Statistics: T-Tests and ANOVA
T-Tests and ANOVA: Statistics

Independent sample t-tests and ANOVA are both used to test for differences in means of unrelated, independent groups. However, ANOVA has been shown to be more effective than the t-test when the number of groups is more than two. This is because ANOVA controls the risk of type I error by holding the probability constant at a .05 significance level. This text explores the differences between the two tests, and the specific situations when each one is more effective.

Independent Sample t-Tests

My week 1 research questions were geared at assessing the impact of community youth sporting programs on adolescents' academic performance, discipline, and social well-being. Q4 was selected to be used for this particular analysis. It read:

"Are there any significant differences between the levels of discipline of adolescents who engage in community youth sporting activities and those that do not?"

Well, this research question lends itself…...

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References

Lane, D. M. (n.d.). Online Statistics Education: A Multimedia Course of Study. Rice University. Retrieved October 8, 2015 from  http://onlinestatbook.com/ 

Sukal, M. (2013). Research Methods: Applying Statistics in Research. San Diego, CA: Bridgepoint Education Inc.

Data Set AnalysisHypothesesThere are two sets of hypotheses that could be tested using an independent means and dependent means t-test:Independent means t-test: Null hypothesis (H0): There is no significant difference in mean scores between group A and group B on the IQ test. Alternative hypothesis (H1): There is a significant difference in mean scores between group A and group B on the IQ test.Dependent means t-test: Null hypothesis (H0): There is no significant difference in mean scores on the pre-test and post-test for the participants in the study. Alternative hypothesis (H1): There is a significant difference in mean scores on the pre-test and post-test for the participants in the study.For the first hypothesis that can be tested using an independent means t-test, the variables used are gender and the total number of words recalled. The null hypothesis is that there is no significant difference in the mean number of words…...

Performing t-tests for means Part 1
1. Explain how the t distribution is similar to a normal distribution, and how it is different from a normal distribution
There are a number of similarities between the t distribution and the normal z distribution. To begin with, both of these distributions are symmetric, in the sense that they have a bell-like shape, about a mean of zero. In this regard, the t distribution can be utilized as a substitute to the normal distribution in the instances where the sample sizes are small so as to make an estimation of the confidence. However, at the same time, there are dissimilarities between the two distributions. First of all, the t distribution is in fact more variable as compared to the normal distribution. This implies that it is spread out and therefore has a smaller peak and end tails that are fatter. Secondly, whilst there is solely one…...

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References

Ríos, V. R., & del Campo, E. P. (2013). Business research methods: theory and practice. ESIC editorial.

Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2012). Introduction to probability and statistics. New York: Cengage Learning.

Independent Samples and Paired Samples T-Test:
The Paired Samples T-test, which is commonly known as the correlated-samples T-test or matched-samples T-Test has some similarities with the Independent Samples because they are both used to compare two samples of observations. These procedures are also used to determine whether the mean of one sample is significantly different from the mean of another sample. Notably, the Paired Samples T-test is also known as the dependent samples T-test since its used to identify important mean differences between two groups on a certain measure such as GPA, ACT scores, SAT scores, height, or weight. Through the use of this procedure, the specific groups of interest are seemingly related as siblings or pre-treatment environment or post-treatment setting. Generally, the two groups being compared must be somehow related in order to be suitable for the procedures of Paired Samples T-test.

Despite of the previously stated similarities between the Paired…...

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Reference:

O'Rourke, N., Hatcher, L. & Stepanksi, E.J. (2005). T-tests: Independent Samples and Paired

Samples. In A step-by-step approach to using SAS for univariate and multivariate statistics (2nd ed.). Cary, NC: SAS Institute Inc.

T TestThe t-test statistic from the article "Using the Student's t-test with Extremely Small Sample Sizes" by J.C.F. de Winter (2013) is:"An independent samples t-test was conducted to compare the mean scores of Group A (M = 3.2, SD = 0.6, N = 3) and Group B (M = 2.8, SD = 0.5, N = 3) on the variable X. The t-test revealed no significant difference between the groups, t(4) = 1.08, p > .05."In this example, the author used an independent samples t-test to compare the means of two groups (Group A and Group B) on a continuous variable (X), with sample sizes of N = 3 in each group. The t-value is 1.08 and the degrees of freedom are 4. The p-value is greater than .05, indicating that the difference between the groups is not statistically significant.The author used this type of t-test because they were comparing two…...

