This chapter discusses inferential statistics and their underlying concepts. It covers key topics like types of inferential statistics (parametric vs nonparametric), important perspectives like generalizing from samples to populations, conceptual underpinnings such as null/alternative hypotheses and errors. Specific statistical techniques are explained like t-tests, ANOVA, regression as well as important considerations like sample distributions, standard error, degrees of freedom, and the steps to conduct statistical tests.
This document provides an overview of common statistical significance tests including Pearson's chi-square test, t-tests, and analysis of variance (ANOVA). It defines key concepts like significance, level of significance (p-value), and conditions for applying each test. Chi-square can test for goodness of fit, homogeneity, and independence. T-tests compare means between two groups. ANOVA determines if multiple sample means are equal and has assumptions of independence, normality, and equal variances. One-way ANOVA considers one factor between subjects.
This chapter discusses inferential statistics and the concepts underlying them. It covers key topics like types of inferential statistics (parametric vs nonparametric), important perspectives like generalizing from samples to populations, underlying concepts like null/alternative hypotheses and types of errors. Specific statistical techniques are explained like t-tests, ANOVA, regression, along with key ideas like sampling distributions, standard error, degrees of freedom, and the steps to conduct statistical tests. Different types of samples and issues with gain scores are also addressed.
This document provides an overview of key concepts in inferential statistics. Inferential statistics allows researchers to make inferences about populations based on samples. It includes techniques like hypothesis testing, t-tests, analysis of variance (ANOVA), regression analysis, and more. The goal is to determine if observed differences are statistically significant rather than due to chance. Inferential statistics helps estimate parameters and analyze variability using statistical models and software.
This document provides an overview of multivariate analysis techniques. It defines multiple regression, discriminant analysis, MANOVA, structural equation modeling, conjoint analysis, factor analysis, cluster analysis, and multidimensional scaling. For each technique, it outlines their uses, outputs, and key concepts. The overall purpose is to help readers understand how to classify and apply different multivariate methods to analyze relationships between multiple variables and classify objects.
This document provides an overview of quantitative analysis techniques using SPSS, including data manipulation, transformation, and cleaning methods. It also covers univariate, bivariate, and other statistical analysis methods for exploring relationships between variables and differences between groups. Specific techniques discussed include computing new variables, recoding, selecting cases, imputing missing values, aggregating data, sorting, merging files, descriptive statistics, correlations, regressions, t-tests, ANOVA, non-parametric tests, and more.
This document discusses key concepts related to sampling and measurement in research. It covers topics such as population and sampling criteria when selecting a sample. It also discusses levels of measurement, reliability, validity, and different measurement strategies like interviews, questionnaires, and scales. Finally, it provides an overview of statistical analysis, including descriptive statistics, levels of measurement, and common statistical tests. The overall purpose is to introduce fundamental concepts for designing research studies and analyzing quantitative data.
An Overview and Application of Discriminant Analysis in Data AnalysisIOSR Journals
This document provides an overview of discriminant analysis, including its history, key assumptions, and different types (e.g. linear, quadratic). It discusses advantages of discriminant analysis compared to logistic regression, such as its ability to handle small sample sizes. The document also describes steps to develop a discriminant model, including variable selection, assumptions checking, and evaluation. It then presents an application of discriminant analysis to classify failed vs successful companies in Nigeria based on financial ratios. The model was able to predict company failure up to 3 years in advance.
This document provides an overview of common statistical significance tests including Pearson's chi-square test, t-tests, and analysis of variance (ANOVA). It defines key concepts like significance, level of significance (p-value), and conditions for applying each test. Chi-square can test for goodness of fit, homogeneity, and independence. T-tests compare means between two groups. ANOVA determines if multiple sample means are equal and has assumptions of independence, normality, and equal variances. One-way ANOVA considers one factor between subjects.
This chapter discusses inferential statistics and the concepts underlying them. It covers key topics like types of inferential statistics (parametric vs nonparametric), important perspectives like generalizing from samples to populations, underlying concepts like null/alternative hypotheses and types of errors. Specific statistical techniques are explained like t-tests, ANOVA, regression, along with key ideas like sampling distributions, standard error, degrees of freedom, and the steps to conduct statistical tests. Different types of samples and issues with gain scores are also addressed.
This document provides an overview of key concepts in inferential statistics. Inferential statistics allows researchers to make inferences about populations based on samples. It includes techniques like hypothesis testing, t-tests, analysis of variance (ANOVA), regression analysis, and more. The goal is to determine if observed differences are statistically significant rather than due to chance. Inferential statistics helps estimate parameters and analyze variability using statistical models and software.
This document provides an overview of multivariate analysis techniques. It defines multiple regression, discriminant analysis, MANOVA, structural equation modeling, conjoint analysis, factor analysis, cluster analysis, and multidimensional scaling. For each technique, it outlines their uses, outputs, and key concepts. The overall purpose is to help readers understand how to classify and apply different multivariate methods to analyze relationships between multiple variables and classify objects.
