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The chi-square distribution is related to the normal distribution, as it is the distribution of the sum of squared normal random variables. The F distribution is the ratio of two chi-square random variables, each divided by its degrees of freedom. Both the chi-square and F distributions are used to test hypotheses about variances and compare variance estimates. To test if two samples have equal variances, the F test compares the ratio of the two sample variance estimates to the critical values of the F distribution with the degrees of freedom of each sample.

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Top schools in India | Delhi NCR | Noida |

This document discusses four common statistical distributions: the z, t, chi-square, and F distributions. It focuses on explaining the chi-square and F distributions. The chi-square distribution results from summing squared, normally distributed values and depends on degrees of freedom. The F distribution is the ratio of two chi-square variables divided by their degrees of freedom and depends on two degrees of freedom parameters. Both the chi-square and F distributions are used for hypothesis testing of variances from sample data.

Top schools in ghaziabad

This document discusses four common statistical distributions - the z, t, chi-square, and F distributions. The chi-square distribution represents the sum of squared normal random variables and its shape depends on the degrees of freedom. The F distribution is the ratio of two chi-square random variables divided by their degrees of freedom and is used to test hypotheses about variances. Both the chi-square and F distributions are used to conduct statistical tests about variances and evaluate confidence intervals.

Review on probability distributions, estimation and hypothesis testing

This document provides an overview of probability distributions, estimation, and hypothesis testing. It discusses key concepts such as:
- Common discrete and continuous probability distributions including binomial, Poisson, normal, uniform, and exponential.
- Estimation techniques including point estimates, confidence intervals for means and proportions.
- Hypothesis testing frameworks including stating null and alternative hypotheses, determining test statistics, critical values, and statistical decisions.
- Specific hypothesis tests are described for means when the population standard deviation is known or unknown.
The document is intended as a review of these statistical concepts and includes sample test questions to help with learning.

Statistics-2 : Elements of Inference

Elements of Inference covers the following concepts and takes off right from where we left off in the previous slide https://www.slideshare.net/GiridharChandrasekar1/statistics1-the-basics-of-statistics.
Population Vs Sample (Measures)
Probability
Random Variables
Probability Distributions
Statistical Inference – The Concept

ch-4-measures-of-variability-11 2.ppt for nursing

This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.

measures-of-variability-11.ppt

This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.

Frequency Distributions

This document discusses frequency distributions, which organize and simplify data by tabulating how often values occur within categories. Frequency distributions can be regular, listing all categories, or grouped, combining categories into intervals. They are presented in tables showing categories/intervals and frequencies. Graphs like histograms and polygons also display distributions. Distributions describe data through measures of central tendency, variability, and shape. Percentiles indicate the percentage of values at or below a given score.

Stat2013

The document provides information about performing chi-square tests and choosing appropriate statistical tests. It discusses key concepts like the null hypothesis, degrees of freedom, and expected versus observed values. Examples are provided to illustrate chi-square tests for goodness of fit and comparison of proportions. The document also compares parametric and non-parametric tests, providing examples of when each would be used.

Top schools in India | Delhi NCR | Noida |

This document discusses four common statistical distributions: the z, t, chi-square, and F distributions. It focuses on explaining the chi-square and F distributions. The chi-square distribution results from summing squared, normally distributed values and depends on degrees of freedom. The F distribution is the ratio of two chi-square variables divided by their degrees of freedom and depends on two degrees of freedom parameters. Both the chi-square and F distributions are used for hypothesis testing of variances from sample data.

Top schools in ghaziabad

This document discusses four common statistical distributions - the z, t, chi-square, and F distributions. The chi-square distribution represents the sum of squared normal random variables and its shape depends on the degrees of freedom. The F distribution is the ratio of two chi-square random variables divided by their degrees of freedom and is used to test hypotheses about variances. Both the chi-square and F distributions are used to conduct statistical tests about variances and evaluate confidence intervals.

Review on probability distributions, estimation and hypothesis testing

This document provides an overview of probability distributions, estimation, and hypothesis testing. It discusses key concepts such as:
- Common discrete and continuous probability distributions including binomial, Poisson, normal, uniform, and exponential.
- Estimation techniques including point estimates, confidence intervals for means and proportions.
- Hypothesis testing frameworks including stating null and alternative hypotheses, determining test statistics, critical values, and statistical decisions.
- Specific hypothesis tests are described for means when the population standard deviation is known or unknown.
The document is intended as a review of these statistical concepts and includes sample test questions to help with learning.

Statistics-2 : Elements of Inference

Elements of Inference covers the following concepts and takes off right from where we left off in the previous slide https://www.slideshare.net/GiridharChandrasekar1/statistics1-the-basics-of-statistics.
Population Vs Sample (Measures)
Probability
Random Variables
Probability Distributions
Statistical Inference – The Concept

ch-4-measures-of-variability-11 2.ppt for nursing

This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.

measures-of-variability-11.pptThis document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.