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References

De Winter, J. C. (2013). Using the Student\\\\\\'s t-test with extremely small sample sizes. Practical

Assessment, Research, and Evaluation, 18(1), 10. https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1307&context=pare

epeated Measures ANOVA and Dependent Samples t-Test: Week 3 Assignment
Week 3 Assignment: epeated Measures ANOVA and Dependent Samples t-test

My research questions in week one sought to assess the impact of community youth sporting programs on adolescents' well-being, discipline and academic performance. None of the questions used then lends itself effectively to the repeated measures ANOVA or the dependent samples t-test; however, we could adjust Q4 to make it qualify for the same. Originally, Q4 read, "Are there any significant differences between the levels of discipline of students who engage in youth sporting activities and those that do not?"

To make it appropriate for the repeated measures ANOVA, we modified it as follows:

"Is there a difference in students' discipline levels before, after a three-month, and after a six-month period of engagement in community sporting activities?"

In this case, we would be interested in finding out how students' discipline levels vary based on the…...

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References

Lane, D. M. (n.d.). Online Statistics Education: A Multimedia Course of Study. Rice University. Retrieved October 8, 2015 from  http://onlinestatbook.com/ 

Sukal, M. (2013). Research Methods: Applying Statistics in Research. San Diego, CA: Bridgepoint Education Inc.

Correlation, Regression, and T-Tests
Linear regression analyses are conducted after correlation has been established (Cohen, West & Aiken, 2014). Correlation shows how two variables are related, that is how one variable behaves when the other changes. Regression analyses somehow quantify this relationship -- we use it to predict the value of the dependent variable at different values of the independent variable. Since regression analyses yield numerical values, they can only be performed on quantitative, measurable values. RQ1 in the week one assignment -- how does engagement in social media relate to loneliness -- fits the qualification for simple regression analyses -- the independent variable (engagement in social media is measured in terms of the number of hours one spends on the internet) whereas the dependent variable is measured in terms of quantified categories ranging from 'very low' to 'very high', where quantification would involve assigning numbers to categories, for instance, 'very…...

Testing and Assessment
Describe the basic characteristics of a standardized test and norms.

Standardized tests are administered and scored in a consistent manner. When standardized tests are given, conditions are held consistent and conducted in a predetermined way that is considered the standard for the test. Some of the variables that are held constant include, such as the test questions, the conditions for administering the tests, the scoring procedures and interpretations of the answers. Norms are generated by using a single test score to relate it to the test scores of other students, or by the same students at different times. Norms are generally established on a nation-wide basis on standardized tests rather than classroom tests that are made by teachers.

A test measuring basic math skills in adults is normally distributed, with mean = 20 and standard deviation = 7.

Calculate the z score and T score for each of the following test…...

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Reference

Aiken, L.R. And Groth-Marnat, G. (2006). Psychological testing and assessment (12th ed.). Boston, MA: Allyn & Bacon.

Achievement and Intelligence Tests
Achievement tests measure more specific areas compared to general intelligence tests. They are meant to focus on measuring skill levels within certain specific talent ranges. Often known as standardized tests, achievement tests break down traditional intelligence assessment into very definitive categories. Typically, schools use achievement tests for state standards reporting, and the commonly taken SAT and ACT are standardized tests that represent achievement evaluation, rather than general intelligence testing. These tests are helpful when educators or researchers want to focus in a certain academic category, or to measure the general skill levels of large groups of students against state and national averages. Still, there are some major issues with achievement tests, primarily the fact that they often do not allow for the incorporation of higher level critical thinking skills or problem solving abilities.

On the other hand, intelligence tests have a much broader subject matter when compared to…...