This document provides an overview of quantitative analysis techniques using SPSS, including data manipulation, transformation, and cleaning methods. It also covers univariate, bivariate, and other statistical analysis methods for exploring relationships between variables and differences between groups. Specific techniques discussed include computing new variables, recoding, selecting cases, imputing missing values, aggregating data, sorting, merging files, descriptive statistics, correlations, regressions, t-tests, ANOVA, non-parametric tests, and more.
This document discusses key concepts related to sampling and measurement in research. It covers topics such as population and sampling criteria when selecting a sample. It also discusses levels of measurement, reliability, validity, and different measurement strategies like interviews, questionnaires, and scales. Finally, it provides an overview of statistical analysis, including descriptive statistics, levels of measurement, and common statistical tests. The overall purpose is to introduce fundamental concepts for designing research studies and analyzing quantitative data.
An Overview and Application of Discriminant Analysis in Data AnalysisIOSR Journals
This document provides an overview of discriminant analysis, including its history, key assumptions, and different types (e.g. linear, quadratic). It discusses advantages of discriminant analysis compared to logistic regression, such as its ability to handle small sample sizes. The document also describes steps to develop a discriminant model, including variable selection, assumptions checking, and evaluation. It then presents an application of discriminant analysis to classify failed vs successful companies in Nigeria based on financial ratios. The model was able to predict company failure up to 3 years in advance.
The presentation covered key steps in analyzing survey data including defining goals, designing valid and reliable survey questions, collecting data, cleaning data, conducting descriptive statistics and correlations, comparing mean differences between groups, and clearly presenting results along with conclusions and recommendations. Piloting surveys and continuously improving methods was also emphasized.
This document provides definitions and explanations of key concepts in biostatistics and statistical hypothesis testing, including:
- Types of data/variables, measures of central tendency, measures of dispersion
- Descriptive vs inferential statistics, populations and samples
- Assumptions of parametric tests, tests of normality, homogeneity of variance
- Components of hypothesis testing, types of errors, significance levels and p-values
- T-tests, ANOVA, within-subjects and between-subjects designs
This document discusses hypothesis testing and inferential statistics. It covers topics like hypothesis testing process, types of errors, differentiating between critical value method and probability value method, tests for one and two populations including z-test, t-test, Wilcoxon test and binomial test. It also discusses assumptions and procedures for tests like pooled t-test, paired t-test, Mann-Whitney test and paired Wilcoxon test. Examples of applying these tests on quantitative and qualitative data are provided.
This document provides an overview of quantitative data analysis techniques for hypothesis testing, including types of errors, statistical power, and tests for single and multiple sample means. It also discusses regression analysis, issues of multicollinearity, and other multivariate tests such as discriminant analysis, logistic regression, and canonical correlation.
Research Methodology: Questionnaire, Sampling, Data Preparationamitsethi21985
As per PTU's MBA Syllabus, Unit No. 2: Sources Of Data: Primary And Secondary; Data Collection Methods; Questionnaire Designing: Construction, Types And Developing A Good Questionnaire. Sampling Design and Techniques, Scaling Techniques, Meaning, Types, Data Processing Operations, Editing, Coding, Classification, Tabulation. Research Proposal/Synopsis Writing. Practical Framework
The document discusses inferential statistics and its applications. It defines statistics as dealing with collecting, classifying, presenting, comparing, and interpreting numerical data to make inferences about a population. Inferential statistics help decision makers present information, draw conclusions from samples, seek relationships between variables, and make reliable forecasts. The document also distinguishes between descriptive statistics, parametric inferential statistics that assume normal distributions, and non-parametric inferential statistics that make no distribution assumptions.
This document outlines statistical analysis techniques that can be performed in SPSS, including loading and preparing data, descriptive statistics like frequencies and cross tabulations, inferential statistics like t-tests, ANOVA, correlation, and reliability analysis, and exporting results. Chi-square tests examine relationships between categorical variables while t-tests compare means and ANOVA examines differences in means between groups. Correlation analyzes relationships between interval variables.
Researchers use several tools and procedures for analyzing quantitative data obtained from different types of experimental designs. Different designs call for different methods of analysis. This presentation focuses on:
T-test
Analysis of variance (F-test), and
Chi-square test
Modul Ajar Statistika Inferensia ke-13: Analisis Variansi, Eksperimentasi Fak...Arif Rahman
This document discusses statistical analysis and experimental design. It defines statistics as the branch of mathematics concerned with collecting, organizing, summarizing, simplifying, presenting, interpreting, analyzing and synthesizing data to help solve problems and make decisions. It discusses the goals and principles of experimental design, including replication to estimate experimental error, randomization to ensure statistical validity, and local control to reduce experimental error. Key aspects like blocking, balancing and grouping techniques are explained as methods to control nuisance factors and refine heterogeneous data in experimental design.
This document provides an overview of essentials for manuscript review, including how to organize a manuscript, use statistics, identify types of studies and levels of evidence, address bias, interpret results, and write an abstract, introduction, methods, discussion, and conclusion. It discusses key aspects of each section and how to effectively review a submitted manuscript.
This document provides an overview of descriptive statistics and graphing techniques used in survey research and psychology. It discusses getting to know data, levels of measurement, descriptive statistics for different data types, properties of the normal distribution, and non-normal distributions. Graphical techniques covered include bar graphs, histograms, pie charts, and box plots. The principles of graphing to maximize clarity and minimize clutter are also outlined.
