Reporting Statistics in Psychology
This document provides guidelines for reporting statistics in psychology research. It outlines how to round numbers and report means, standard deviations, p-values, effect sizes, and results from t-tests, ANOVAs, and other statistical analyses. Key recommendations include reporting exact p-values to two or three decimal places, using abbreviations like M and SD consistently, and noting any violations of statistical assumptions.
This document provides guidelines for writing up results sections based on APA style. It discusses reporting statistical tests, including describing test statistics, significance levels, means, standard deviations, and directions of effects. Examples are provided for how to report results from t-tests, ANOVAs, post hoc tests, chi-square tests, correlations, and regressions. Tables and figures can help report complex results. The guidelines emphasize identifying analyses and their relation to hypotheses, and assuming reader knowledge of statistics.
A two-way ANOVA was conducted to examine the effects of athlete type (football, basketball, soccer) and age (younger, older) on slices of pizza eaten. There were significant main effects of athlete type and an interaction between athlete type and age, but no main effect of age. Football players ate the most pizza, followed by basketball players and then soccer players.
The document provides guidance on reporting the results of a one-way ANOVA in APA format. It recommends including that a one-way ANOVA was conducted to examine the effect of an independent variable on a dependent variable. It provides a template for reporting the F-statistic, degrees of freedom, and significance level based on the ANOVA output. Filling in the specifics of the independent variable, dependent variable, and ANOVA results completes the report.
Reporting Pearson Correlation Test of Independence in APAKen Plummer
A Pearson correlation test of independence was conducted to determine if student height and GPA were related. A weak correlation was found between height and GPA (r = .217, p > .05), indicating that student height and GPA are independent of each other.
Reporting a one way repeated measures anovaKen Plummer
The document provides guidance on reporting the results of a one-way repeated measures ANOVA in APA style. It includes templates for reporting the main ANOVA results and any post-hoc pairwise comparisons between conditions. Key sections are highlighted to fill in values from an example SPSS output to generate a complete APA-style results section reporting a significant effect of time of season on pizza consumption.
This document discusses how to report the results of a Pearson correlation analysis in APA style. It provides an example of a problem investigating the relationship between broccoli extract consumption and well-being scores. The template shown reports that a strong positive correlation was found between broccoli extract consumption and well-being (r = .88, p < .05).
A One-way ANOVA was conducted to compare the effect of type of athlete on the number of pizza slices eaten. The ANOVA results showed that the effect of type of athlete on number of pizza slices eaten was significant, F(2,66) = 99.82, p = .000.
Reporting an independent sample t- testAmit Sharma
An independent samples t-test was conducted to compare truck driver drowsiness scores for country music listening and no country music listening conditions. There was a significant difference in scores for country music listening (M=4.2, SD=1.3) and no country music listening (M=2.2, SD=0.84); t(8)=2.89, p=0.02.
This document provides guidelines for writing up results sections based on APA style. It discusses reporting statistical tests, including describing test statistics, significance levels, means, standard deviations, and directions of effects. Examples are provided for how to report results from t-tests, ANOVAs, post hoc tests, chi-square tests, correlations, and regressions. Tables and figures can help report complex results. The guidelines emphasize identifying analyses and their relation to hypotheses, and assuming reader knowledge of statistics.
A two-way ANOVA was conducted to examine the effects of athlete type (football, basketball, soccer) and age (younger, older) on slices of pizza eaten. There were significant main effects of athlete type and an interaction between athlete type and age, but no main effect of age. Football players ate the most pizza, followed by basketball players and then soccer players.
The document provides guidance on reporting the results of a one-way ANOVA in APA format. It recommends including that a one-way ANOVA was conducted to examine the effect of an independent variable on a dependent variable. It provides a template for reporting the F-statistic, degrees of freedom, and significance level based on the ANOVA output. Filling in the specifics of the independent variable, dependent variable, and ANOVA results completes the report.
Reporting Pearson Correlation Test of Independence in APAKen Plummer
A Pearson correlation test of independence was conducted to determine if student height and GPA were related. A weak correlation was found between height and GPA (r = .217, p > .05), indicating that student height and GPA are independent of each other.
Reporting a one way repeated measures anovaKen Plummer
The document provides guidance on reporting the results of a one-way repeated measures ANOVA in APA style. It includes templates for reporting the main ANOVA results and any post-hoc pairwise comparisons between conditions. Key sections are highlighted to fill in values from an example SPSS output to generate a complete APA-style results section reporting a significant effect of time of season on pizza consumption.
This document discusses how to report the results of a Pearson correlation analysis in APA style. It provides an example of a problem investigating the relationship between broccoli extract consumption and well-being scores. The template shown reports that a strong positive correlation was found between broccoli extract consumption and well-being (r = .88, p < .05).
A One-way ANOVA was conducted to compare the effect of type of athlete on the number of pizza slices eaten. The ANOVA results showed that the effect of type of athlete on number of pizza slices eaten was significant, F(2,66) = 99.82, p = .000.
Reporting an independent sample t- testAmit Sharma
An independent samples t-test was conducted to compare truck driver drowsiness scores for country music listening and no country music listening conditions. There was a significant difference in scores for country music listening (M=4.2, SD=1.3) and no country music listening (M=2.2, SD=0.84); t(8)=2.89, p=0.02.
A mixed between-within subjects ANOVA was conducted to examine the impact of different instruction methods (lecture, slides, instruction with student presentation, pair work) on linguistics test scores over two time periods (pretest and posttest) among 32 students randomly assigned to four groups. There was a significant interaction between time and instruction method, and time had a significant main effect. The different instruction methods also had a significant main effect on test scores. Post hoc tests revealed significant differences in scores between the lecture and student presentation groups, and the student presentation and pair work groups.
