The Mann-Whitney U Test is used to compare two independent groups on an ordinal scale. It tests the null hypothesis that there is no difference between the groups' rankings. The document provides an example comparing traditional language learning to immersion learning. Students' Spanish test scores were ranked, and the Mann-Whitney U Test found a significant difference, rejecting the null hypothesis. The immersion group had higher rankings than the traditional group, showing greater Spanish proficiency from immersion learning.
Through this ppt you could learn what is Wilcoxon Signed Ranked Test. This will teach you the condition and criteria where it can be run and the way to use the test.
This presentation contains information about Mann Whitney U test, what is it, when to use it and how to use it. I have also put an example so that it may help you to easily understand it.
Through this ppt you could learn what is Wilcoxon Signed Ranked Test. This will teach you the condition and criteria where it can be run and the way to use the test.
This presentation contains information about Mann Whitney U test, what is it, when to use it and how to use it. I have also put an example so that it may help you to easily understand it.
Assumptions of parametric and non-parametric tests
Testing the assumption of normality
Commonly used non-parametric tests
Applying tests in SPSS
Advantages of non-parametric tests
Limitations
Statistical tests of significance and Student`s T-TestVasundhraKakkar
Statistical tests of significance is explained along with steps involve in Statistical tests of significance and types of significance test are also mentioned. Student`s T-Test is explained
Today’s overwhelming number of techniques applicable to data analysis makes it extremely difficult to define the most beneficial approach while considering all the significant variables.
The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear across factor levels. Interpretation is easy when data is balanced across factors but much deeper understanding is needed for unbalanced data.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
Sir Ronald Fisher pioneered the development of ANOVA for analyzing results of agricultural experiments.1 Today, ANOVA is included in almost every statistical package, which makes it accessible to investigators in all experimental sciences. It is easy to input a data set and run a simple ANOVA, but it is challenging to choose the appropriate ANOVA for different experimental designs, to examine whether data adhere to the modeling assumptions, and to interpret the results correctly. The purpose of this report, together with the next 2 articles in the Statistical Primer for Cardiovascular Research series, is to enhance understanding of ANVOA and to promote its successful use in experimental cardiovascular research. My colleagues and I attempt to accomplish those goals through examples and explanation, while keeping within reason the burden of notation, technical jargon, and mathematical equations.
01 parametric and non parametric statisticsVasant Kothari
Definition of Parametric and Non-parametric Statistics
Assumptions of Parametric and Non-parametric Statistics
Assumptions of Parametric Statistics
Assumptions of Non-parametric Statistics
Advantages of Non-parametric Statistics
Disadvantages of Non-parametric Statistical Tests
Parametric Statistical Tests for Different Samples
Parametric Statistical Measures for Calculating the Difference Between Means
Significance of Difference Between the Means of Two Independent Large and
Small Samples
Significance of the Difference Between the Means of Two Dependent Samples
Significance of the Difference Between the Means of Three or More Samples
Parametric Statistics Measures Related to Pearson’s ‘r’
Non-parametric Tests Used for Inference
Assumptions of parametric and non-parametric tests
Testing the assumption of normality
Commonly used non-parametric tests
Applying tests in SPSS
Advantages of non-parametric tests
Limitations
Statistical tests of significance and Student`s T-TestVasundhraKakkar
Statistical tests of significance is explained along with steps involve in Statistical tests of significance and types of significance test are also mentioned. Student`s T-Test is explained
Today’s overwhelming number of techniques applicable to data analysis makes it extremely difficult to define the most beneficial approach while considering all the significant variables.
The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear across factor levels. Interpretation is easy when data is balanced across factors but much deeper understanding is needed for unbalanced data.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
Sir Ronald Fisher pioneered the development of ANOVA for analyzing results of agricultural experiments.1 Today, ANOVA is included in almost every statistical package, which makes it accessible to investigators in all experimental sciences. It is easy to input a data set and run a simple ANOVA, but it is challenging to choose the appropriate ANOVA for different experimental designs, to examine whether data adhere to the modeling assumptions, and to interpret the results correctly. The purpose of this report, together with the next 2 articles in the Statistical Primer for Cardiovascular Research series, is to enhance understanding of ANVOA and to promote its successful use in experimental cardiovascular research. My colleagues and I attempt to accomplish those goals through examples and explanation, while keeping within reason the burden of notation, technical jargon, and mathematical equations.