In the presentation, hypothesis test has been explained with scrap. Tree diagram is there to understand in which situation u can apply which parametric test
This document discusses statistical significance and its role in statistical hypothesis testing. It defines statistical significance as obtaining a p-value less than the predetermined significance level (often 0.05). The significance level is the probability of rejecting the null hypothesis when it is true. A statistically significant result means the observed effect is unlikely due to chance and reflects a true population characteristic. The concept originated with Fisher and was later developed by Neyman and Pearson to involve setting the significance level before data collection.
This document discusses various statistical tests used to analyze data, including tests of significance, parametric vs. non-parametric tests, and limitations. It provides background on key tests such as:
1) Student's t-test, developed by Gosset, which is used to compare two means from small samples with unknown variances.
2) ANOVA (analysis of variance), developed by Fisher, which compares variance between and within groups to test for significant differences between means of more than two groups.
3) Correlation analysis, which measures the strength and direction of association between two continuous variables using Pearson's correlation coefficient.
4) Chi-square test, which analyzes relationships between categorical variables to
The document discusses factor analysis as an exploratory and confirmatory multivariate technique. It explains that factor analysis is commonly used for data reduction, scale development, and evaluating the dimensionality of variables. Factor analysis determines underlying factors or dimensions from a set of interrelated variables. It reduces a large number of variables to a smaller number of factors. The key steps in factor analysis include computing a correlation matrix, extracting factors, rotating factors, and making decisions on the number of factors.
marketing research & applications on SPSSANSHU TIWARI
The document discusses various statistical techniques used in marketing research to analyze survey data, including frequency distributions, measures of central tendency and variability, hypothesis testing, and cross-tabulation. Frequency distributions are used to determine the mean, mode, median and answer questions about single variables. Hypothesis testing involves forming hypotheses, selecting a test, determining significance levels, collecting data, and making statistical decisions. Cross-tabulation examines relationships between two or more variables using techniques like chi-square tests. Both parametric and non-parametric tests are used depending on variable scales.
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.
Explains use of statistical power, inferential decision making, effect sizes, confidence intervals in applied social science research, and addresses the issue of publication bias and academic integrity.
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making.
The document provides a graphic organizer for presenting learning resources on the topic of volleyball for 4th year students. It lists resources that are available, may be purchased, or will be made. Available resources include nets, balls, flags, whistles, volleyball courts, penalty cards, score sheets, and volleyball attire. The analysis section asks for benefits of surveying available materials before making your own and tips for teachers in preparing teaching materials. The reflections section asks which material was most enjoyable to make, difficulties encountered, and advice for teachers.
The document describes an evaluation of bulletin boards at a school. It rates the boards on various criteria such as effectiveness of communication, attractiveness, balance, unity, interactivity, legibility, correctness, and durability. Overall, the boards were found to be satisfactory but some needed improvement, particularly in areas like unity, durability, and legibility. Recommendations included repairing damaged boards and using more colorful materials.
The presentation covered key steps in analyzing survey data including defining goals, designing valid and reliable survey questions, collecting data, cleaning data, conducting descriptive statistics and correlations, comparing mean differences between groups, and clearly presenting results along with conclusions and recommendations. Piloting surveys and continuously improving methods was also emphasized.
This document provides definitions and explanations of key concepts in biostatistics and statistical hypothesis testing, including:
- Types of data/variables, measures of central tendency, measures of dispersion
- Descriptive vs inferential statistics, populations and samples
- Assumptions of parametric tests, tests of normality, homogeneity of variance
- Components of hypothesis testing, types of errors, significance levels and p-values
- T-tests, ANOVA, within-subjects and between-subjects designs
This document discusses hypothesis testing and inferential statistics. It covers topics like hypothesis testing process, types of errors, differentiating between critical value method and probability value method, tests for one and two populations including z-test, t-test, Wilcoxon test and binomial test. It also discusses assumptions and procedures for tests like pooled t-test, paired t-test, Mann-Whitney test and paired Wilcoxon test. Examples of applying these tests on quantitative and qualitative data are provided.
This document provides an overview of quantitative data analysis techniques for hypothesis testing, including types of errors, statistical power, and tests for single and multiple sample means. It also discusses regression analysis, issues of multicollinearity, and other multivariate tests such as discriminant analysis, logistic regression, and canonical correlation.
Research Methodology: Questionnaire, Sampling, Data Preparationamitsethi21985
As per PTU's MBA Syllabus, Unit No. 2: Sources Of Data: Primary And Secondary; Data Collection Methods; Questionnaire Designing: Construction, Types And Developing A Good Questionnaire. Sampling Design and Techniques, Scaling Techniques, Meaning, Types, Data Processing Operations, Editing, Coding, Classification, Tabulation. Research Proposal/Synopsis Writing. Practical Framework
The document discusses inferential statistics and its applications. It defines statistics as dealing with collecting, classifying, presenting, comparing, and interpreting numerical data to make inferences about a population. Inferential statistics help decision makers present information, draw conclusions from samples, seek relationships between variables, and make reliable forecasts. The document also distinguishes between descriptive statistics, parametric inferential statistics that assume normal distributions, and non-parametric inferential statistics that make no distribution assumptions.
