided to demonstrate hypothesis tests for a mean when the population standard deviation is known or unknown.

Nonparametric and Distribution- Free Statistics _contd

This document summarizes the Wilcoxon signed-rank test, a nonparametric test used to test hypotheses about the median or location of a population when the assumptions of the t-test are not met. It provides an example applying the test to data on cardiac output measurements from 15 patients. The test calculates the differences between each observation and the hypothesized median, ranks the absolute values of the differences, and sums the ranks with positive and negative signs. The smaller of the two sums is the test statistic, which is compared to a critical value to determine if the null hypothesis that the population median equals the hypothesized value can be rejected.

Test of significance

The document discusses various statistical tests used for hypothesis testing, including parametric and non-parametric tests. It provides information on descriptive statistics, inferential statistics, and the Gaussian distribution. Key tests covered include the z-test, t-test, chi-square test, ANOVA, and their appropriate uses and calculations. Examples are given to illustrate how to apply and interpret each test.

Day-2_Presentation for SPSS parametric workshop.pptx

This document provides an overview of parametric statistical tests, including t-tests and analysis of variance (ANOVA). It discusses the concepts of statistical inference, hypothesis testing, null and alternative hypotheses, types of errors, critical regions, p-values, assumptions of t-tests, and procedures for one-sample t-tests, independent and paired t-tests, one-way ANOVA, and repeated measures ANOVA. The document is intended as part of an online workshop on using SPSS for advanced statistical data analysis.

Research methodology - Estimation Theory & Hypothesis Testing, Techniques of ...

Fundamentals, Standard Error, Estimation, Interval Estimation, Hypothesis, Characteristics of Hypothesis, Testing The Hypothesis, Type I & Type II error, One tailed & Two tailed test, Tabulated Values, Chi-square (2) Test, Analysis of variance (ANOVA)Introduction, The Sign Test, The rank sum test or The Mann-Whitney U test, Determination of Sample Size

hypothesis.pptx

Hypothesis testing involves setting up a null hypothesis and alternative hypothesis, determining a significance level, calculating a test statistic, identifying the critical region, computing the test statistic value based on a sample, and making a decision to reject or fail to reject the null hypothesis. The z-test is used when the sample size is large and the population standard deviation is known, while the t-test is used for small samples when the population standard deviation is unknown. Both tests involve calculating a test statistic and comparing it to critical values to determine if there is sufficient evidence to reject the null hypothesis. Limitations include that the tests only indicate differences and not the reasons for them, and inferences are based on probabilities rather than certainty.

Statistics for Lab Scientists

Statistics and experimental design are important for drawing valid conclusions from research. Well-designed experiments produce unbiased comparisons, precise estimates, and account for variability. Hypothesis tests answer yes/no questions about population values and aim to reject false null hypotheses. P-values indicate the likelihood of obtaining extreme data if the null is true. Multiple testing increases chances of false positives, requiring adjustments. Sample size impacts power to detect effects and precision of estimates. Both statistical and practical significance must be considered.

Basics of Hypothesis testing for Pharmacy

This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data

Unit 3

This document discusses hypothesis testing and the t-test. It covers:
1) The basics of hypothesis testing including null and alternative hypotheses, types of hypotheses, and types of errors.
2) The t-test, which is used for small samples from a normally distributed population. It relies on the t-distribution and the degree of freedom.
3) Applications of the t-test including testing the significance of a single mean, difference between two means, and paired t-tests.
4) When sample sizes are large, the normal distribution can be used instead in Z-tests for similar applications.

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.

Topic 7 stat inference

The document discusses statistical hypothesis testing. It defines key terms like the null hypothesis, alternative hypothesis, test statistic, rejection region, Type I and Type II errors, significance level, and p-value. It also describes the steps to conduct a hypothesis test including stating the hypotheses, choosing a test statistic, determining critical values, and interpreting the conclusions. Specific hypothesis tests for a population mean are also covered, including tests when the population variance is known versus unknown.

K.A.Sindhura-t,z,f tests

This document provides information about statistical hypothesis testing procedures including t-tests, z-tests, and F-tests. It defines key terms like the null hypothesis, alternative hypothesis, and level of significance. It explains the steps to conduct hypothesis tests including setting the hypotheses, fixing the significance level, choosing a test criterion, performing calculations, and making a conclusion. Specifically, it discusses one-sample and two-sample z-tests for large samples and one-sample and two-sample t-tests for small samples. The assumptions, conditions, and procedures for each test are outlined in detail over multiple pages.