01 parametric and non parametric statisticsVasant Kothari
Definition of Parametric and Non-parametric Statistics
Assumptions of Parametric and Non-parametric Statistics
Assumptions of Parametric Statistics
Assumptions of Non-parametric Statistics
Advantages of Non-parametric Statistics
Disadvantages of Non-parametric Statistical Tests
Parametric Statistical Tests for Different Samples
Parametric Statistical Measures for Calculating the Difference Between Means
Significance of Difference Between the Means of Two Independent Large and
Small Samples
Significance of the Difference Between the Means of Two Dependent Samples
Significance of the Difference Between the Means of Three or More Samples
Parametric Statistics Measures Related to Pearson’s ‘r’
Non-parametric Tests Used for Inference
Calculating Analysis of Variance (ANOVA) and Post Hoc Analyses Follo.docxaman341480
Calculating Analysis of Variance (ANOVA) and Post Hoc Analyses Following ANOVA
Analysis of variance (ANOVA)
is a statistical procedure that compares data between two or more groups or conditions to investigate the presence of differences between those groups on some continuous dependent variable (see
Exercise 18
). In this exercise, we will focus on the
one-way ANOVA
, which involves testing one independent variable and one dependent variable (as opposed to other types of ANOVAs, such as factorial ANOVAs that incorporate multiple independent variables).
Why ANOVA and not a
t
-test? Remember that a
t
-test is formulated to compare two sets of data or two groups at one time (see
Exercise 23
for guidance on selecting appropriate statistics). Thus, data generated from a clinical trial that involves four experimental groups, Treatment 1, Treatment 2, Treatments 1 and 2 combined, and a Control, would require 6
t
-tests. Consequently, the chance of making a Type I error (alpha error) increases substantially (or is inflated) because so many computations are being performed. Specifically, the chance of making a Type I error is the number of comparisons multiplied by the alpha level. Thus, ANOVA is the recommended statistical technique for examining differences between more than two groups (
Zar, 2010
).
ANOVA is a procedure that culminates in a statistic called the
F
statistic. It is this value that is compared against an
F
distribution (see
Appendix C
) in order to determine whether the groups significantly differ from one another on the dependent variable. The formulas for ANOVA actually compute two estimates of variance: One estimate represents differences between the groups/conditions, and the other estimate represents differences among (within) the data.
Research Designs Appropriate for the One-Way ANOVA
Research designs that may utilize the one-way ANOVA include the randomized experimental, quasi-experimental, and comparative designs (
Gliner, Morgan, & Leech, 2009
). The independent variable (the “grouping” variable for the ANOVA) may be active or attributional. An active independent variable refers to an intervention, treatment, or program. An attributional independent variable refers to a characteristic of the participant, such as gender, diagnosis, or ethnicity. The ANOVA can compare two groups or more. In the case of a two-group design, the researcher can either select an independent samples
t
-test or a one-way ANOVA to answer the research question. The results will always yield the same conclusion, regardless of which test is computed; however, when examining differences between more than two groups, the one-way ANOVA is the preferred statistical test.
Example 1: A researcher conducts a randomized experimental study wherein she randomizes participants to receive a high-dosage weight loss pill, a low-dosage weight loss pill, or a placebo. She assesses the number of pounds lost from baseline to post-treatment
378
for the thre ...
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The slides discuss comparing two means to ascertain which mean is of greater statistical significance. In these slides we will learn about three research questions in which the t-test can be used to analyze the data and compare the means from two independent groups, two paired samples, and a sample and a population.
Researchers use several tools and procedures for analyzing quantitative data obtained from different types of experimental designs. Different designs call for different methods of analysis. This presentation focuses on:
T-test
Analysis of variance (F-test), and
Chi-square test
This presentation consist of analysis of data in education aspects. This presentation deals about bivariate, multivariate anlaysis and it is also describes the descriptive and inferential statistics.
The presentation slides describes about the analysis of data. The presentation slides deals about scales of measurement, t test, ANOVA, ANCOVA, MANOVA, regression and SPSS help desk.
The presentation slides describes about the analysis of data. The presentation slides deals about scales of measurement, t test, ANOVA, ANCOVA, MANOVA, regression and SPSS help desk.
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2. Ordinal Data
Usually interested in how participants rank order some set of stimuli within the
context of an experiment.