Reporting a multiple linear regression in apaKen Plummer
A multiple linear regression was calculated to predict weight based on height and sex. A significant regression equation was found (F(2,13)=981.202, p<.000), with an R2 of .993. Participants' predicted weight is equal to 47.138 + 2.101(height) - 39.133(sex), where height is measured in inches and sex is coded as 0 for male and 1 for female. Both height and sex were significant predictors of weight.
The document provides guidance on reporting the results of an ANCOVA analysis in APA format. It recommends including that a one-way ANCOVA was conducted to determine differences between levels of an independent variable on a dependent variable while controlling for a covariate. An example is given using athlete type as the independent variable, slices of pizza eaten as the dependent variable, and weight as the covariate. The document also provides a template for reporting the F-ratio, degrees of freedom, and significance level.
The document describes how to report a partial correlation in APA format. It provides a template for reporting that there is a significant positive partial correlation of .82 between intense fanaticism for a professional sports team and proximity to the city the team resides when controlling for age, with a p-value of .000.
The document discusses factorial analysis of variance (ANOVA). It explains how total sums of squares can be partitioned into explained and unexplained components. An example shows an F ratio of 5.0 for one data set, indicating variation between groups is rare. This allows rejecting the null hypothesis with a low probability of Type I error. Finally, it describes how factorial ANOVA can analyze the effects of multiple independent variables on a single dependent variable.
Reporting a single linear regression in apaKen Plummer
The document provides a template for reporting the results of a simple linear regression analysis in APA format. It explains that a linear regression was conducted to predict weight based on height. The regression equation was found to be significant, F(1,14)=25.925, p<.000, with an R2 of .649. The predicted weight is equal to -234.681 + 5.434 (height in inches) pounds.
1) ANOVA is used to compare the means of more than two populations and determine if observed differences are due to chance or actual differences in the population means.
2) The document provides an example of using a one-way single factor ANOVA to analyze the effects of different teaching formats on student exam scores.
3) The ANOVA compares the between-treatment variability to the within-treatment variability using an F-test. If the between-treatment variability is significantly larger, it suggests the population means differ. In this example, the F-test showed no significant difference between the teaching formats.
Reporting the wilcoxon signed ranks testKen Plummer
A Wilcoxon Signed-Ranks Test was conducted to compare pre-test and post-test ranks. The results indicated that post-test ranks were statistically significantly higher than pre-test ranks, with a Z score of 21 and p value less than .027. The document provided guidance and examples for reporting the results of the Wilcoxon Signed-Ranks Test in APA style.
The document provides a template for reporting the results of an independent samples t-test in APA format. It demonstrates how to write a sentence summarizing that there was a significant/non-significant difference between two groups by including the group means, standard deviations, t-statistic, and p-value filled in from a sample SPSS output.
Reporting Chi Square Test of Independence in APAKen Plummer
This document provides guidance on reporting the results of a chi-square test of independence in APA style. It presents an example problem investigating the relationship between heart disease and gender. It then shows the general template for how to report a chi-square test, including reporting the chi-square value, degrees of freedom, and statistical significance. The template example finds a significant relationship between heart disease and gender, with men more likely to have heart disease than women.
Repeated measures ANOVA is used to compare mean scores on the same individuals across multiple time points or conditions. It extends the dependent t-test to allow for more than two time points or conditions. Key assumptions include having a continuous dependent variable, at least two related groups or conditions, no outliers, normally distributed differences between groups, and sphericity. Repeated measures ANOVA separates variance into between-subjects, between-measures, and error components to test if there are differences in mean scores between related groups while accounting for correlations between measures on the same individuals.
This document provides guidance on reporting the results of a single sample t-test in APA format. It includes templates for describing the test and population in the introduction and reporting the mean, standard deviation, t-value and significance in the results. An example is given of a hypothetical single sample t-test comparing IQ scores of people who eat broccoli regularly to the general population.
The document provides guidance on reporting the results of a paired sample t-test in APA format. It includes templates for reporting the study design, results, and statistical analysis. Key details include reporting the means, standard deviations, and standard errors for each condition. It also notes reporting the t-statistic, degrees of freedom, and significance level based on the t-test output.
This document discusses repeated measures designs and analyzing data from such designs using repeated measures ANOVA. It explains that repeated measures ANOVA involves comparing measures taken from the same subjects across different treatment conditions while controlling for individual differences. The document provides details on the null and alternative hypotheses, calculating variance components, and assumptions of repeated measures ANOVA.
This document provides information on two-way repeated measures designs, including when to use them, their structure, and how to analyze the data. A two-way repeated measures design is used to investigate the effects of two within-subjects factors on a dependent variable simultaneously. All subjects are tested at each level of both factors. This design allows comparison of mean differences between groups split on the two within-subject factors. The document describes the analysis process, including testing for main effects, interactions, and simple effects using SPSS. An example is provided to illustrate a two-way repeated measures design investigating the effects of music and environment on work performance.
The document provides guidance on reporting paired sample t-test results in APA format. It includes an example of how to write the results in a sentence, explaining that there was a significant/not significant difference between the scores for condition 1 (providing the mean and standard deviation) and condition 2 (providing the mean and standard deviation). It also demonstrates how to fill in the t-statistic, degrees of freedom, and p-value using output from SPSS.