Frequency Distributions

This document discusses frequency distributions, which organize and simplify data by tabulating how often values occur within categories. Frequency distributions can be regular, listing all categories, or grouped, combining categories into intervals. They are presented in tables showing categories/intervals and frequencies. Graphs like histograms and polygons also display distributions. Distributions describe data through measures of central tendency, variability, and shape. Percentiles indicate the percentage of values at or below a given score.

Stat2013

The document provides information about performing chi-square tests and choosing appropriate statistical tests. It discusses key concepts like the null hypothesis, degrees of freedom, and expected versus observed values. Examples are provided to illustrate chi-square tests for goodness of fit and comparison of proportions. The document also compares parametric and non-parametric tests, providing examples of when each would be used.

Measures of Variability.pptx

Here are the steps to solve this problem:
(i) Given data: 41, 47, 48, 50, 51, 53, 60
Mean (x̅) = ∑x/n = (41 + 47 + 48 + 50 + 51 + 53 + 60)/7 = 350/7 = 50
Q1 = 48, Q3 = 53
IQR = Q3 - Q1 = 53 - 48 = 5
Q = (Q3 - Q1)/2 = (53 - 48)/2 = 2.5
AD = ∑|x - x̅|/n = (9 + 3 + 2 + 0 + 1 + 3 + 10)/7 = 28/7 =

F-Distribution

Here are the steps to solve this problem:
1) State the null and alternative hypotheses:
H0: σ1^2 = σ2^2 (the variances are equal)
Ha: σ1^2 ≠ σ2^2 (the variances are unequal)
2) Specify the significance level: α = 0.05
3) Calculate the F-statistic:
F = (0.0428/120) / (0.0395/80) = 1.0833
4) Find the p-value:
This is a left-tailed test since s1 < s2. From the F-distribution table with degrees of freedom v1 = 80-1

Chapter 7 Powerpoint

The document outlines the goals and key concepts of a chapter on continuous probability distributions. It discusses the differences between discrete and continuous distributions. It then focuses on the uniform, normal, and binomial distributions, explaining how to calculate probabilities and values for each. Key points covered include the mean, standard deviation, and shape of each distribution as well as how to find z-values and probabilities using the normal distribution and binomial approximation.

Chi square distribution and analysis of frequencies.pptx

Chi square distribution and analysis of frequencies.pptx

The Chi-Square Statistic: Tests for Goodness of Fit and Independence

Chapter 15 Power Points for Essentials of Statistics for the Behavioral Sciences, Gravetter & Wallnau, 8th ed

Chapter 3 Standard scores.pptx

- The document discusses transforming raw scores into z-scores and standardized distributions. It covers how to calculate z-scores, what z-scores represent in terms of distance from the mean, and how standardizing distributions makes them comparable. The key aspects of standardizing include transforming the raw scores to have a mean of 0 and standard deviation of 1 while maintaining the same shape.

Dr.Dinesh-BIOSTAT-Tests-of-significance-1-min.pdf

This document discusses various statistical tests used to analyze dental research data, including parametric and non-parametric tests. It provides information on tests of significance such as the t-test, Z-test, analysis of variance (ANOVA), and non-parametric equivalents. Key points covered include the differences between parametric and non-parametric tests, assumptions and applications of the t-test, Z-test, ANOVA, and non-parametric alternatives like the Mann-Whitney U test and Kruskal-Wallis test. Examples are provided to illustrate how to perform and interpret common statistical analyses used in dental research.

Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdf

Biostatistics, Unit-I, Measures of Dispersion, Dispersion
Range
variation of mean
standard deviation
Variance
coefficient of variation
standard error of the mean

descriptive statistics.pptx

This document provides information on measures of central tendency and dispersion. It discusses the mean, median, and mode as the three main measures of central tendency. It provides formulas and examples for calculating the mean, median, and mode for both ungrouped and grouped data. The document also covers measures of dispersion including range, semi-interquartile range, variance, standard deviation, and coefficient of variation. It provides formulas and examples for calculating each of these measures. Finally, the document briefly discusses chi-square tests, Pearson's correlation, and using scatterplots to examine relationships between variables.

The T-test

The t-test is used to test hypotheses about population means when the population variance is unknown. It is closely related to the z-test but uses the t distribution instead of the normal. There are three main types of t-tests: single sample, independent samples, and dependent samples. The t-test compares the sample mean to the population mean and takes into account factors like sample size and variability. Larger sample sizes and stronger associations between variables increase the power of the t-test to detect significant differences or relationships.

Chapter 2 Standard scores.pptx

- The document discusses transforming raw scores into z-scores, which standardizes distributions and allows comparison of scores across different distributions.
- A z-score indicates how many standard deviations an observation is above or below the mean, with a positive z-score above the mean and negative below.
- Transforming distributions to z-scores changes the mean to 0 and standard deviation to 1, while maintaining the same shape, allowing comparison of scores from different distributions.