How can ordinal or “ranked” data be analyzed?
Ordinal data cannot be analyzed by the chi-square or any of the other inferential
(parametric) tests we examined.
Three tests to test hypotheses with ordinal data:
1. The Man-Whitney U test,
2. The Wilcoxon signed-ranks test
3. The Spearman Correlation Coefficient, or Spearman r.
3. The Mann-Whitney U Test
The Mann-Whitney U Test is a nonparametric statistic used to identify a difference
between two independent samples of rank-ordered (ordinal) data.
Statistical Assumptions underlying this test:
* The data are based on an ordinal scale of measurement
* The observations were drawn or selected independently of one another.
* There are no “ties” (i.e., same values with different ranks) between rankings (ties
do occur, however, and a quick procedure for dealing with them is presented in
Data Box 14.D When the majority of ranks in a data set are tied, however, consult
statistical works like Hays (1988) or Kirk (1990) for guidance.
4. EXAMPLE:
Perhaps a linguist is interested in comparing the effectiveness of traditional,
classroom-based language learning versus total immersion learning where
elementary students are concerned. The linguist randomly assigns a group of 18
fourth-graders to either a traditional Spanish language class(i.e., the teacher
gives directions in English, though the emphasis is on learning to speak
Spanish) or a total immersion class (i.e., the teacher speaks exclusively in
Spanish).At the end of the school year, a panel of judges gives an age-appropriate
Spanish-language test to the students, subsequently using the scores to rank the
children’s linguistic skills from 0 to 100 (the judges remain unaware of which
learning technique each child was exposed to). The rankings were then
categorized by the respective teaching techniques the students were exposed to
(see Table 14.4).
5. Hypotheses: Null versus Alternative
H0: There will be no systematic difference
between the Spanish-speaking skills of the
traditional-learning group and the total
immersion group.
H1: There will be systematic difference
between the Spanish-speaking skills of the
traditional-learning group and the total
immersion group.
6. Traditional classroom (English &
Spanish spoken)
Total Immersion (Spanish only
spoken)
35 75
56 83
42 77
78 92
82 85
72 95
62 73
42 83
51
38
Tables 14.4 Spanish-Speaking Skills Resulting from Linguistic Pedagogy
Note: Each number represents the relative ranking of a student’s ability to speak Spanish after 1 year of
receiving one mode of instruction.
7. 1
Ordered Raw
Scores of Two
Groups
2
Ranks of Scores
of Two Groups
3
Group
Identification
4
Ranks for Group
A
5
Ranks for Group
B
35 1 A 1
38 2 A 2
42 3.5 A 3.5
42 3.5 A 3.5
51 5 A 5
56 6 A 6
62 7 A 7
72 8 A 8
73 9 B 9
75 10 B 10
77 11 B 11
78 12 A 12
82 13 A 13
83 14 B 14
85 15 B 15
Table 14.5. Combined Ranks for Spanish-Speaking Skills Resulting from Linguistic Pedagogy
8. Handling Tied Ranks in Ordinal Data
Rank of tied scores = sum of rank positions by tied scores
number of tied scores present
Rank of tied Scores 3 + 4 /2
Rank of tied Scores = 7/2
Rank of tied Scores = 3.5
Rank of tied Scores = 5 + 6 + 7/ 3
Rank of tied Scores = 18/3
Rank of tied Scores = 6
9. Formula U statistic:
UA = NANB + NA (NA + 1) - ∑RA.
2
UA = (10) (8) + 10 (10 +1) – 61
2
UA = 135-61
UA = 74.
11. Rejection or Acceptance of Hypothesis (see Table B.8
in Appendix B)
To select the Ucritical value for Mann-Whitney Utest
Sample sizes of the groups must be known A (NA = 10) & B (NB = 8)
Significance level of step 2 (i.e., .05)
To be significant, the smaller computed U must be equal to or less than critical U.
To determine whether we can reject H0, we compare the two values UA (74) and
UB (6) against the Ucritical value 17.
Because the UB of 6 is less than the U critical value of 17, we reject H0.
12. Reject H0
The two groups of ranks represent different populations, such that students in
language immersion group had higher language proficiency rankings than those
students who learned in the traditional manner A and B in columns 4 and 5,
respectively. Table 14.5.
Which means the language immersion group demonstrated relatively greater
proficiency speaking Spanish than the traditional learning group.