This document discusses using one-way ANOVA in SPSS to compare mean salaries among employee age groups. It finds a significant difference in monthly salaries between the three age groups. Post hoc tests show that all three group means are significantly different from one another. Two other examples are presented: the first finds no significant difference in the importance of growth and development between age groups, while the second does find a significant difference in the importance of a safe work environment between the youngest and oldest age groups specifically.
The document discusses conducting a factorial analysis of variance (ANOVA) to analyze the effects of two independent variables, athlete type (football, basketball, soccer players) and age (adults vs teenagers), on the dependent variable of number of slices of pizza consumed. It outlines setting up a 2x3 factorial design to compare the six groups that results from the two independent variables, each with multiple levels, and determining that a factorial ANOVA is the appropriate statistical analysis for this research question and study design.
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.
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.
The document provides an overview of different statistical analysis methods including independent ANOVA, repeated measures ANOVA, and MANOVA. It discusses key aspects of each method such as their appropriate uses, assumptions, and how to conduct the analyses and interpret results in SPSS. For ANOVA, it covers topics like F-ratio, significance levels, post-hoc tests, effect sizes, and examples. For MANOVA, it compares it to ANOVA and explains how MANOVA can assess differences across groups on multiple dependent variables simultaneously.
A mixed between-within subjects ANOVA was conducted to examine the impact of different instruction methods (lecture, slides, instruction with student presentation, pair work) on linguistics test scores over two time periods (pretest and posttest) among 32 students randomly assigned to four groups. There was a significant interaction between time and instruction method, and time had a significant main effect. The different instruction methods also had a significant main effect on test scores. Post hoc tests revealed significant differences in scores between the lecture and student presentation groups, and the student presentation and pair work groups.
Reporting a multiple linear regression in apaKen Plummer
A multiple linear regression was calculated to predict weight based on height and sex. A significant regression equation was found (F(2,13)=981.202, p<.000), with an R2 of .993. Participants' predicted weight is equal to 47.138 + 2.101(height) - 39.133(sex), where height is measured in inches and sex is coded as 0 for male and 1 for female. Both height and sex were significant predictors of weight.
The document provides guidance on reporting the results of an ANCOVA analysis in APA format. It recommends including that a one-way ANCOVA was conducted to determine differences between levels of an independent variable on a dependent variable while controlling for a covariate. An example is given using athlete type as the independent variable, slices of pizza eaten as the dependent variable, and weight as the covariate. The document also provides a template for reporting the F-ratio, degrees of freedom, and significance level.
The document describes how to report a partial correlation in APA format. It provides a template for reporting that there is a significant positive partial correlation of .82 between intense fanaticism for a professional sports team and proximity to the city the team resides when controlling for age, with a p-value of .000.
The document discusses factorial analysis of variance (ANOVA). It explains how total sums of squares can be partitioned into explained and unexplained components. An example shows an F ratio of 5.0 for one data set, indicating variation between groups is rare. This allows rejecting the null hypothesis with a low probability of Type I error. Finally, it describes how factorial ANOVA can analyze the effects of multiple independent variables on a single dependent variable.
Reporting a single linear regression in apaKen Plummer
The document provides a template for reporting the results of a simple linear regression analysis in APA format. It explains that a linear regression was conducted to predict weight based on height. The regression equation was found to be significant, F(1,14)=25.925, p<.000, with an R2 of .649. The predicted weight is equal to -234.681 + 5.434 (height in inches) pounds.
1) ANOVA is used to compare the means of more than two populations and determine if observed differences are due to chance or actual differences in the population means.
2) The document provides an example of using a one-way single factor ANOVA to analyze the effects of different teaching formats on student exam scores.
3) The ANOVA compares the between-treatment variability to the within-treatment variability using an F-test. If the between-treatment variability is significantly larger, it suggests the population means differ. In this example, the F-test showed no significant difference between the teaching formats.
Reporting the wilcoxon signed ranks testKen Plummer
A Wilcoxon Signed-Ranks Test was conducted to compare pre-test and post-test ranks. The results indicated that post-test ranks were statistically significantly higher than pre-test ranks, with a Z score of 21 and p value less than .027. The document provided guidance and examples for reporting the results of the Wilcoxon Signed-Ranks Test in APA style.
The document provides a template for reporting the results of an independent samples t-test in APA format. It demonstrates how to write a sentence summarizing that there was a significant/non-significant difference between two groups by including the group means, standard deviations, t-statistic, and p-value filled in from a sample SPSS output.
Reporting Chi Square Test of Independence in APAKen Plummer
This document provides guidance on reporting the results of a chi-square test of independence in APA style. It presents an example problem investigating the relationship between heart disease and gender. It then shows the general template for how to report a chi-square test, including reporting the chi-square value, degrees of freedom, and statistical significance. The template example finds a significant relationship between heart disease and gender, with men more likely to have heart disease than women.
Repeated measures ANOVA is used to compare mean scores on the same individuals across multiple time points or conditions. It extends the dependent t-test to allow for more than two time points or conditions. Key assumptions include having a continuous dependent variable, at least two related groups or conditions, no outliers, normally distributed differences between groups, and sphericity. Repeated measures ANOVA separates variance into between-subjects, between-measures, and error components to test if there are differences in mean scores between related groups while accounting for correlations between measures on the same individuals.
This document provides guidance on reporting the results of a single sample t-test in APA format. It includes templates for describing the test and population in the introduction and reporting the mean, standard deviation, t-value and significance in the results. An example is given of a hypothetical single sample t-test comparing IQ scores of people who eat broccoli regularly to the general population.