Stat1008 Tutorial

This document provides an overview and examples for a STAT1008 tutorial covering 9 sections: 1) data collection, 2) variables and statistics, 3) probability, 4) continuous probability distributions, 5) sampling distributions, 6) interval estimation, 7) hypothesis testing, 8) hypothesis tests for variances, and 9) regression analysis. Key concepts are explained for each section along with examples from past exams. The tutorial aims to cover the key points needed to understand the material and do well on exams through challenging questions and general hints.

Str t-test1

This document describes the steps for conducting an independent samples t-test. The t-test is used to compare the means of two independent groups on a continuous dependent variable. It tests whether the means of the two groups are statistically significantly different from each other. The steps include: 1) stating the null and alternative hypotheses, 2) setting the significance level, 3) calculating the t-value, 4) finding the critical t-value, and 5) making a conclusion about whether to reject the null hypothesis based on the t-values. An example compares math test scores of male and female college students to determine if gender significantly impacts scores.

Location Scores

The document discusses the risks of investing heavily in stocks compared to other investment strategies. It notes that stocks have historically returned around 9.6% annually on average but with significant volatility, ranging from a 12% loss to a 31% gain in any given year. This level of volatility would require an investor to have a strong stomach and tolerance for risk. The article suggests that a major stock position close to retirement could force an investor to reconsider their retirement plans if a bad year for the market coincided with their retirement.

State presentation2

This document summarizes various statistical measures used to analyze and describe data distributions, including measures of central tendency (mean, median, mode), dispersion (range, standard deviation, variance), skewness, and kurtosis. It provides formulas and methods for calculating each measure along with interpretations of the results. Measures of central tendency provide a single value to represent the center of the data set. Measures of dispersion describe how spread out or varied the data values are. Skewness and kurtosis measure the symmetry and peakedness of distributions compared to the normal curve.

Measures of Variability

Chapter 4 Power Points for Essentials of Statistics for the Behavioral Sciences, Gravetter & Wallnau, 8th ed

Chapter 3 Ken Black 2.ppt

This document provides an overview of descriptive statistics concepts including measures of central tendency (mean, median, mode), measures of variability (range, standard deviation, variance), and how to compute them from both ungrouped and grouped data. It defines key terms like mean, median, mode, percentiles, quartiles, range, standard deviation, variance, and coefficient of variation. It also discusses how standard deviation can be used to measure financial risk and the empirical rule and Chebyshev's theorem for interpreting standard deviation.

Location scores

The document discusses standardizing distributions using z-scores. It explains that z-scores provide a description of a score's location in a distribution based on the number of standard deviations it is from the mean. All z-scores are comparable even when derived from different distributions. Transforming a full data set to z-scores standardizes the distribution, giving it a mean of 0 and standard deviation of 1 while maintaining the original shape. This allows comparison of scores across variables and individuals.

Z-scores: Location of Scores and Standardized Distributions

Chapter 5 Power Points for Essentials of Statistics for the Behavioral Sciences, Gravetter & Wallnau, 8th ed

NON-PARAMETRIC TESTS.pptx

• Non parametric tests are distribution free methods, which do not rely on assumptions that the data are drawn from a given probability distribution. As such it is the opposite of parametric statistics
• In non- parametric tests we do not assume that a particular distribution is applicable or that a certain value is attached to a parameter of the population.
When to use non parametric test???
1) Sample distribution is unknown.
2) When the population distribution is abnormal
Non-parametric tests focus on order or ranking
1) Data is changed from scores to ranks or signs
2) A parametric test focuses on the mean difference, and equivalent non-parametric test focuses on the difference between medians.
1) Chi – square test
• First formulated by Helmert and then it was developed by Karl Pearson
• It is both parametric and non-parametric test but more of non - parametric test.
• The test involves calculation of a quantity called Chi square.
• Follows specific distribution known as Chi square distribution
• It is used to test the significance of difference between 2 proportions and can be used when there are more than 2 groups to be compared.
Applications
1) Test of proportion
2) Test of association
3) Test of goodness of fit
Criteria for applying Chi- square test
• Groups: More than 2 independent
• Data: Qualitative
• Sample size: Small or Large, random sample
• Distribution: Non-Normal (Distribution free)
• Lowest expected frequency in any cell should be greater than 5
• No group should contain less than 10 items
Example: If there are two groups, one of which has received oral hygiene instructions and the other has not received any instructions and if it is desired to test if the occurrence of new cavities is associated with the instructions.
2) Fischer Exact Test
• Used when one or more of the expected counts in a 2×2 table is small.
• Used to calculate the exact probability of finding the observed numbers by using the fischer exact probability test.
3) Mc Nemar Test
• Used to compare before and after findings in the same individual or to compare findings in a matched analysis (for dichotomous variables).
Example: comparing the attitudes of medical students toward confidence in statistics analysis before and after the intensive statistics course.
4) Sign Test
• Sign test is used to find out the statistical significance of differences in matched pair comparisons.
• Its based on + or – signs of observations in a sample and not on their numerical magnitudes.
• For each subject, subtract the 2nd score from the 1st, and write down the sign of the difference.
It can be used
a. in place of a one-sample t-test
b. in place of a paired t-test or
c. for ordered categorial data where a numerical scale is inappropriate but where it is possible to rank the observations.
5) Wilcoxon signed rank test
• Analogous to paired ‘t’ test
6) Mann Whitney Test
• similar to the student’s t test
7) Spearman’s rank correlation - similar to pearson's correlation.