Hypothesis testing

The document provides an overview of hypothesis testing. It begins by defining a hypothesis test and its purpose of ruling out chance as an explanation for research study results. It then outlines the logic and steps of a hypothesis test: 1) stating hypotheses, 2) setting decision criteria, 3) collecting data, 4) making a decision. Key concepts discussed include type I and type II errors, statistical significance, test statistics like the z-score, and assumptions of hypothesis testing. Factors that can influence a hypothesis test like effect size, sample size, and alpha level are also covered.

Inferential statistics

This document discusses inferential statistics and provides examples to illustrate key concepts. Inferential statistics involves drawing conclusions about populations from sample data using probability and statistical testing. Common situations where inferential statistics are used include comparing differences between two or more samples, estimating population parameters from samples, and assessing correlations. Key steps involve defining a null hypothesis, choosing an appropriate statistical test based on the type of variable (qualitative or quantitative) and sample size, calculating a test statistic, determining the probability, and interpreting results to either reject or fail to reject the null hypothesis. Examples are provided to demonstrate applying concepts like hypothesis testing, choosing between tests, and interpreting outcomes.

RM U3 MGR Hypothesis Testing.ppt

Hypothesis testing is used to determine if a treatment has an effect by ruling out chance as an explanation for study results. It involves taking a sample from a population, administering a treatment, measuring outcomes, and comparing the sample to the original population. If the sample is noticeably different, it provides evidence the treatment had an effect. However, differences could also be due to sampling error. Hypothesis testing decides between two explanations: the difference is due to sampling error or the difference is too large to be due to chance and indicates a treatment effect.

312320.pptx

312320.pptx

Malimu statistical significance testing.

Malimu statistical significance testing.

inferentialstatistics-210411214248.pdf

inferentialstatistics-210411214248.pdf

Inferential statistics

Inferential statistics

Nonparametric and Distribution- Free Statistics

Nonparametric and Distribution- Free Statistics

Hypothesis

Hypothesis

Nonparametric and Distribution- Free Statistics _contd

Nonparametric and Distribution- Free Statistics _contd

Test of significance

Test of significance

Day-2_Presentation for SPSS parametric workshop.pptx

Day-2_Presentation for SPSS parametric workshop.pptx

Research methodology - Estimation Theory & Hypothesis Testing, Techniques of ...

Research methodology - Estimation Theory & Hypothesis Testing, Techniques of ...

hypothesis.pptx

hypothesis.pptx

Statistics for Lab Scientists

Statistics for Lab Scientists

Basics of Hypothesis testing for Pharmacy

Basics of Hypothesis testing for Pharmacy

Unit 3

Unit 3

Lecture2 hypothesis testing

Lecture2 hypothesis testing

Topic 7 stat inference

Topic 7 stat inference

K.A.Sindhura-t,z,f tests

K.A.Sindhura-t,z,f tests

Hypothesis testing

Hypothesis testing

Inferential statistics

Inferential statistics

RM U3 MGR Hypothesis Testing.ppt

RM U3 MGR Hypothesis Testing.ppt

sesion1.ppt

Este documento presenta una introducción a la econometría. Explica que la econometría ayuda a combinar la teoría económica y los datos económicos para tomar mejores decisiones económicas. También describe los modelos econométricos básicos, incluido el modelo de regresión lineal simple, y los supuestos subyacentes a estos modelos. Finalmente, introduce conceptos clave como el término de error y los mínimos cuadrados ordinarios.

Part-6-1-D-Motion-Free Fall-Physics 101.pdf

The document summarizes key concepts about freely falling objects and one-dimensional motion. It discusses that freely falling objects only experience the downward force of gravity. Galileo's experiment showing that objects of different masses fall at the same rate is mentioned. Equations of motion are provided for objects falling with initial velocities of zero, upward, or downward. Several example problems are worked through applying these equations to calculate time, displacement, velocity, and position at different times for balls thrown, dropped, or falling from heights.