The document provides guidance on reporting the results of a paired sample t-test in APA format. It includes templates for reporting the study design, results, and statistical analysis. Key details include reporting the means, standard deviations, and standard errors for each condition. It also notes reporting the t-statistic, degrees of freedom, and significance level based on the t-test output.
This document discusses repeated measures designs and analyzing data from such designs using repeated measures ANOVA. It explains that repeated measures ANOVA involves comparing measures taken from the same subjects across different treatment conditions while controlling for individual differences. The document provides details on the null and alternative hypotheses, calculating variance components, and assumptions of repeated measures ANOVA.
This document provides information on two-way repeated measures designs, including when to use them, their structure, and how to analyze the data. A two-way repeated measures design is used to investigate the effects of two within-subjects factors on a dependent variable simultaneously. All subjects are tested at each level of both factors. This design allows comparison of mean differences between groups split on the two within-subject factors. The document describes the analysis process, including testing for main effects, interactions, and simple effects using SPSS. An example is provided to illustrate a two-way repeated measures design investigating the effects of music and environment on work performance.
The document provides guidance on reporting paired sample t-test results in APA format. It includes an example of how to write the results in a sentence, explaining that there was a significant/not significant difference between the scores for condition 1 (providing the mean and standard deviation) and condition 2 (providing the mean and standard deviation). It also demonstrates how to fill in the t-statistic, degrees of freedom, and p-value using output from SPSS.
This document discusses using one-way ANOVA in SPSS to compare mean salaries among employee age groups. It finds a significant difference in monthly salaries between the three age groups. Post hoc tests show that all three group means are significantly different from one another. Two other examples are presented: the first finds no significant difference in the importance of growth and development between age groups, while the second does find a significant difference in the importance of a safe work environment between the youngest and oldest age groups specifically.
The document discusses conducting a factorial analysis of variance (ANOVA) to analyze the effects of two independent variables, athlete type (football, basketball, soccer players) and age (adults vs teenagers), on the dependent variable of number of slices of pizza consumed. It outlines setting up a 2x3 factorial design to compare the six groups that results from the two independent variables, each with multiple levels, and determining that a factorial ANOVA is the appropriate statistical analysis for this research question and study design.
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.
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.
The document provides an overview of different statistical analysis methods including independent ANOVA, repeated measures ANOVA, and MANOVA. It discusses key aspects of each method such as their appropriate uses, assumptions, and how to conduct the analyses and interpret results in SPSS. For ANOVA, it covers topics like F-ratio, significance levels, post-hoc tests, effect sizes, and examples. For MANOVA, it compares it to ANOVA and explains how MANOVA can assess differences across groups on multiple dependent variables simultaneously.
This document is a social psychology research report submitted by a group of students. It includes an introduction outlining the concepts covered in an accompanying video, including first impressions, stereotyping, CORFing, social facilitation, observational learning, and bystander effect. The method section describes how the video was filmed, focusing on a girl's reactions to different students in her classroom. The concept section then defines and explains each of the six concepts in more detail.
The document summarizes a group project for a social psychology class. It includes an introduction describing the project requirements and concepts covered. It then details the group members, materials used, and filming procedures. Finally, it discusses how five concepts were incorporated into the group's video: social facilitation and how being watched improved performance; illusion of control and relying on a lucky item; observational learning; BIRGing; and self-fulfilling prophecy. The document provides context and examples for how each concept was demonstrated in the scenes filmed for the video assignment.
The document is a research report submitted by a group of students for their social psychology class. It details the production of a short video applying several key social psychology concepts. The group chose concepts around relationships, including self-serving bias, confirmation bias, self-verification theory, negativity bias, and stereotyping. They developed a storyline and shot scenes on campus depicting these concepts. For each concept, the group provided definitions, explanations, and analyses of how it was applied in their video scenes. Their goal was to integrate course theories into a practical video project.
Descriptive statistics are methods of describing the characteristics of a data set. It includes calculating things such as the average of the data, its spread and the shape it produces.
A chapter describing the use and application of exploratory factor analysis using principal axis factoring with oblique rotation.
Provides a step by step guide to exploratory factor analysis using SPSS.
Parametric or non parametric relationship practice problemsKen Plummer
1. The document presents 6 practice problems involving determining whether to use parametric or non-parametric methods to analyze relationships between variables.
2. The problems involve different variable types including continuous/scaled, categorical/nominal, and ranked variables.
3. The correct method - parametric or non-parametric - depends on whether the variables are normally distributed and meet other assumptions as well as whether they are continuous or categorical.
Predictive or arbitrary relationship practice problemsKen Plummer
The director of a health clinic asked if patients' age influences their systolic blood pressure. The data shows higher blood pressure levels generally associated with older patient ages, indicating a predictive relationship between age and blood pressure.
The director also asked if there is a relationship between systolic blood pressure and stress levels. The data presented suggests blood pressure levels tend to be higher with greater reported stress levels, indicative of a predictive relationship between stress and blood pressure.
The director provided two datasets and asked if age influences blood pressure in one case and if there is a relationship between blood pressure and stress in the other, with both situations presenting predictive relationships between the variables based on the information given.
The document explains the one-sample Wilcoxon test, which is used to determine if a sample is statistically similar to or different from a population. It provides an example comparing IQ scores, where researchers took a random sample of 20 people and want to know if the sample's mean of 70 is representative of the overall population's mean of 100. The one-sample Wilcoxon test compares the sample and population medians to determine the probability that the sample and population are statistically similar or different.