Advanced Biostatistics presentation pptx

This document provides an introduction to biostatistics. It defines statistics as the collection, organization, and analysis of data to draw inferences about a sample population. Biostatistics applies statistical methods to biological and medical data. The document discusses why biostatistics is studied, including that more aspects of medicine and public health are now quantified and biological processes have inherent variation. It also covers types of data, methods of data collection like questionnaires and observation, and considerations for designing questionnaires and conducting interviews.

Regression Analysis.ppt

Regression analysis can be used to analyze the relationship between variables. A scatter plot should first be created to determine if the variables have a linear relationship required for regression analysis. A regression line is fitted to best describe the linear relationship between the variables, with an R-squared value indicating how well it fits the data. Multiple regression allows for analysis of the relationship between a dependent variable and multiple independent variables and their individual contributions to explaining the variance in the dependent variable.

Measures of Variability.pptx

Here are the steps to solve this problem:
(i) Given data: 41, 47, 48, 50, 51, 53, 60
Mean (x̅) = ∑x/n = (41 + 47 + 48 + 50 + 51 + 53 + 60)/7 = 350/7 = 50
Q1 = 48, Q3 = 53
IQR = Q3 - Q1 = 53 - 48 = 5
Q = (Q3 - Q1)/2 = (53 - 48)/2 = 2.5
AD = ∑|x - x̅|/n = (9 + 3 + 2 + 0 + 1 + 3 + 10)/7 = 28/7 =

F-Distribution

Here are the steps to solve this problem:
1) State the null and alternative hypotheses:
H0: σ1^2 = σ2^2 (the variances are equal)
Ha: σ1^2 ≠ σ2^2 (the variances are unequal)
2) Specify the significance level: α = 0.05
3) Calculate the F-statistic:
F = (0.0428/120) / (0.0395/80) = 1.0833
4) Find the p-value:
This is a left-tailed test since s1 < s2. From the F-distribution table with degrees of freedom v1 = 80-1

Chapter 7 Powerpoint

The document outlines the goals and key concepts of a chapter on continuous probability distributions. It discusses the differences between discrete and continuous distributions. It then focuses on the uniform, normal, and binomial distributions, explaining how to calculate probabilities and values for each. Key points covered include the mean, standard deviation, and shape of each distribution as well as how to find z-values and probabilities using the normal distribution and binomial approximation.

Chi square distribution and analysis of frequencies.pptx

Chi square distribution and analysis of frequencies.pptx

The Chi-Square Statistic: Tests for Goodness of Fit and Independence

Chapter 15 Power Points for Essentials of Statistics for the Behavioral Sciences, Gravetter & Wallnau, 8th ed

Chapter 3 Standard scores.pptx

- The document discusses transforming raw scores into z-scores and standardized distributions. It covers how to calculate z-scores, what z-scores represent in terms of distance from the mean, and how standardizing distributions makes them comparable. The key aspects of standardizing include transforming the raw scores to have a mean of 0 and standard deviation of 1 while maintaining the same shape.

Dr.Dinesh-BIOSTAT-Tests-of-significance-1-min.pdf

This document discusses various statistical tests used to analyze dental research data, including parametric and non-parametric tests. It provides information on tests of significance such as the t-test, Z-test, analysis of variance (ANOVA), and non-parametric equivalents. Key points covered include the differences between parametric and non-parametric tests, assumptions and applications of the t-test, Z-test, ANOVA, and non-parametric alternatives like the Mann-Whitney U test and Kruskal-Wallis test. Examples are provided to illustrate how to perform and interpret common statistical analyses used in dental research.

Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdf

Biostatistics, Unit-I, Measures of Dispersion, Dispersion
Range
variation of mean
standard deviation
Variance
coefficient of variation
standard error of the mean

descriptive statistics.pptx

This document provides information on measures of central tendency and dispersion. It discusses the mean, median, and mode as the three main measures of central tendency. It provides formulas and examples for calculating the mean, median, and mode for both ungrouped and grouped data. The document also covers measures of dispersion including range, semi-interquartile range, variance, standard deviation, and coefficient of variation. It provides formulas and examples for calculating each of these measures. Finally, the document briefly discusses chi-square tests, Pearson's correlation, and using scatterplots to examine relationships between variables.

The T-test

The t-test is used to test hypotheses about population means when the population variance is unknown. It is closely related to the z-test but uses the t distribution instead of the normal. There are three main types of t-tests: single sample, independent samples, and dependent samples. The t-test compares the sample mean to the population mean and takes into account factors like sample size and variability. Larger sample sizes and stronger associations between variables increase the power of the t-test to detect significant differences or relationships.