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References

Aiken, L.R. & Groth-Marnat, G. (2006). Psychological testing and assessment,(12th ed.).Boston, MA: Allyn & Bacon. ISBN: 0205457428.

Burkam, David T. & Lee, Valerie E. (2002). Inequality at the starting gate: Social background differences in achievement as children begin school. Economic Policy Institute. Web.  http://www.epi.org/publication/books_starting_gate/ 

Fair Test. (2012). What's wrong with standardized tests. National Center for Fair and Open Testing. Web.  http://www.fairtest.org/whats-wrong-standardized-tests

standardized achievement tests and diagnostic tests.
Standardized tests are usually administered after the material has been taught, and they are used to determine whether or not the class has successfully met the district and state standards. The tests are administered under strict conditions and the tests are scored by machine rather than by hand. These tests are used to evaluate students as groups rather than individuals, and they show the performance of students by grade or by school.

Diagnostic tests are used to evaluate students who are having reading difficulties (Gillet 2008). These tests are somewhat less difficult than the standardized tests because they are mainly used for students who are having reading problems. They are usually administered to individual students rather than in a large group. The test questions and scores are broken down into skills and subskills, and each section is evaluated to determine where the student is having…...

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References

Briggs, C., Tully, B. & Stiefer, T. (1998). Direct Informed Assessment: Frequency of Use in Preservice Teacher Education Programs within a Five-State Region. Action in Teacher Education, 20(3), 30-38.

Cole, K. (1999, January). Walking Around: Getting More from Informal Assessment. Mathematics Teaching in the Middle School, 4(4), 224-227.

Gillet, J., Temple, C., & Crawford, A. (2008). Understanding Reading Problems: Assessment and Instruction. (7th ed.). Boston: Pearson Education, Inc.

Ruiz-Primo, M. & Furtak, E. (2004). Informal Formative Assessment of Students' Understanding of Scientific Inquiry. Los Angeles, CA: National Center for Research on Evaluation, Standards, and Student Testing.

Independent T-Test for Lower Level of Depression
T-Test

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Group Statistics

Currently employed?

Mean

Deviation

Error Mean

CES-D Score

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

df

Sig. (2-tailed)

Mean Difference

Error Difference

95% Confidence Interval of the Difference

Lower

Upper

CES-D Score

Equal variances assumed

Equal variances not assumed

The total sample size is 960. Out of the sample size, 524 women are unemployed versus 436 women are employed. The standard deviation of each group is 12.46 for unemployed women and 15.82 for employed women. The significant level of the two variables is 0.000 less than .05 showing that there is no statistically significant difference between them showing that there is no statistical difference between their means. Since the Sig is < .05, the study agrees that Equal variances not assumed. The value of the t statistic is 6,825 and p-value is 0.000, and number of degrees of freedom is .74326 and .72949. (Kent State University, 2016).

PAT II

T-TEST PAIS=cesd WITH cesdwav1 (PAIED)

/CITEIA=CI (.9500)

/MISSING=ANALYSIS.

T-Test

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Paired Samples…...

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Reference

Kent State University (2016). SPSS Tutorials: Independent Samples t Test. USA.

T-tests in Quantitative Doctoral Business Research Quantitative research is one of the methodologies that is commonly used in doctoral business research. The use of this approach is attributable to the availability of more data that requires analysis to help generate competitive advantage in the business field. The use of quantitative research entails conducting statistical analysis, which involves the use of different methods such as t-tests and ANOVA. T-test is used in hypothesis testing in quantitative studies to determine whether variations between the averages of two groups is unlikely to have emerged because of a random chance in selection of a sample. In essence, t-tests help to compare whether two groups have varying average values. In light of the role and significance of the assumptions underlying each parametric test, this paper provides a comparison of one-sample, paired-samples, and independent-sample t-tests within the context of quantitative doctoral business research. The comparison is based…...