This document outlines statistical analysis techniques that can be performed in SPSS, including loading and preparing data, descriptive statistics like frequencies and cross tabulations, inferential statistics like t-tests, ANOVA, correlation, and reliability analysis, and exporting results. Chi-square tests examine relationships between categorical variables while t-tests compare means and ANOVA examines differences in means between groups. Correlation analyzes relationships between interval variables.
Researchers use several tools and procedures for analyzing quantitative data obtained from different types of experimental designs. Different designs call for different methods of analysis. This presentation focuses on:
T-test
Analysis of variance (F-test), and
Chi-square test
Modul Ajar Statistika Inferensia ke-13: Analisis Variansi, Eksperimentasi Fak...Arif Rahman
This document discusses statistical analysis and experimental design. It defines statistics as the branch of mathematics concerned with collecting, organizing, summarizing, simplifying, presenting, interpreting, analyzing and synthesizing data to help solve problems and make decisions. It discusses the goals and principles of experimental design, including replication to estimate experimental error, randomization to ensure statistical validity, and local control to reduce experimental error. Key aspects like blocking, balancing and grouping techniques are explained as methods to control nuisance factors and refine heterogeneous data in experimental design.
This document provides an overview of essentials for manuscript review, including how to organize a manuscript, use statistics, identify types of studies and levels of evidence, address bias, interpret results, and write an abstract, introduction, methods, discussion, and conclusion. It discusses key aspects of each section and how to effectively review a submitted manuscript.
This document provides an overview of descriptive statistics and graphing techniques used in survey research and psychology. It discusses getting to know data, levels of measurement, descriptive statistics for different data types, properties of the normal distribution, and non-normal distributions. Graphical techniques covered include bar graphs, histograms, pie charts, and box plots. The principles of graphing to maximize clarity and minimize clutter are also outlined.
In the presentation, hypothesis test has been explained with scrap. Tree diagram is there to understand in which situation u can apply which parametric test
This document discusses statistical significance and its role in statistical hypothesis testing. It defines statistical significance as obtaining a p-value less than the predetermined significance level (often 0.05). The significance level is the probability of rejecting the null hypothesis when it is true. A statistically significant result means the observed effect is unlikely due to chance and reflects a true population characteristic. The concept originated with Fisher and was later developed by Neyman and Pearson to involve setting the significance level before data collection.
This document discusses various statistical tests used to analyze data, including tests of significance, parametric vs. non-parametric tests, and limitations. It provides background on key tests such as:
1) Student's t-test, developed by Gosset, which is used to compare two means from small samples with unknown variances.
2) ANOVA (analysis of variance), developed by Fisher, which compares variance between and within groups to test for significant differences between means of more than two groups.
3) Correlation analysis, which measures the strength and direction of association between two continuous variables using Pearson's correlation coefficient.
4) Chi-square test, which analyzes relationships between categorical variables to
The document discusses factor analysis as an exploratory and confirmatory multivariate technique. It explains that factor analysis is commonly used for data reduction, scale development, and evaluating the dimensionality of variables. Factor analysis determines underlying factors or dimensions from a set of interrelated variables. It reduces a large number of variables to a smaller number of factors. The key steps in factor analysis include computing a correlation matrix, extracting factors, rotating factors, and making decisions on the number of factors.
marketing research & applications on SPSSANSHU TIWARI
The document discusses various statistical techniques used in marketing research to analyze survey data, including frequency distributions, measures of central tendency and variability, hypothesis testing, and cross-tabulation. Frequency distributions are used to determine the mean, mode, median and answer questions about single variables. Hypothesis testing involves forming hypotheses, selecting a test, determining significance levels, collecting data, and making statistical decisions. Cross-tabulation examines relationships between two or more variables using techniques like chi-square tests. Both parametric and non-parametric tests are used depending on variable scales.
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.
Explains use of statistical power, inferential decision making, effect sizes, confidence intervals in applied social science research, and addresses the issue of publication bias and academic integrity.
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making.
The document provides a graphic organizer for presenting learning resources on the topic of volleyball for 4th year students. It lists resources that are available, may be purchased, or will be made. Available resources include nets, balls, flags, whistles, volleyball courts, penalty cards, score sheets, and volleyball attire. The analysis section asks for benefits of surveying available materials before making your own and tips for teachers in preparing teaching materials. The reflections section asks which material was most enjoyable to make, difficulties encountered, and advice for teachers.
The document describes an evaluation of bulletin boards at a school. It rates the boards on various criteria such as effectiveness of communication, attractiveness, balance, unity, interactivity, legibility, correctness, and durability. Overall, the boards were found to be satisfactory but some needed improvement, particularly in areas like unity, durability, and legibility. Recommendations included repairing damaged boards and using more colorful materials.
The document describes a board display evaluation form that rates bulletin boards on various criteria such as effectiveness of communication, attractiveness, balance, unity, interactivity, legibility, correctness, and durability. Based on the evaluation, some boards need improvement in areas like clarity of writing and repair. The document recommends repairing damaged boards and using colorful materials to better engage audiences.