Chapter 2 Standard scores.pptx

- The document discusses transforming raw scores into z-scores, which standardizes distributions and allows comparison of scores across different distributions.
- A z-score indicates how many standard deviations an observation is above or below the mean, with a positive z-score above the mean and negative below.
- Transforming distributions to z-scores changes the mean to 0 and standard deviation to 1, while maintaining the same shape, allowing comparison of scores from different distributions.

Stat1008 Tutorial

This document provides an overview and examples for a STAT1008 tutorial covering 9 sections: 1) data collection, 2) variables and statistics, 3) probability, 4) continuous probability distributions, 5) sampling distributions, 6) interval estimation, 7) hypothesis testing, 8) hypothesis tests for variances, and 9) regression analysis. Key concepts are explained for each section along with examples from past exams. The tutorial aims to cover the key points needed to understand the material and do well on exams through challenging questions and general hints.

Str t-test1

This document describes the steps for conducting an independent samples t-test. The t-test is used to compare the means of two independent groups on a continuous dependent variable. It tests whether the means of the two groups are statistically significantly different from each other. The steps include: 1) stating the null and alternative hypotheses, 2) setting the significance level, 3) calculating the t-value, 4) finding the critical t-value, and 5) making a conclusion about whether to reject the null hypothesis based on the t-values. An example compares math test scores of male and female college students to determine if gender significantly impacts scores.

Location Scores

The document discusses the risks of investing heavily in stocks compared to other investment strategies. It notes that stocks have historically returned around 9.6% annually on average but with significant volatility, ranging from a 12% loss to a 31% gain in any given year. This level of volatility would require an investor to have a strong stomach and tolerance for risk. The article suggests that a major stock position close to retirement could force an investor to reconsider their retirement plans if a bad year for the market coincided with their retirement.

State presentation2

This document summarizes various statistical measures used to analyze and describe data distributions, including measures of central tendency (mean, median, mode), dispersion (range, standard deviation, variance), skewness, and kurtosis. It provides formulas and methods for calculating each measure along with interpretations of the results. Measures of central tendency provide a single value to represent the center of the data set. Measures of dispersion describe how spread out or varied the data values are. Skewness and kurtosis measure the symmetry and peakedness of distributions compared to the normal curve.

Measures of Variability

Chapter 4 Power Points for Essentials of Statistics for the Behavioral Sciences, Gravetter & Wallnau, 8th ed

Chapter 3 Ken Black 2.ppt

This document provides an overview of descriptive statistics concepts including measures of central tendency (mean, median, mode), measures of variability (range, standard deviation, variance), and how to compute them from both ungrouped and grouped data. It defines key terms like mean, median, mode, percentiles, quartiles, range, standard deviation, variance, and coefficient of variation. It also discusses how standard deviation can be used to measure financial risk and the empirical rule and Chebyshev's theorem for interpreting standard deviation.

Location scores

The document discusses standardizing distributions using z-scores. It explains that z-scores provide a description of a score's location in a distribution based on the number of standard deviations it is from the mean. All z-scores are comparable even when derived from different distributions. Transforming a full data set to z-scores standardizes the distribution, giving it a mean of 0 and standard deviation of 1 while maintaining the original shape. This allows comparison of scores across variables and individuals.

Z-scores: Location of Scores and Standardized Distributions

Chapter 5 Power Points for Essentials of Statistics for the Behavioral Sciences, Gravetter & Wallnau, 8th ed

NON-PARAMETRIC TESTS.pptx

• Non parametric tests are distribution free methods, which do not rely on assumptions that the data are drawn from a given probability distribution. As such it is the opposite of parametric statistics
• In non- parametric tests we do not assume that a particular distribution is applicable or that a certain value is attached to a parameter of the population.
When to use non parametric test???
1) Sample distribution is unknown.
2) When the population distribution is abnormal
Non-parametric tests focus on order or ranking
1) Data is changed from scores to ranks or signs
2) A parametric test focuses on the mean difference, and equivalent non-parametric test focuses on the difference between medians.
1) Chi – square test
• First formulated by Helmert and then it was developed by Karl Pearson
• It is both parametric and non-parametric test but more of non - parametric test.
• The test involves calculation of a quantity called Chi square.
• Follows specific distribution known as Chi square distribution
• It is used to test the significance of difference between 2 proportions and can be used when there are more than 2 groups to be compared.
Applications
1) Test of proportion
2) Test of association
3) Test of goodness of fit
Criteria for applying Chi- square test
• Groups: More than 2 independent
• Data: Qualitative
• Sample size: Small or Large, random sample
• Distribution: Non-Normal (Distribution free)
• Lowest expected frequency in any cell should be greater than 5
• No group should contain less than 10 items
Example: If there are two groups, one of which has received oral hygiene instructions and the other has not received any instructions and if it is desired to test if the occurrence of new cavities is associated with the instructions.
2) Fischer Exact Test
• Used when one or more of the expected counts in a 2×2 table is small.
• Used to calculate the exact probability of finding the observed numbers by using the fischer exact probability test.
3) Mc Nemar Test
• Used to compare before and after findings in the same individual or to compare findings in a matched analysis (for dichotomous variables).
Example: comparing the attitudes of medical students toward confidence in statistics analysis before and after the intensive statistics course.
4) Sign Test
• Sign test is used to find out the statistical significance of differences in matched pair comparisons.
• Its based on + or – signs of observations in a sample and not on their numerical magnitudes.
• For each subject, subtract the 2nd score from the 1st, and write down the sign of the difference.
It can be used
a. in place of a one-sample t-test
b. in place of a paired t-test or
c. for ordered categorial data where a numerical scale is inappropriate but where it is possible to rank the observations.
5) Wilcoxon signed rank test
• Analogous to paired ‘t’ test
6) Mann Whitney Test
• similar to the student’s t test
7) Spearman’s rank correlation - similar to pearson's correlation.