Question 1 If Mary wants to study the impact of background noise level on sixth grader learning in a math lesson, the independent variable is the background noise condition. Mary has decided to use a t-test, which means that she will only have two conditions that differ from one another (“T Test (Student’s T-Test),” n.d.). In this case, the experimental condition would be high background noise (measured by decibel level perhaps), and the control condition would be low background noise (also measured by decibel level).
The independent variable in this experiment would be learning in a mathematics lesson. Learning can be assessed using a number of different instruments appropriate to the specific lesson, with a simple quantifiable quiz the most appropriate. A quiz that had absolute right or wrong answers, whether by solving a math problem or answering multiple choice questions, would help to standardize the results and minimize bias. Mary would…...

1. If I were designing my research study in the field of psychology, I would most likely use a t-test as the method of data analysis. A t-test is best used when the researcher wants to determine deviations from a normal distribution curve. If there are one or more normal distributions (bell curves), t he researcher can compare the two groups using the t-test method. The variances do not need to be known to perform a t-test either, which is another reason why I would select this method of data analysis in my particular research question. Furthermore, the researcher can use the t-test to measure the differences between two populations regardless of how small or large the sample size. The t-test, also known as the student t-test, is one of the best methods applied to studies using a small sample size. If my research were to progress to where I…...

Independent – Samples t-Test The Independent sample t-test is among the group of inferential statistical test. This test seeks to compare the means of two unrelated samples in a survey. The t-test determines whether the mean of the two sample is significantly different statistically (Paul & Garg, 2014). According to Ruane (2005) for this test to be undertaken, both samples must have scores with one carrying nominal scale and another one a numerical scale. The sample carrying the nominal is a grouping variable and is the independent variable. The sample with the numerical scale is a test variable and is the dependent variable (Ruane, 2005).
This paper seeks to determine the statistical significance between the means of work shift (day and night shift) and the mean of the number of widgets produced in either shifts. This will be undertaken by use of the independent sample t-test. The work shift is the independent…...

There are a number of fantastic slave narratives that really describe the experiences of people in slavery.  However, there is a problem with most of these narratives.  Written by former slaves, these narratives are going to represent a rarity among slaves because their authors could read and write, while teaching a slave to read or write was punishable under many slave codes.  Therefore, we strongly suggest looking at a more comprehensive collection of slave narratives.  Fortunately, the Works Progress Administration compiled slave narratives under a few different programs, most notably the Federal Writer’s Project. ....

I. Introduction
A. Explanation of career exploration
B. Importance of career exploration

II. Benefits of career exploration
A. Helps in making informed career decisions
B. Allows for the exploration of various career options

III. Tools and resources for career exploration
A. Online career assessment tests
B. Career counseling services
C. Networking with professionals in various fields

IV. Steps in career exploration
A. Self-assessment of interests, values, and skills
B. Researching various career options
C. Gaining hands-on experience through internships or job shadowing

V. Challenges in career exploration
A. Fear....

1. The Interwoven Tapestry: Faith and Family in a Tapestry of Life

2. Sanctuary and Struggle: Family as a Haven and a Battlefield for Religion

3. The Crucible of Kinship: Family as a Crucible that Tests and Shapes Faith

4. The Sacred and the Secular: Faith and Family in Tension and Harmony

5. The Legacy of Belief: Religion's Enduring Influence on Family Traditions and Values

6. The Collision of Convictions: When Family Bonds Clash with Religious Dogma

7. The Evolution of Faith: Family Dynamics as Catalyst for Religious Shifts

8. The Role of Religion in Intergenerational Relationships: Faith as a Bridge or a Barrier

9. Faith and Family:....

1. The Impact of Socioeconomic Status on Legal Representation

Thesis: Individuals from lower socioeconomic backgrounds face significant barriers in obtaining adequate legal representation, leading to disparities in access to justice.
Explore:
Systemic bias in the legal system that favors the wealthy.
Lack of pro bono legal services for low-income individuals.
Financial constraints that prevent access to private attorneys.
Impact on legal outcomes and the ability to enforce rights.

2. Social Class and Sentencing Disparities

Thesis: Social class significantly influences sentencing outcomes, resulting in harsher punishments for individuals from lower socioeconomic backgrounds.
Explore:
Disproportionate representation of minority and low-income defendants in the....