The document describes a board display evaluation form that rates bulletin boards on various criteria such as effectiveness of communication, attractiveness, balance, unity, interactivity, legibility, correctness, and durability. Based on the evaluation, some boards need improvement in areas like clarity of writing and repair. The document recommends repairing damaged boards and using colorful materials to better engage audiences.
Dokumen tersebut merangkum sejarah Khalifah Bani Abbasiyah Al Mu'tashim Billah, dinasti Mesir pada abad ke-7 dan 8 H, serta kedatangan dan kejahatan bangsa Tartar di bawah pimpinan Jenghis Khan yang menyerang dan menghancurkan Kekhalifahan Abbasiyah pada abad ke-13 M.
This document provides instructions for teachers on how to use a student learning app. It explains how teachers can add students, create assignments, tests and homework, review student work, and conduct live learning sessions with students. Key features include adding students, assigning worksheets and setting due dates, reviewing student answers and scores in detail, and using a shared whiteboard for live video sessions between teachers and students.
Why Interactive is a Hong Kong design studio specializing in interactive and online creative works. Since being established in 2008, they have worked with clients across various industries including media, sports, banking, and more. Their services include website and mobile app development, online advertising, and brand identity. Why Interactive has received several design awards and their work is regularly featured in media and design events.
Il World Energy Focus è il nuovo mensile online della WEC's community, una e-publication gratuita per essere sempre aggiornato sugli sviluppi del settore energetico. Il World Energy Focus contiene news, interviste esclusive e uno spazio dedicato agli eventi promossi dai singoli Comitati Nazionali.
This document contains the author's analysis of feedback received on their recipe cards. For feedback 1, the author agrees they could improve the color scheme by mixing colors on the cards. They also agree the cards could look brighter by adding different elements. Feedback 2 notes the cards seem aimed at a younger audience, so the author will change fonts to look more sophisticated. It also suggests bigger images, which the author agrees could improve the cards. The layout and professional look were praised. The author finds the feedback helpful to further develop the quality of their recipe cards.
This document outlines the checklist and documentation required for a minor returning to Israel through the Aliyah process. It lists identification documents like passports, photos, and proof of Judaism that the applicant must provide as well as additional documents from parents, such as entry/exit forms and passports from when the applicant was age 14 to 18. Fees including an application fee and ticket vouchers fee must also be submitted with the completed forms and documentation.
Het was een uitgewoond en onoverzichtelijk theater. Na een in veel opzichten ingrijpende verbouwing kreeg de Lawei een heldere structuur, een nieuwe vlakkevloerzaal en een fonkelend goudgele buitenmuur. Als je er wat langer in rondloopt, stel je vast dat het eigenlijk een kleine stad is.
This document provides an overview of statistical inferences and inferential statistics. It discusses key concepts like the null hypothesis, sampling error vs measurement error, and different types of statistical tests like t-tests, ANOVA, ANCOVA, and chi-square. It emphasizes the importance of sample size, reliability of measurement tools, and properly interpreting statistical significance and effect size when evaluating inferential analyses.
This document provides an overview of statistical methods used in clinical research. It discusses different data types, descriptive statistics for summarizing data, standard error and confidence intervals. It also covers statistical tests such as t-tests, ANOVA, chi-squared tests, and non-parametric tests for comparing groups. Sample size calculations and the concept of type 1 and type 2 errors are also reviewed. The document serves as an introduction to common statistical analyses and concepts in clinical research.
This document discusses multivariate analysis and some key concepts in multivariate analysis including:
1. Variates, measurement scales (metric and non-metric), measurement error, statistical significance versus statistical power.
2. Types of measurement scales including nominal, ordinal, interval and ratio scales.
3. Measurement error and how it relates to validity and reliability in multivariate measurement.
4. Statistical significance and types of statistical errors in multivariate analysis.
Parametric and non-parametric tests differ in their assumptions about the population from which data is drawn. Parametric tests assume the population is normally distributed and variables are measured on an interval scale, while non-parametric tests make fewer assumptions. Examples of parametric tests include t-tests and ANOVA, while non-parametric examples include chi-square, Mann-Whitney U, and Wilcoxon signed-rank. Parametric tests are more powerful but rely on stronger assumptions, while non-parametric tests are more flexible but less powerful. Researchers must consider the characteristics of their data and questions being asked to determine the appropriate test.
This is the handout version of a lecture I give to medical residents and fellows on the basics of clinical research designs and the inherent issues that go along with each one. I give this lecture as part of a multi-module lecture series on research design and statistical analysis.
This document discusses key concepts related to sampling theory and measurement in research studies. It defines important sampling terms like population, sampling criteria, sampling methods, sampling error and bias. It also covers levels of measurement, reliability, validity and various measurement strategies like physiological measures, observations, interviews, questionnaires and scales. Finally, it provides an overview of statistical analysis techniques including descriptive statistics, inferential statistics, the normal curve and common tests like t-tests, ANOVA, and regression analysis.