The document discusses normal and skewed distributions. It provides an example of student study hours to illustrate how to create a distribution from a data set. The distribution plots hours of study on the x-axis and number of occurrences on the y-axis. It then calculates the mean of the example data set to demonstrate that the mean describes the center point of a normal distribution when the majority of the data is in the middle with decreasing amounts towards the tails.
Quickreminder nature of the data (relationship)Ken Plummer
This document provides guidance on which statistical tests to use when analyzing different variable types. It recommends using the phi coefficient for dichotomous by dichotomous variables, point-biserial for dichotomous by scaled variables, Spearman's rho for ordinal by any other variable or scaled by scaled with one variable skewed and less than 30 subjects, and Kendall's tau for ordinal with ties by any other variable or scaled by scaled with one variable skewed and less than 30 subjects with ties.
This presentation discusses parametric and non-parametric methods for analyzing relationships between variables. Parametric methods can be used when sample data is normally distributed and scaled, representing population parameters. They involve examining relationships between variables like death anxiety and religiosity through statistical tests. Non-parametric methods do not require normal distribution or scaling and can be used as an alternative.
A repeated measures ANOVA is used to test whether a single group of people change over time by comparing distributions from the same group at different time periods, rather than comparing distributions from different groups. The overall F-ratio reveals if there are differences among time periods, and post hoc tests identify exactly where the differences occurred. In contrast, a one-way ANOVA compares distributions between two or more different groups to determine if there are statistical differences between them.
This document discusses statistical analysis using SPSS. It describes descriptive statistics, which present data in a usable form by describing frequency, central tendency, and dispersion. Inferential statistics make broader generalizations from samples to populations using hypothesis testing. Hypothesis testing involves research hypotheses, null hypotheses, levels of significance, and type I and II errors. Choosing an appropriate statistical test depends on the hypothesis and measurement levels of the variables. SPSS is a comprehensive system for statistical analysis that can analyze many file types and generate reports and statistics.
The document summarizes statistical analysis concepts and methods used to analyze biological data, including calculating means, standard deviations, and using t-tests to determine the significance of differences between data sets. It provides an example comparing bill length measurements in two hummingbird species. The mean bill length is slightly higher in C. latirostris, but A. colubris shows greater variability. A t-test is needed to determine if the difference in means is statistically significant given the overlap between the error bars representing standard deviation.
Reporting a non parametric Friedman test in APAKen Plummer
The document discusses reporting a Friedman test in APA format. It includes sample data comparing the number of pizza slices eaten by football players before, during, and after their season. A Friedman test found a chi-square value of 18.20 (p<0.01), indicating a significant difference in pizza eating across the three time periods. The recommended reporting statement is that a Friedman test found a significant effect among repeated measures, with a chi-square value and p-value provided.
1. The document discusses key concepts in biostatistics including measures of central tendency, dispersion, correlation, regression, and sampling.
2. Measures of central tendency described are the mean, median, and mode. Measures of dispersion include range, standard deviation, and quartile deviation.
3. The importance of statistical analysis for living organisms in areas like medicine, biology and public health is highlighted. Examples are provided to demonstrate calculation of statistical measures.
- A sample is a small group selected from a population to represent that population. Sampling provides benefits like being less time-consuming, less expensive, and allowing results to be repeated.
- There are two main types of samples: probability and non-probability. Probability samples include simple random, systematic, stratified, and cluster samples. Sample size is determined based on factors like the type of study, expected results, costs, and available resources.
- Inferential statistics allow generalization from a sample to a population through hypothesis testing and significance tests. Tests include t-tests, F-tests, chi-squared tests, and correlation/regression to analyze relationships between variables. Significant results suggest differences are likely not due to chance
This document provides an overview of statistics and statistical tests. It defines descriptive statistics as concerned with data collection, presentation and interpretation, while inferential statistics involves drawing conclusions from statistical analysis. Parametric tests can be applied to normally distributed interval/ratio data, while non-parametric tests do not require normality assumptions. Examples of parametric and non-parametric tests are provided, along with guidelines for applying a two-sample t-test to compare means between two independent groups. Two examples of applying a t-test are given to test differences between groups.
This document provides information about various statistical concepts including variables, probability, distributions, hypothesis testing, and Python libraries for statistical analysis. It defines different types of variables, such as continuous, discrete, categorical, and their examples. It also explains concepts like population, sample, central tendency, dispersion, probability, distributions, hypothesis testing, t-test, z-test, ANOVA. Finally, it mentions commonly used Python libraries like SciPy for conducting statistical tests and analysis.
This document provides an overview of biostatistics and various statistical concepts used in dental sciences. It discusses measures of central tendency including mean, median, and mode. It also covers measures of dispersion such as range, mean deviation, and standard deviation. The normal distribution curve and properties are explained. Various statistical tests are mentioned including t-test, ANOVA, chi-square test, and their applications in dental research. Steps for testing hypotheses and types of errors are summarized.
This document provides an overview of elementary statistics topics including descriptive statistics, inferential statistics, probability, different types of data and scales of measurement, common statistical tests like t-tests, z-tests, F-tests, chi-square tests, ANOVA, correlation, and regression. It also includes examples of how to calculate and interpret descriptive statistics like the mean, median, mode, variance, and standard deviation. Examples are provided on how to set up and conduct hypothesis tests using Excel.
This document summarizes statistical tests for comparing two samples, including paired and independent samples t-tests, confidence intervals, and effect sizes. For paired samples from within-subject designs, a paired t-test is used to test for differences between means. For independent samples from between-subject designs, an independent samples t-test is used. Both tests calculate a t-statistic based on the mean difference and standard error. Confidence intervals and effect sizes can also be calculated for paired and independent sample designs. Examples are provided to demonstrate how to perform the statistical tests and calculations.