FRD.pdf

PDF

hypothesis_testing-ch9-39-14402.pdf

1. The document discusses the basic principles of hypothesis testing, including stating the null and alternative hypotheses, selecting a significance level, choosing a test statistic, determining critical values, and making a decision to reject or fail to reject the null hypothesis.
2. It outlines the five steps of hypothesis testing: state hypotheses, select significance level, select test statistic, determine critical value, and make a decision.
3. Key terms discussed include type I and type II errors, significance levels, critical values, test statistics such as z and t, and the decision to reject or fail to reject the null hypothesis.

series.pdf

This document provides an overview of sequences and series. It defines what a sequence is, discusses concepts like convergence and divergence of sequences, and introduces common types of sequences like an = n and an = 1/n. It also presents rules for determining limits of sequences, such as the sum and product rules. Examples are provided to demonstrate applying these rules and the squeeze theorem for limits.

One-tailed-Test-or-Two-tailed-Test(1).pdf

This document discusses one-tailed and two-tailed hypothesis tests. It explains that a one-tailed test looks for an increase or decrease in a parameter, while a two-tailed test looks for any change. If the claim uses words like "increased" or "decreased", it is a one-tailed test, while terms like "change" or "different" indicate a two-tailed test. A one-tailed test has a critical region in one tail, while a two-tailed test has critical regions in both tails. The example given is a one-tailed test comparing civil engineering and B.A. salaries, with the alternative hypothesis that engineering salaries are greater than B.A. salaries.

One-tailed-Test-or-Two-tailed-Test.pdf

This document discusses one-tailed and two-tailed hypothesis tests. It explains that a one-tailed test looks for an increase or decrease in a parameter, while a two-tailed test looks for any change. If the claim uses words like "increased" or "decreased", it is a one-tailed test, while terms like "change" or "different" indicate a two-tailed test. A one-tailed test has a critical region in one tail, while a two-tailed test has critical regions in both tails. The example given is a one-tailed test comparing civil engineering and B.A. salaries, with the alternative hypothesis that engineering salaries are greater than B.A. salaries.