Vergoulas Choosing the appropriate statistical test (2019 Hippokratia journal)Vaggelis Vergoulas
This document provides a step-by-step guide for choosing the appropriate statistical test for data analysis. It outlines 7 key steps: 1) determining if the analysis is univariate or multivariable, 2) identifying if the study examines differences or correlations, 3) determining if the data is paired or independent, 4) characterizing the type of outcome variable, 5) assessing the normality of distribution for continuous variables, 6) identifying the number of groups for independent variables, and 7) selecting valid statistical tests that match the characteristics identified in the previous steps, such as t-tests, ANOVA, regression analyses. Examples of applying this process are provided.
Introduction-to-Hypothesis-Testing Explained in detailShriramKargaonkar
This document provides an introduction to hypothesis testing, covering key concepts such as:
- The null and alternative hypotheses, which represent the proposed claim versus the default position.
- Type I and Type II errors in hypothesis testing and balancing the risks.
- The level of significance and p-value in determining if the null hypothesis can be rejected.
- Choosing between one-tailed and two-tailed tests based on directional predictions.
- Comparing test statistics to sampling distributions to evaluate the null hypothesis.
- Assumptions that must be met, such as normality and independence, for valid hypothesis testing.
The document discusses hypothesis testing using parametric and non-parametric tests. It defines key concepts like the null and alternative hypotheses, type I and type II errors, and p-values. Parametric tests like the t-test, ANOVA, and Pearson's correlation assume the data follows a particular distribution like normal. Non-parametric tests like the Wilcoxon, Mann-Whitney, and chi-square tests make fewer assumptions and can be used when sample sizes are small or the data violates assumptions of parametric tests. Examples are provided of when to use parametric or non-parametric tests depending on the type of data and statistical test being performed.
Inferential statistics allow researchers to draw conclusions about populations based on data from samples. They estimate population parameters and test hypotheses about populations that extend beyond the sample data. Hypothesis testing provides objective criteria for deciding whether to accept or reject research hypotheses as true or false based on the probability that any observed differences are due to chance. It involves selecting a test statistic, significance level, computing the test statistic, and comparing it to critical values to determine whether to reject the null hypothesis. Type I and Type II errors can occur but the significance level controls the risk of Type I errors.
This document provides an overview of inferential statistics. It defines inferential statistics as using samples to draw conclusions about populations and make predictions. It discusses key concepts like hypothesis testing, null and alternative hypotheses, type I and type II errors, significance levels, power, and effect size. Common inferential tests like t-tests, ANOVA, and meta-analyses are also introduced. The document emphasizes that inferential statistics allow researchers to generalize from samples to populations and test hypotheses about relationships between variables.
This document provides an overview of different types of statistical tests used for data analysis and interpretation. It discusses scales of measurement, parametric vs nonparametric tests, formulating hypotheses, types of statistical errors, establishing decision rules, and choosing the appropriate statistical test based on the number and types of variables. Key statistical tests covered include t-tests, ANOVA, chi-square tests, and correlations. Examples are provided to illustrate how to interpret and report the results of these common statistical analyses.
This document provides an overview of key concepts related to statistical estimation and hypothesis testing, including:
- The difference between point estimation and interval estimation, and examples like confidence intervals for the mean and proportion.
- How to calculate and interpret confidence intervals.
- The roles of the null and alternative hypotheses in hypothesis testing and how to interpret p-values.
- Types I and II errors and how the significance level affects these.
- When to use parametric vs. nonparametric tests and examples of selected nonparametric tests like the chi-square test of goodness of fit.
1. The document discusses key concepts in inferential statistics including point estimation, interval estimation, hypothesis testing, types of errors, p-values, power, and one-tailed and two-tailed tests.
2. It explains that inferential statistics allows generalization from a sample to a population and includes estimation of parameters and hypothesis testing.
3. Common statistical techniques covered are confidence intervals, which provide a range of values that likely contain the true population parameter, and hypothesis testing, which evaluates theories about populations.
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.
The document discusses sample size determination for clinical and epidemiological research. It explains that proper sample size is important for validity, accuracy, and reliability of research findings. Key factors to consider in sample size calculations include the study objective, details of the intervention, outcomes, covariates, research design, and study subjects. Precision analysis and power analysis are two common approaches, with power analysis being most suitable for studies aiming to detect an effect. The document provides formulas and examples for calculating sample sizes for comparative and descriptive studies with both continuous and dichotomous outcomes. It also discusses the concepts of type I and II errors and their relationship to statistical power.
Descriptive And Inferential Statistics for Nursing Researchenamprofessor
This document provides an overview of descriptive and inferential statistics. Descriptive statistics summarize and organize data through frequency distributions, graphs, measures of central tendency, and measures of variability. Inferential statistics allow generalization from samples to populations through hypothesis testing, which involves specifying a null hypothesis and alternative hypothesis. Statistical significance is determined by calculating a p-value and rejecting the null hypothesis if the p-value is less than a predetermined alpha level, typically 0.05. Type I and type II errors can occur in hypothesis testing.
This document provides an overview of descriptive and inferential statistics. Descriptive statistics summarize and organize data through frequency distributions, graphs, measures of central tendency, and measures of variability. Inferential statistics allow generalization from samples to populations through hypothesis testing, which involves specifying a null hypothesis and alternative hypothesis. Statistical significance is determined by calculating a p-value and comparing it to the significance level alpha to either reject or fail to reject the null hypothesis, with Type I and Type II errors a possibility. Common inferential tests include t-tests, ANOVAs, and meta-analyses.