This document provides an overview of key concepts in applied statistics and design of experiments (DOE). It defines common measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation, coefficient of variation). It also describes hypothesis testing using z-tests, t-tests, F-tests and ANOVA. Key concepts in regression, correlation and different experimental designs like factorial, fractional factorial and response surface methodology are summarized.
The document discusses elementary statistics and statistical methodology. It covers descriptive statistics topics like mean, median, mode, variance and standard deviation. It also covers inferential statistics topics like hypothesis testing, t-tests, z-tests, F-tests, ANOVA, correlation, and regression. Examples of applying statistical analyses in Excel are provided, including calculating confidence intervals and performing hypothesis tests to compare sample means.
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
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.
The document presents a case study where Lisa wants to open a beauty store and needs data to support her belief that women in her local area spend more than the national average of $59 every 3 months on fragrance products. Lisa takes a random sample of 25 women in her area and finds the sample mean is $68.10 with a standard deviation of $14.46. She conducts a one-sample t-test to test if the population mean is greater than $59. The test statistic is 3.1484 with a p-value of 0.0021, which is less than the significance level of 0.05. Therefore, there is sufficient evidence to conclude that the population mean is indeed greater than $
Test of significance (t-test, proportion test, chi-square test)Ramnath Takiar
The presentation discusses the concept of test of significance including the test of significance examples of t-test, proportion test and chi-square test.
This document presents a statistical analysis of survey data from 65 respondents. The analysis includes descriptive statistics on respondent demographics like age, gender, work category, education level, and more. Inferential statistics like t-tests, ANOVA, correlation, and regression are used to compare motivation scores across these demographic groups and examine the relationship between motivation and experience. The results show no significant differences in motivation between groups defined by gender, organization type, marital status, age, or work category. Regression analysis finds that demographic variables together explain only 9% of variance in motivation.
This document provides an overview of various statistical analysis techniques used in inferential statistics, including t-tests, ANOVA, ANCOVA, chi-square, regression analysis, and interpreting null hypotheses. It defines key terms like alpha levels, effect sizes, and interpreting graphs. The overall purpose is to explain common statistical methods for analyzing data and determining the probability that results occurred by chance or were statistically significant.
The document discusses different measures of central tendency (mean, median, mode) and how to determine which is most appropriate based on the type of data. It also covers measures of dispersion like range, standard deviation, and variance which provide information about how spread out values are from the central point. The mean is the most commonly used measure of central tendency but the median is less affected by outliers, while the mode represents the most frequent value.
Running head Statistics 2Statistics Statistics Na.docxagnesdcarey33086
Running head: Statistics
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Statistics
Statistics
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Assignment #4: Model Diagnostics
A fundamental requirement in the classical linear regression is that the regression error term must be normally distributed with zero mean and constant variance (Greene, 2008). The normality tests results are presented below.
All the plots have values greater than the threshold probability value of 0.05 thus the null hypothesis of normality of the regression residuals could not be rejected at 5 per cent significance level. Conclusion is thus made that the regression residuals from the estimated equations followed a normal distribution. Since any linear function of normally distributed variables is considered to be normally distributed, normal distribution of the residuals had the implication that the coefficients of the estimates were also themselves normally distributed (Gujarati, 2008).
The residual plot is shown below:
From the residual plot it can be seen that all the residuals fall within the standard error bands thus confirming that the model is stable and can thus be used for forecasting.
References
Greene, W. (2008). Econometric analysis, 6th ed. . New Jersey: Pearson-Prentice Hall.
Gujarati, D. (2004). Basic econometrics 4th ed. . New York: McGraw Hill Companies.
Normal Probability Plot
2.6315789473684208 7.8947368421052602 13.15789473684211 18.421052631578942 23.684210526315791 28.947368421052641 34.21052631578948 39.473684210526301 44.73684210526315 50 55.26315789 4736857 60.526315789473699 65.789473684210563 71.052631578947384 76.315789473684163 81.578947368420984 86.842105263157904 92.105263157894726 97.368421052631547 10.7 11.3 11.8 11.9 12 12 12 12.4 12.5 12.6 13.1 13.2 13.4 13.5 13.5 14.2 14.5 14.5 14.6
Sample Percentile
MedianSchoolYears
Age Residual Plot
60 30 62 44 0 30 62 68 46 56 36 28 0 0 34 26 52 50 44 0.50878516451792 1.7144464705013149 -0.42159945482941003 0.54117037792769895 0.71299080887547295 1.269413932725179 0.26951686627728799 0.22131431339594501 -0.13472012994437299 0.22075061567252199 -1.3199768562363781 -0.18681496091028299 0.380020030213299 -1.451131014273024 -0.56052688701790399 -0.116260966970037 -0.67291294283960901 -0.49015761805784802 -0.48430774902780499
Age
Residuals
RUNNING HEADER: WEEK 3 ASSIGNMENT 4 1
WEEK 3 ASSIGNMENT 4 13
Week 3 Assignment 4
Introduction
In this project I selected six variables from the ' SampleDataSet.xlsx'. Among these six variables three of them were continuous and the reaming three were discrete variables. The continuous variables selected for this study are Age, WealthScore and MedianSchoolYears. The discrete variables selected for this study are NumberOfChildren, MailResponder and NumberOfCars.
Analysis
Age
The age is a continuous variable which takes only positive values even though we usually consider the integer part of it. The descriptive statistics summary of the age variable .
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.