Gerstman_PP09.ppt

This document provides an overview of hypothesis testing and the steps involved. It discusses:
1) Defining the null and alternative hypotheses based on the research question. The null hypothesis represents "no difference" while the alternative hypothesis claims the null is false.
2) Calculating the test statistic, which is used to test the null hypothesis. For a one-sample z-test, this involves calculating the z-score when the population standard deviation is known.
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- 2. CONTENT OUTLINE Logic of Hypothesis Testing Error & Alpha Hypothesis Tests Effect Size Statistical Power HYPOTHESIS TESTING 2
- 3. HYPOTHESIS TESTING LOGIC OF HYPOTHESIS TESTING how we conceptualize hypotheses 3
- 4. HYPOTHESIS TESTING HYPOTHESIS TESTING LOGIC Hypothesis Test statistical method that uses sample data to evaluate a hypothesis about a population The Logic State a hypothesis about a population, usually concerning a population parameter Predict characteristics of a sample Obtain a random sample from the population Compare obtained data to prediction to see if they are consistent 4
- 5. HYPOTHESIS TESTING STEPS IN HYPOTHESIS TESTING Step 1: State the Hypotheses Null Hypothesis (H0) in the general population there is no change, no difference, or no relationship; the independent variable will have no effect on the dependent variable o Example • All dogs have four legs. • There is no difference in the number of legs dogs have. Alternative Hypothesis (H1) in the general population there is a change, a difference, or a relationship; the independent variable will have an effect on the dependent variable o Example • 20% of dogs have only three legs. 5
- 6. HYPOTHESIS TESTING STEP 1: STATE THE HYPOTHESES (EXAMPLE) Example 6 How to Acea Statistics Exam little known facts about the positive impact of alcohol on memory during “cram” sessions
- 7. HYPOTHESIS TESTING STEP 1: STATE THE HYPOTHESES (EXAMPLE) Dependent Variable Amount of alcohol consumed the night before a statistics exam Independent/Treatment Variable Intervention: Pamphlet (treatment group) or No Pamphlet (control group) Null Hypothesis (H0) No difference in alcohol consumption between the two groups the night before a statistics exam. Alternative Hypothesis (H1) The treatment group will consume more alcohol than the control group. 7
- 8. HYPOTHESIS TESTING STEP 2: SET CRITERIA FOR DECISION Example Exam 1 (Previous Semester): μ = 85 Null Hypothesis (H0): treatment group will have mean exam score of M = 85 (σ = 8) Alternative Hypothesis (H1): treatment group mean exam score will differ from M = 85 8
- 9. HYPOTHESIS TESTING STEP 2: SET CRITERIA FOR DECISION Alpha Level/Level of Significance probability value used to define the (unlikely) sample outcomes if the null hypothesis is true; e.g., α = .05, α = .01, α = .001 Critical Region extreme sample values that are very unlikely to be obtained if the null hypothesis is true Boundaries determined by alpha level If sample data falls within this region (the shaded tails), reject the null hypothesis 9
- 10. HYPOTHESIS TESTING STEP 2: SET CRITERIA FOR DECISION Critical Region Boundaries Assume normal distribution Alpha Level + Unit Normal Table Example: if α = .05, boundaries of critical region divide middle 95% from extreme 5% o 2.5% in each tail (2-tailed) 10
- 11. HYPOTHESIS TESTING STEP 2: SET CRITERIA FOR DECISION Boundaries for Critical Region 11 α = .001 z = ±3.30 α = .01 z = ±2.58 α = .05 z = ±1.96
- 12. HYPOTHESIS TESTING STEP 3: COLLECT, COMPUTE Collect data Compute sample mean Transform sample mean M to z-score Example #2 12 M M z 85 . 8 13 . 1 10 13 . 1 85 95 z
- 13. HYPOTHESIS TESTING STEP 4: MAKE A DECISION Compare z-score with boundary of critical region for selected level of significance If… z-score falls in the tails, our mean is significantly different from H0 o Reject H0 z-score falls between the tails, our mean is not significantly different from H0 o Fail to reject H0 13
- 14. HYPOTHESIS TESTING HYPOTHESIS TESTING: AN EXAMPLE (2-TAIL) How to Ace a Statistics Exam… Population: μ = 85, σ = 8 Hypotheses o H0: Sample mean will not differ from M = 85 o H1: Sample mean will differ from M = 85 Set Criteria (Significance Level/Alpha Level) o α = .05 14
- 15. HYPOTHESIS TESTING HYPOTHESIS TESTING: EXAMPLE (2-TAIL) How to Ace a Statistics Exam… Collect Data & Compute Statistics o Intervention to 9 students o Mean exam score, M = 90 15 67 . 2 3 8 9 M 87 . 1 67 . 2 5 67 . 2 85 90 z
- 16. HYPOTHESIS TESTING HYPOTHESIS TESTING: EXAMPLE (2-TAIL) How to Ace a Statistics Exam… Decision: Fail to reject H0 16 σM = 2.67 μ = 85 M = 90 Reject H0 -1.96 z = 0 +1.96 Reject H0
- 17. HYPOTHESIS TESTING REVISITING Z-SCORE STATISTICS A Test Statistic Single, specific statistic Calculated from the sample data Used to test H0 Rule of Thumb… Large values of z o Sample data pry DID NOT occur by chance – result of IV Small values of z o Sample data pry DID occur by chance – not result of IV 17
- 18. HYPOTHESIS TESTING ERROR & ALPHA uncertainty leads to error 18
- 19. HYPOTHESIS TESTING UNCERTAINTY & ERROR Hypothesis Testing = Inferential Process LOTS of room for error Types of Error Type I Error Type II Error 19