This document discusses descriptive and inferential statistics. Descriptive statistics summarize and organize data through frequency distributions, graphs, and summary statistics like the mean, median, mode, variance, and standard deviation. Inferential statistics allow generalization from samples to populations through hypothesis testing, where the null hypothesis is tested against the alternative hypothesis. Type I and type II errors are possible, and significance tests control the probability of type I errors through the alpha level while power analysis aims to reduce type II errors. Common inferential tests mentioned include t-tests, ANOVA, and meta-analysis.
2. Topics Discussed in this Chapter
Concepts underlying inferential statistics
Types of inferential statistics
Parametric
T tests
ANOVA
One-way
Factorial
Post-hoc comparisons
Multiple regression
ANCOVA
Nonparametric
Chi square
3. Important Perspectives
Inferential statistics
Allow researchers to generalize to a population of
individuals based on information obtained from a
sample of those individuals
Assess whether the results obtained from a
sample are the same as those that would have
been calculated for the entire population
Probabilistic nature of inferential analyses
4. Underlying Concepts
Sampling distributions
Standard error
Null and alternative hypotheses
Tests of significance
Type I and Type II errors
One-tailed and two-tailed tests
Degrees of freedom
Tests of significance
5. Sampling Distributions
A distribution of sample statistics
A distribution of mean scores
A distribution of the differences between two mean scores
A distribution of the ratio of two variances
Known statistical properties of sampling distributions
The mean of the sampling distribution of means is an
excellent estimate of the population mean
The standard error of the mean is an excellent estimate of
the “standard deviation” of the sampling distribution of the
mean
Objectives 1.1 & 1.2
6. Standard Error
Sampling error – the expected random or chance
variation of means in sampling distributions
The calculation of standard errors to estimate
sampling error
Standard error of the mean
Formula
Dependency on sample size with n in the denominator
The larger the sample, the smaller the standard error of the mean
Standard error of the differences between two means
Objectives 1.2, 1.3, & 1.4
7. Null and Alternative Hypotheses
The null hypothesis represents a
statistical tool important to inferential
tests of significance
The alternative hypothesis usually
represents the research hypothesis
related to the study
8. Null and Alternative Hypotheses
Comparisons between groups
Null: no difference between the mean scores of
the groups
Alternative: differences between the mean scores
of the groups
Relationships between variables
Null: no relationship exists between the variables
being studied
Alternative: a relationship exists between the
variables being studied
Objectives 3.1, 3.2, & 3.4
9. Null and Alternative Hypotheses
Acceptance of the null Rejection of the null
hypothesis hypothesis
The difference between
The difference between
groups is so large it can
groups is too small to
be attributed to
attribute it to anything but something other than
chance chance (e.g.,
The relationship between experimental treatment)
variables is too small to The relationship between
attribute it to anything but variables is so large it
chance can be attributed to
something other than
chance (e.g., a real
relationship)
Objectives 3.3 & 4.2
10. Tests of Significance
Statistical analyses to help decide whether to
accept or reject the null hypothesis
Alpha level
An established probability level which serves as
the criterion to determine whether to accept or
reject the null hypothesis
Common levels in education
.01
.05
.10
Objectives 4.1 & 6.1
11. Tests of Significance
Specific tests are used in specific
situations based on the number of
samples and the statistics of interest
One-sample tests of the mean, variance,
proportions, correlations, etc.
Two-sample tests of means, variances,
proportions, correlations, etc.
Objective 4.1
12. Type I and Type II Errors
Correct decisions
The null hypothesis is true and it is accepted
The null hypothesis is false and it is rejected
Incorrect decisions
Type I error - the null hypothesis is true and it is
rejected
Type II error - the null hypothesis is false and it is
accepted
Objectives 5.1 & 5.2
13. Type I and Type II Errors
Reciprocal relationship between Type I and
Type II errors
Control of Type I errors using alpha level
As alpha becomes smaller (.10, .05, .01, .001,
etc.) there is less chance of a Type I error
Value and contextual based nature of
concerns related to Type I and Type II errors
Objective 5.3
14. One-Tailed and Two-Tailed Tests
One-tailed – an anticipated outcome in a specific
direction
Treatment group is significantly higher than the control group
Treatment group is significantly lower than the control group
Two-tailed – anticipated outcome not directional
Treatment and control groups are equal
Ample justification needed for using one-tailed tests
Objectives 7.1 & 7.2
15. Degrees of Freedom
Statistical artifacts that affect the
computational formulas used in tests of
significance
Used when entering statistical tables to
establish the critical values of the test
statistics
17. Tests of Significance
Four assumptions of parametric tests
Normal distribution of the dependent variable
Interval or ratio data
Independence of subjects
Homogeneity of variance
Advantages of parametric tests
More statistically powerful
More versatile
Objectives 8.1 & 8.2
18. Tests of Significance
Assumptions of nonparametric tests
No assumptions about the shape of the
distribution of the dependent variable
Ordinal or categorical data
Disadvantages of nonparametric tests
Less statistically powerful
Require large samples
Cannot answer some research questions