Measures of Central Tendency-Mean, Median , Mode- Dr. Vikramjit SinghVikramjit Singh
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Reporting statistics in psychology
1. Reporting Statistics in Psychology
This document contains general guidelines for the reporting of statistics in psychology re-
search. The details of statistical reporting vary slightly among different areas of science and
also among different journals.
General Guidelines
Rounding Numbers
For numbers greater than 100, report to the nearest whole number (e.g., M = 6254). For
numbers between 10 and 100, report to one decimal place (e.g., M = 23.4). For numbers be-
tween 0.10 and 10, report to two decimal places (e.g., M = 4.34, SD = 0.93). For numbers
less than 0.10, report to three decimal places, or however many digits you need to have a
non-zero number (e.g., M = 0.014, SEM = 0.0004).
For numbers... Round to... SPSS Report
Greater than 100 Whole number 1034.963 1035
10 - 100 1 decimal place 11.4378 11.4
0.10 - 10 2 decimal places 4.3682 4.37
0.001 - 0.10 3 decimal places 0.0352 0.035
Less than 0.001 As many digits as needed for non-zero 0.00038 0.0004
Do not report any decimal places if you are reporting something that can only be a whole
number. For example, the number of participants in a study should be reported as N = 5, not
N = 5.0.
Report exact p-values (not p < .05), even for non-significant results. Round as above, unless
SPSS gives a p-value of .000; then report p < .001. Two-tailed p-values are assumed. If
you are reporting a one-tailed p-value, you must say so.
Omit the leading zero from p-values, correlation coefficients (r), partial eta-squared (ηp2), and
other numbers that cannot ever be greater than 1.0 (e.g., p = .043, not p = 0.043).
Statistical Abbreviations
Abbreviations using Latin letters, such as mean (M) and standard deviation (SD), should be
italicised, while abbreviations using Greek letters, such as partial eta-squared (ηp2), should
not be italicised and can be written out in full if you cannot use Greek letters. There should
be a space before and after equal signs. The abbreviations should only be used inside of pa-
rentheses; spell out the names otherwise.
Inferential statistics should generally be reported in the style of:
“statistic(degrees of freedom) = value, p = value, effect size statistic = value”
Statistic Example
Mean and standard deviation M = 3.45, SD = 1.21
Mann-Whitney U = 67.5, p = .034, r = .38
Wilcoxon signed-ranks Z = 4.21, p < .001
Sign test Z = 3.47, p = .001
t-test t(19) = 2.45, p = .031, d = 0.54
ANOVA F(2, 1279) = 6.15, p = .002, ηp2 = 0.010
Pearson’s correlation r(1282) = .13, p < .001
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2. Reporting Statistics in Psychology
Descriptive Statistics
Means and standard deviations should be given either in the text or in a table, but not both.
The average age of participants was 25.5 years (SD = 7.94).
The age of participants ranged from 18 to 70 years (M = 25.5, SD = 7.94). Age was
non-normally distributed, with skewness of 1.87 (SE = 0.05) and kurtosis of 3.93
(SE = 0.10)
Participants were 98 men and 132 women aged 17 to 25 years (men: M = 19.2,
SD = 2.32; women: M = 19.6, SD = 2.54).
Non-parametric tests
Do not report means and standard deviations for non-parametric tests. Report the median
and range in the text or in a table. The statistics U and Z should be capitalised and italicised.
A measure of effect size, r, can be calculated by dividing Z by the square root of N
(r = Z / √N).
Mann-Whitney Test (2 Independent Samples...)
A Mann-Whitney test indicated that self-rated attractiveness was greater for women
who were not using oral contraceptives (Mdn = 5) than for women who were using oral
contraceptives (Mdn = 4), U = 67.5, p = .034, r = .38.
Wilcoxon Signed-ranks Test (2 Related Samples...)
A Wilcoxon Signed-ranks test indicated that femininity was preferred more in female
faces (Mdn = 0.85) than in male faces (Mdn = 0.65), Z = 4.21, p < .001, r = .76.
2
3. Reporting Statistics in Psychology
Sign Test (2 Related Samples...)
A sign test indicated that femininity was preferred more in female faces than in male
faces, Z = 3.47, p = .001.
T-tests
Report degrees of freedom in parentheses. The statistics t, p and Cohen’s d should be re-
ported and italicised.
One-sample t-test
One-sample t-test indicated that femininity preferences were greater than the chance
level of 3.5 for female faces (M = 4.50, SD = 0.70), t(30) = 8.01, p < .001, d = 1.44, but
not for male faces (M = 3.46, SD = 0.73), t(30) = -0.32, p = .75, d = 0.057.
The number of masculine faces chosen out of 20 possible was compared to the
chance value of 10 using a one-sample t-test. Masculine faces were chosen more
often than chance, t(76) = 4.35, p = .004, d = 0.35.
Paired-samples t-test
Report paired-samples t-tests in the same way as one-sample t-tests.
A paired-samples t-test indicated that scores were significantly higher for the pathogen
subscale (M = 26.4, SD = 7.41) than for the sexual subscale (M = 18.0, SD = 9.49),
t(721) = 23.3, p < .001, d = 0.87.
3
4. Reporting Statistics in Psychology
Scores on the pathogen subscale (M = 26.4, SD = 7.41) were higher than scores on
the sexual subscale (M = 18.0, SD = 9.49), t(721) = 23.3, p < .001, d = 0.87. A one-
tailed p-value is reported due to the strong prediction of this effect.