- 20. HYPOTHESIS TESTING TYPE 1 ERRORS error that occurs when the null hypothesis is rejected even though it is really true; the researcher identifies a treatment effect that does not really exist (a false positive) Common Cause & Biggest Problem Sample data are misleading due to sampling error Significant difference reported in literature even though it isn’t real Type I Errors & Alpha Level Alpha level = probability of committing a Type I Error Lower alphas = less chances of Type I Error 20
- 21. HYPOTHESIS TESTING TYPE II ERRORS error that occurs when the null hypothesis is not rejected even it is really false; the researcher does not identify a treatment effect that really exists (a false negative) Common Cause & Biggest Problem Sample mean in not in critical region even though there is a treatment effect Overlook effectiveness of interventions Type II Errors & Probability β = probability of committing a Type II Error 21
- 22. HYPOTHESIS TESTING TYPE I & TYPE II ERRORS Experimenter’s Decision 22 Actual Situation No Effect, H0 True Effect Exists, H0 False Reject H0 Type I Error Retain H0 Type II Error
- 23. HYPOTHESIS TESTING SELECTING AN ALPHA LEVEL Functions of Alpha Level Critical region boundaries Probability of a Type I error Primary Concern in Alpha Selection Minimize risk of Type I Error without maximizing risk of Type II Error Common Alpha Levels α = .05, α = .01, α = .001 23
- 24. HYPOTHESIS TESTING HYPOTHESIS TESTS testing null hypotheses 24
- 25. HYPOTHESIS TESTING HYPOTHESIS TESTS: INFLUENTIAL FACTORS Magnitude of difference between sample mean and population mean (in z- score formula, larger difference larger numerator) Variability of scores (influences σM; more variability larger σM) Sample size (influences σM; larger sample size smaller σM) 25 M M z n M
- 26. HYPOTHESIS TESTING HYPOTHESIS TESTS: ASSUMPTIONS Random Sampling Independent Observations Value of σ is Constant Despite treatment Normal sampling distribution 26
- 27. HYPOTHESIS TESTING NON-DIRECTIONAL HYPOTHESIS TESTS Critical regions for 2-tailed tests 27 α = .001 z = ±3.30 α = .01 z = ±2.58 α = .05 z = ±1.96
- 28. HYPOTHESIS TESTING DIRECTIONAL HYPOTHESIS TESTS Critical regions for 1-tailed tests Blue or Green tail of distribution – NOT BOTH 28 z = -3.10 α = .01 α = .05 α = .001 z = -1.65 z = -2.33 z = +1.65 z = +3.10 z = +2.33 α = .01 α = .05 α = .001
- 29. HYPOTHESIS TESTING ALTERNATIVE HYPOTHESES Alternative Hypotheses for 2-tailed tests Do not specify direction of difference Do not hypothesize whether sample mean should be lower or higher than population mean Alternative Hypotheses for 1-tailed tests Specify a difference Hypothesis specifies whether sample mean should be lower or higher than population mean 29
- 30. HYPOTHESIS TESTING NULL HYPOTHESES Null Hypotheses for 2-tailed tests Specify no difference between sample & population Null Hypotheses for 1-tailed tests Specify the opposite of the alternative hypothesis Example #2 o H0: μ ≤ 85 (There is no increase in test scores.) o H1: μ > 85 (There is an increase in test scores.) 30
- 31. HYPOTHESIS TESTING HYPOTHESIS TESTS: AN EXAMPLE (1-TAIL) How to Ace a Statistics Exam… Population: μ = 85, σ = 8 Hypotheses o H0: Sample mean will be less than or equal to M = 85 o H1: Sample mean be greater than M = 85 Set Criteria (Significance Level/Alpha Level) o α = .05 31
- 32. HYPOTHESIS TESTING HYPOTHESIS TESTS: AN EXAMPLE (1-TAIL) How to Ace a Statistics Exam… Collect Data & Compute Statistics o Intervention to 9 students o Mean exam score, M = 90 32 67 . 2 3 8 9 M 87 . 1 67 . 2 5 67 . 2 85 90 M M z
- 33. HYPOTHESIS TESTING HYPOTHESIS TESTS: AN EXAMPLE (1-TAIL) How to Ace a Statistics Exam… Decision: Reject H0 33 σM = 2.67 μ = 85 M = 90 z = 0 +1.65 Reject H0
- 34. HYPOTHESIS TESTING EFFECT SIZE estimating the magnitude of an effect 34
- 35. HYPOTHESIS TESTING EFFECT SIZE Problem with hypothesis testing Significance ≠ Meaningful/Important/Big Effect o Significance is relative comparison: treatment effect compared to standard error Effect Size statistic that describes the magnitude of an effect Measures size of treatment effect in terms of (population) standard deviation 35
- 36. HYPOTHESIS TESTING EFFECT SIZE: COHEN’S D Not influenced by sample size Evaluating Cohen’s d d = 0.2 – Small Effect (mean difference ≈ 0.2 standard deviation) d = 0.5 – Medium Effect (mean difference ≈ 0.5 standard deviation) d = 0.8 – Large Effect (mean difference ≈ 0.8 standard deviation) Calculated the same for 1-tailed and 2-tailed tests 36 Cohen’s d = mean difference standard deviation
- 37. HYPOTHESIS TESTING STATISTICAL POWER probability of correctly rejecting a false null hypothesis 37
- 38. HYPOTHESIS TESTING STATISTICAL POWER the probability of correctly rejecting a null hypothesis when it is not true; the probability that a hypothesis test will identify a treatment effect when if one really exists A priori Calculate power before collecting data Determine probability of finding treatment effect Power is influenced by… Sample size Expected effect size Significance level for hypothesis test (α) 38