Measures of Variability.pptx

Measures of Variability.pptx

F-Distribution

F-Distribution

Chapter 7 Powerpoint

Chapter 7 Powerpoint

Chi square distribution and analysis of frequencies.pptx

Chi square distribution and analysis of frequencies.pptx

The Chi-Square Statistic: Tests for Goodness of Fit and Independence

The Chi-Square Statistic: Tests for Goodness of Fit and Independence

Chapter 3 Standard scores.pptx

Chapter 3 Standard scores.pptx

Dr.Dinesh-BIOSTAT-Tests-of-significance-1-min.pdf

Dr.Dinesh-BIOSTAT-Tests-of-significance-1-min.pdf

Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdf

Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdf

descriptive statistics.pptx

descriptive statistics.pptx

The T-test

The T-test

Chapter 2 Standard scores.pptx

Chapter 2 Standard scores.pptx

Stat1008 Tutorial

Stat1008 Tutorial

Str t-test1

Str t-test1

Location Scores

Location Scores

State presentation2

State presentation2

Measures of Variability

Measures of Variability

Chapter 3 Ken Black 2.ppt

Chapter 3 Ken Black 2.ppt

Location scores

Location scores

Z-scores: Location of Scores and Standardized Distributions

Z-scores: Location of Scores and Standardized Distributions

NON-PARAMETRIC TESTS.pptx

NON-PARAMETRIC TESTS.pptx

Advanced Biostatistics presentation pptx

This document provides an introduction to biostatistics. It defines statistics as the collection, organization, and analysis of data to draw inferences about a sample population. Biostatistics applies statistical methods to biological and medical data. The document discusses why biostatistics is studied, including that more aspects of medicine and public health are now quantified and biological processes have inherent variation. It also covers types of data, methods of data collection like questionnaires and observation, and considerations for designing questionnaires and conducting interviews.

Regression Analysis.ppt

Regression analysis can be used to analyze the relationship between variables. A scatter plot should first be created to determine if the variables have a linear relationship required for regression analysis. A regression line is fitted to best describe the linear relationship between the variables, with an R-squared value indicating how well it fits the data. Multiple regression allows for analysis of the relationship between a dependent variable and multiple independent variables and their individual contributions to explaining the variance in the dependent variable.

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The document provides a summary of topics related to conditional probability, Bayes' theorem, and independent events. It includes examples and formulas for conditional probability, multiplication rule of probability, total probability rule, Bayes' rule, and independent events. It also discusses pairwise and mutually independent events. The document concludes with examples demonstrating applications of conditional probability, Bayes' theorem, multiplication rule, total probability rule, and independent events.

3. Statistical inference_anesthesia.pptx

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dokumen.tips_biostatistics-basics-biostatistics.ppt

This document provides an introduction to common statistical terms and concepts used in biostatistics. It defines key terms like data, variables, independent and dependent variables. It also discusses populations and samples, and how random samples and random assignment are used in research. The document outlines descriptive statistics and different levels of measurement. It also explains concepts like measures of central tendency, frequency distributions, normal distributions, and skewed distributions. Finally, it discusses properties of normal curves and what the standard deviation represents.

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Cynthia Aristei
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End-tidal carbon dioxide (ETCO2) is the level of carbon dioxide that is released at the end of an exhaled breath. ETCO2 levels reflect the adequacy with which carbon dioxide (CO2) is carried in the blood back to the lungs and exhaled.
Non-invasive methods for ETCO2 measurement include capnometry and capnography. Capnometry provides a numerical value for ETCO2. In contrast, capnography delivers a more comprehensive measurement that is displayed in both graphical (waveform) and numerical form.
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The facial nerve, also known as cranial nerve VII, is one of the 12 cranial nerves originating from the brain. It's a mixed nerve, meaning it contains both sensory and motor fibres, and it plays a crucial role in controlling various facial muscles, as well as conveying sensory information from the taste buds on the anterior two-thirds of the tongue.

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Hypertension and it's role of physiotherapy in it.