Independent-samples t-test
An independent-samples t-test indicated that scores were significantly higher for
women (M = 27.0, SD = 7.21) than for men (M = 24.2, SD = 7.69), t(734) = 4.30,
p < .001, d = 0.35.
If Levene’s test for equality of variances is significant, report the statistics for the row equal
variances not assumed with the altered degrees of freedom rounded to the nearest whole
number.
Scores on the pathogen subscale were higher for women (M = 27.0, SD = 7.21) than
for men (M = 24.2, SD = 7.69), t(340) = 4.30, p < .001, d = 0.35. Levene’s test
indicated unequal variances (F = 3.56, p = .043), so degrees of freedom were adjusted
from 734 to 340.
ANOVAs
ANOVAs have two degrees of freedom to report. Report the between-groups df first and the
within-groups df second, separated by a comma and a space (e.g., F(1, 237) = 3.45). The
measure of effect size, partial eta-squared (ηp2), may be written out or abbreviated, omits the
leading zero and is not italicised.
One-way ANOVAs and Post-hocs
Analysis of variance showed a main effect of self-rated attractiveness (SRA) on
preferences for femininity in female faces, F(2, 1279) = 6.15, p = .002, ηp2 = .010. Post-
hoc analyses using Tukey’s HSD indicated that femininity preferences were lower for
participants with low SRA than for participants with average SRA (p = .014) and high
SRA (p = .004), but femininity preferences did not differ significantly between
participants with average and high SRA (p = .82).
4
5. Reporting Statistics in Psychology
2-way Factorial ANOVAs
A 3x2 ANOVA with self-rated attractiveness (low, average, high) and oral contraceptive
use (true, false) as between-subjects factors revealed a main effects of SRA,
F(2, 1276) = 6.11, p = .002, ηp2 = .009, and oral contraceptive use, F(1, 1276) = 4.38, p
= .037, ηp2 = 0.003. These main effects were not qualified by an interaction between
SRA and oral contraceptive use, F(2, 1276) = 0.43, p = .65, ηp2 = .001.
3-way ANOVAs and Higher
Although some textbooks suggest that you report all main effects and interactions, even if not
significant, this reduces the understandability of the results of a complex design (i.e. 3-way or
higher). Report all significant effects and all predicted effects, even if not significant. If there
are more than two non-significant effects that are irrelevant to your main hypotheses (e.g.
you predicted an interaction among three factors, but did not predict any main effects or 2-
way interactions), you can summarise them as in the example below.
A mixed-design ANOVA with sex of face (male, female) as a within-subjects factor and
self-rated attractiveness (low, average, high) and oral contraceptive use (true, false) as
between-subjects factors revealed a main effect of sex of face, F(1, 1276) = 1372,
p < .001, ηp2 = .52. This was qualified by interactions between sex of face and SRA,
F(2, 1276) = 6.90, p = .001, ηp2 = .011, and between sex of face and oral contraceptive
use, F(1, 1276) = 5.02, p = .025, ηp2 = .004. The predicted interaction among sex of
face, SRA and oral contraceptive use was not significant, F(2, 1276) = 0.06, p = .94,
ηp2 < .001. All other main effects and interactions were non-significant and irrelevant to
our hypotheses, all F ≤ 0.94, p ≥ .39, ηp2 ≤ .001.
Violations of Sphericity and Greenhouse-Geisser Corrections
ANOVAs are not robust to violations of sphericity, but can be easily corrected. For each
within-subjects factor with more than two levels, check if Mauchly’s test is significant. If so,
report chi-squared (χ2), degrees of freedom, p and epsilon (ε) as below and report the
Greenhouse-Geisser corrected values for any effects involving this factor (rounded to the
appropriate decimal place). SPSS will report a chi-squared of .000 and no p-value for within-
subjects factors with only two levels; corrections are not needed.
5
6. Reporting Statistics in Psychology
Data were analysed using a mixed-design ANOVA with a within-subjects factor of
subscale (pathogen, sexual, moral) and a between-subject factor of sex (male, female).
Mauchly’s test indicated that the assumption of sphericity had been violated
(χ2(2) = 16.8, p < .001), therefore degrees of freedom were corrected using
Greenhouse-Geisser estimates of sphericity (ε = 0.98). Main effects of subscale,
F(1.91, 1350.8) = 378, p < .001, ηp2 = .35, and sex, F(1, 709) = 78.8, p < .001, ηp2 = .
10, were qualified by an interaction between subscale and sex, F(1.91, 1351) = 30.4,
p < .001, ηp2 = .041.
ANCOVA
An ANCOVA [between-subjects factor: sex (male, female); covariate: age] revealed no
main effects of sex, F(1, 732) = 2.00, p = .16, ηp2 = .003, or age, F(1, 732) = 3.25,
p = .072, ηp2 = .004, and no interaction between sex and age, F(1, 732) = 0.016,
p = .90, ηp2 < .001.
The predicted main effect of sex was not significant, F(1, 732) = 2.00, p = .16,
ηp2 = .003, nor was the predicted main effect of age, F(1, 732) = 3.25, p = .072,
ηp2 = .004. The interaction between sex and age were also not significant,
F(1, 732) = 0.016, p = .90, ηp2 < .001.
6
7. Reporting Statistics in Psychology
Correlations
Italicise r and p. Omit the leading zero from r.
Preferences for femininity in male and female faces were positively correlated,
Pearson’s r(1282) = .13, p < .001.
References
American Psychological Association. (2005). Concise Rules of APA Style. Washington, DC:
APA Publications.
Field, A. P., & Hole, G. J. (2003). How to design and report experiments. London: Sage Pub-
lications.
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