Objectives 8.3 & 8.4
19. Types of Inferential Statistics
Two issues discussed
Steps involved in testing for significance
Types of tests
20. Steps in Statistical Testing
State the null and alternative
hypotheses
Set alpha level
Identify the appropriate test of
significance
Identify the sampling distribution
Identify the test statistic
Compute the test statistic
Objectives 20.1 – 20.9
21. Steps in Statistical Testing
Identify the criteria for significance
If computing by hand, identify the critical value of the test
statistic
If using SPSS-Windows, identify the probability level of the
observed test statistic
Compare the computed test statistic to the criteria for
significance
If computing by hand, compare the observed test statistic to
the critical value
If using SPSS-Windows, compare the probability level of the
observed test statistic to the alpha level
Objectives 20.1 – 20.9
22. Steps in Statistical Testing
Accept or reject the null hypothesis
Accept
The observed test statistic is smaller than the critical
value
The observed probability level of the observed statistic is
smaller than alpha
Reject
The observed test statistic is larger than the critical value
The observed probability level of the observed statistic is
smaller than alpha
Objective 20.9
23. Two Important Issues
Types of samples
Independent samples
Two or more distinct groups are measured on a
single variable
Groups are independent of one another
Dependent samples
One group measured on two or more variables
Objective 10.1
24. Two Important Issues
Gain scores
Subtracting the pretest scores from the posttest
scores
Serious problems with this analysis
Each subject does not have the same opportunity for
“gain”
A person scoring close to the top of the test doesn’t have
as much to gain as someone scoring in the middle of the
test
Low reliability
ANCOVA as an appropriate analysis
Objectives 13.1 & 13.2
25. Specific Statistical Tests
T test for independent samples
Comparison of two means from independent
samples
Samples in which the subjects in one group are not
related to the subjects in the other group
Example - examining the difference between the
mean pretest scores for an experimental and
control group
Computation of the test statistic
SPSS-Windows syntax
Objectives 9.1 & 11.1
26. Specific Statistical Tests
T test for dependent samples
Comparison of two means from dependent
samples
One group is selected and mean scores are compared
for two variables
Two groups are compared but the subjects in each group
are matched
Example – examining the difference between
pretest and posttest mean scores for a single
class of students
Computation of the test statistic
SPSS-Windows syntax
Objectives 9.1 & 12.1
27. Specific Statistical Tests
Simple analysis of variance (ANOVA)
Comparison of two or more means
Example – examining the difference
between posttest scores for two treatment
groups and a control group
Computation of the test statistic
SPSS-Windows syntax
Objective 14.1
28. Specific Statistical Tests
Multiple comparisons
Omnibus ANOVA results
Significant difference indicates whether a difference
exists across all pairs of scores
Need to know which specific pairs are different
Types of tests
A priori contrasts
Post-hoc comparisons
Scheffe
Tukey HSD
Duncan’s Multiple Range
Conservative or liberal control of alpha
Objectives 15.1 & 15.2
29. Specific Statistical Tests
Multiple comparisons (continued)
Example – examining the difference
between mean scores for Groups 1 & 2,
Groups 1 & 3, and Groups 2 & 3
Computation of the test statistic
SPSS-Windows syntax
Objective 15.3
30. Specific Statistical Tests
Two-factor ANOVA
Also known as factorial ANOVA
Comparison of means when two
independent variables are being examined
Effects
Two main effects – one for each independent
variable
One interaction effect for the simultaneous
interaction of the two independent variables
Objective 16.1
31. Specific Statistical Tests
Two-factor ANOVA (continued)
Example – examining the mean score
differences for male and female students in
an experimental or control group
Computation of the test statistic
SPSS-Windows syntax
Objective 16.1
32. Specific Statistical Tests
Analysis of covariance (ANCOVA)
Comparison of two or more means with statistical
control of an extraneous variable
Use of a covariate
Advantages
Statistically controlling for initial group differences (i.e.,
equating the groups)
Increased statistical power
Pretest is typically the covariate
Computation of the test statistic
SPSS-Windows syntax
Objectives 17.1 & 17.2
33. Specific Statistical Tests
Multiple regression
Correlational technique which uses
multiple predictor variables to predict a
single criterion variable
Characteristics
Increased predictability with additional variables
Regression coefficients
Regression equations
Objective 18.1
34. Specific Statistical Tests
Multiple regression (continued)
Example – predicting college freshmen’s
GPA on the basis of their ACT scores, high
school GPA, and high school rank in class
Computation of the test statistic
SPSS-Windows syntax
Objective 18.2
35. Specific Statistical Tests
Chi Square
A nonparametric test in which observed proportions are
compared to expected proportions
Types
One-dimensional – comparing frequencies occurring in different
categories for a single group
Two-dimensional – comparing frequencies occurring in different
categories for two or more groups
Examples
Is there a difference between the proportions of parents in favor
of or opposed to an extended school year?
Is there a difference between the proportions of husbands and
wives who are in favor of or opposed to an extended school
year?
Objectives 19.1 & 19.2
36. Specific Statistical Tests
Chi Square (continued)
Computation of the test statistic
SPSS-Windows syntax
One-dimensional uses Nonparametric Tests
procedures
Two-dimensional uses Crosstabs procedures
Objectives 19.1 & 19.2