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Here is summary of hypertension -
Hypertension, also known as high blood pressure, is a serious medical condition that occurs when blood pressure in the body's arteries is consistently too high. Blood pressure is the force of blood pushing against the walls of blood vessels as the heart pumps it. Hypertension can increase the risk of heart disease, brain disease, kidney disease, and premature death.

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Discover the groundbreaking advancements in stem cell therapy by R3 Stem Cell, offering new hope for women with ovarian failure. This innovative treatment aims to restore ovarian function, improve fertility, and enhance overall well-being, revolutionizing reproductive health for women worldwide.

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Pneumothorax and role of Physiotherapy in it.

This particular slides consist of- what is Pneumothorax,what are it's causes and it's effect on body, risk factors, symptoms,complications, diagnosis and role of physiotherapy in it.
This slide is very helpful for physiotherapy students and also for other medical and healthcare students.
Here is a summary of Pneumothorax:
Pneumothorax, also known as a collapsed lung, is a condition that occurs when air leaks into the space between the lung and chest wall. This air buildup puts pressure on the lung, preventing it from expanding fully when you breathe. A pneumothorax can cause a complete or partial collapse of the lung.

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Our company incorporates various drug formulations covering pharma tablets, syrups, capsules, gels, sachets, ointments, creams, injectables.

Hypotension and role of physiotherapy in it

This particular slides consist of- what is hypotension,what are it's causes and it's effect on body, risk factors, symptoms,complications, diagnosis and role of physiotherapy in it.
This slide is very helpful for physiotherapy students and also for other medical and healthcare students.
Here is the summary of hypotension:
Hypotension, or low blood pressure, is when the pressure of blood circulating in the body is lower than normal or expected. It's only a problem if it negatively impacts the body and causes symptoms. Normal blood pressure is usually between 90/60 mmHg and 120/80 mmHg, but pressures below 90/60 are generally considered hypotensive.

NEEDLE STICK INJURY - JOURNAL CLUB PRESENTATION - DR SHAMIN EABENSON

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Here are some key objectives of communication with children:
Build Trust and Security:
Establish a safe and supportive environment where children feel comfortable expressing themselves.
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Enable children to articulate their thoughts, feelings, and experiences.
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Help children identify and understand their own emotions and the emotions of others.
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Develop children’s ability to listen attentively and respond appropriately.
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Strengthen the bond between children and caregivers, peers, and other adults.
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Offer clear instructions and explanations to help children understand expectations and learn new concepts.
By focusing on these objectives, communication with children can be both effective and nurturing, supporting their overall growth and well-being.

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Hypertension and it's role of physiotherapy in it.

Hypertension and it's role of physiotherapy in it.

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- 1. Chi-square and F Distributions Children of the Normal
- 2. Questions • What is the chi-square distribution? How is it related to the Normal? • How is the chi-square distribution related to the sampling distribution of the variance? • Test a population value of the variance; put confidence intervals around a population value.
- 3. Questions • How is the F distribution related the Normal? To Chi-square?
- 4. Distributions • There are many theoretical distributions, both continuous and discrete. Howell calls these test statistics • We use 4 test statistics a lot: z (unit normal), t, chi-square ( ), and F. • Z and t are closely related to the sampling distribution of means; chi- square and F are closely related to the sampling distribution of variances. 2
- 5. Chi-square Distribution (1) ) ( ; ) ( X z SD X X z 2 2 2 ) ( X z z score z score squared 2 ) 1 ( 2 z Make it Greek What would its sampling distribution look like? Minimum value is zero. Maximum value is infinite. Most values are between zero and 1; most around zero.
- 6. Chi-square (2) What if we took 2 values of z2 at random and added them? 2 2 2 2 2 2 2 1 2 1 ) ( ; ) ( X z X z 2 2 2 1 2 2 2 2 2 1 2 ) 2 ( ) ( ) ( z z X X Chi-square is the distribution of a sum of squares. Each squared deviation is taken from the unit normal: N(0,1). The shape of the chi-square distribution depends on the number of squared deviates that are added together. Same minimum and maximum as before, but now average should be a bit bigger.
- 7. Chi-square 3 The distribution of chi-square depends on 1 parameter, its degrees of freedom (df or v). As df gets large, curve is less skewed, more normal.
- 8. Chi-square (4) • The expected value of chi-square is df. – The mean of the chi-square distribution is its degrees of freedom. • The expected variance of the distribution is 2df. – If the variance is 2df, the standard deviation must be sqrt(2df). • There are tables of chi-square so you can find 5 or 1 percent of the distribution. • Chi-square is additive. 2 ) ( 2 ) ( 2 ) ( 2 1 2 1 v v v v
- 9. Distribution of Sample Variance 1 ) ( 2 2 N y y s Sample estimate of population variance (unbiased). 2 2 2 ) 1 ( ) 1 ( s N N Multiply variance estimate by N-1 to get sum of squares. Divide by population variance to stadnardize. Result is a random variable distributed as chi-square with (N-1) df. We can use info about the sampling distribution of the variance estimate to find confidence intervals and conduct statistical tests.
- 10. Testing Exact Hypotheses about a Variance 2 0 2 0 : H Test the null that the population variance has some specific value. Pick alpha and rejection region. Then: 2 0 2 2 ) 1 ( ) 1 ( s N N Plug hypothesized population variance and sample variance into equation along with sample size we used to estimate variance. Compare to chi-square distribution.
- 11. Example of Exact Test Test about variance of height of people in inches. Grab 30 people at random and measure height. 55 . 4 ; 30 . 25 . 6 : ; 25 . 6 : 2 2 1 2 0 s N H H Note: 1 tailed test on small side. Set alpha=.01. 11 . 21 25 . 6 ) 55 . 4 )( 29 ( 2 29 Mean is 29, so it’s on the small side. But for Q=.99, the value of chi-square is 14.257. Cannot reject null. 55 . 4 ; 30 . 25 . 6 : ; 25 . 6 : 2 2 1 2 0 s N H H Now chi-square with v=29 and Q=.995 is 13.121 and also with Q=.005 the result is 52.336. N. S. either way. Note: 2 tailed with alpha=.01.
- 12. Confidence Intervals for the Variance We use to estimate . It can be shown that: 2 s 2 95 . ) 1 ( ) 1 ( 2 ) 975 ;. 1 ( 2 2 2 ) 025 ;. 1 ( 2 N N s N s N p Suppose N=15 and is 10. Then df=14 and for Q=.025 the value is 26.12. For Q=.975 the value is 5.63. 95 . 63 . 5 ) 10 )( 14 ( 12 . 26 ) 10 )( 14 ( 2 p 95 . 87 . 24 36 . 5 2 p 2 s
- 13. Normality Assumption • We assume normal distributions to figure sampling distributions and thus p levels. • Violations of normality have minor implications for testing means, especially as N gets large. • Violations of normality are more serious for testing variances. Look at your data before conducting this test. Can test for normality.
- 14. Review • You have sample 25 children from an elementary school 5th grade class and measured the height of each. You wonder whether these children are more variable in height than typical children. Their variance in height is 4. Compute a confidence interval for this variance. If the variance of height in children in 5th grade nationally is 2, do you consider this sample ordinary?
- 15. The F Distribution (1) • The F distribution is the ratio of two variance estimates: • Also the ratio of two chi-squares, each divided by its degrees of freedom: 2 2 2 1 2 2 2 1 . . est est s s F 2 2 ( 1 2 ) ( / ) / 2 1 v v F v v In our applications, v2 will be larger than v1 and v2 will be larger than 2. In such a case, the mean of the F distribution (expected value) is v2 /(v2 -2).
- 16. F Distribution (2) • F depends on two parameters: v1 and v2 (df1 and df2). The shape of F changes with these. Range is 0 to infinity. Shaped a bit like chi-square. • F tables show critical values for df in the numerator and df in the denominator. • F tables are 1-tailed; can figure 2-tailed if you need to (but you usually don’t).
- 17. F table – critical values Numerator df: dfB dfW 1 2 3 4 5 5 5% 1% 6.61 16.3 5.79 13.3 5.41 12.1 5.19 11.4 5.05 11.0 10 5% 1% 4.96 10.0 4.10 7.56 3.71 6.55 3.48 5.99 3.33 5.64 12 5% 1% 4.75 9.33 3.89 6.94 3.49 5.95 3.26 5.41 3.11 5.06 14 5% 1% 4.60 8.86 3.74 6.51 3.34 5.56 3.11 5.04 2.96 4.70 e.g. critical value of F at alpha=.05 with 3 & 12 df =3.49
- 18. Testing Hypotheses about 2 Variances • Suppose – Note 1-tailed. • We find • Then df1=df2 = 15, and 2 2 2 1 1 2 2 2 1 0 : ; : H H 7 . 1 ; 16 ; 8 . 5 ; 16 2 2 2 2 1 1 s N s N 41 . 3 7 . 1 8 . 5 2 2 2 1 s s F Going to the F table with 15 and 15 df, we find that for alpha = .05 (1-tailed), the critical value is 2.40. Therefore the result is significant.
- 19. A Look Ahead • The F distribution is used in many statistical tests – Test for equality of variances. – Tests for differences in means in ANOVA. – Tests for regression models (slopes relating one continuous variable to another like SAT and GPA).
- 20. Relations among Distributions – the Children of the Normal • Chi-square is drawn from the normal. N(0,1) deviates squared and summed. • F is the ratio of two chi-squares, each divided by its df. A chi-square divided by its df is a variance estimate, that is, a sum of squares divided by degrees of freedom. • F = t2. If you square t, you get an F with 1 df in the numerator. ) , 1 ( 2 ) ( v v F t
- 21. Review • How is F related to the Normal? To chi-square? • Suppose we have 2 samples and we want to know whether they were drawn from populations where the variances are equal. Sample1: N=50, s2=25; Sample 2: N=60, s2=30. How can we test? What is the best conclusion for these data?