Document Sample

Overview of t-Tests, ANOVAs, & ANCOVAs t-Test The most basic statistical test that measures group differences is the t test, which analyzes significant differences between two group means. Consequently, a t test is appropriate when the IV is defined as having two categories and the DV is quantitative, (e.g., What is the difference between males and females [IV] with respect to SAT scores [DV]? Is this difference statistically significant?). There are two variations of t-tests: an independent-samples t-test and a repeated-measures t-test. When to use a t test? 1 IV (2 categories) Group differences 1 DV (quantitative) One-Way Analysis of Variance One-way analysis of variance (ANOVA) tests the significance of group differences between two or more means as it analyzes variation between and within each group. ANOVA is appropriate when the IV is defined as having three or more categories and the DV is quantitative, (e.g., Do preschoolers of low, middle, and high socio-economic status [IV] have different literacy test scores [DV]? If so, which groups are significantly different?). Since ANOVA only determines the significance of group differences and does not identify which groups are significantly different, post hoc tests are usually conducted in conjunction with ANOVA. When to use a one-way ANOVA? 1 IV (2+ categories) Group differences 1 DV (quantitative) One-Way Analysis of Covariance One-way analysis of covariance (ANCOVA) is similar to ANOVA in that two or more groups are being compared on the mean of some DV, but ANCOVA additionally controls for a variable (covariate) that may influence the DV (e.g., Do preschoolers of low, middle, and high socio-economic status [IV] have different literacy test scores [DV] after adjusting for family type [covariate]?) Many times the covariate may be pretreatment differences, in which groups are equated in terms of the covariate(s). In general, ANCOVA is appropriate when the IV is defined as having two or more categories, the DV is quantitative, and the effects of one or more covariates needs to be removed. When to use a one-way ANCOVA? 1 IV (2+ categories) Group differences 1 DV (quantitative) 1+ covariate Source: Mertler, C. A., & Vannatta, R. A. (2005). Advanced and multivariate statistical methods: Practical application and interpretation (3rd ed.). Los Angeles, CA: Pyrczak. t-Test I. Research Questions… Generically-Stated Research Questions: Independent-samples: What is the difference between Group 1 and Group 2 on Variable A? Is this difference statistically significant? Repeated-measures: What is the difference between Measure 1 (i.e., Var. 1) and Measure 2 (i.e., Var. 2) for this sample? Is this difference statistically significant? Examples of Appropriately-Stated Research Questions: What is the difference between males and females with respect to SAT scores? Is this difference statistically significant? What is the difference between pretest and posttest scores for high school sophomores following an OGT prep course? Is this difference statistically significant? [ALT: How effective is an OGT prep course for high school sophomores?] Examples of Inappropriately-Stated Research Questions: What is the relationship between gender and SAT scores? Is there a difference between pretest and posttest scores for high school sophomores following an OGT prep course? II. Sampling & Data… Samples should always be selected randomly (probability samples) Allows for generalization of results to larger population, especially using any inferential statistical test Data must be quantitative Scale of measurement (i.e., nominal, ordinal, interval, ratio) – grouping variable is nominal (categorical); actual measures must be interval or ratio III. Data Analysis & Interpretation… Analysis involves the calculation and interpretation of a t- statistic (& its associated statistical significance) Sample output from SPSS… Descriptive statistics for the two groups Tests Ho that the variances of the 2 populations are equal t-statistic & significance (p-value); if < .05, then difference between 2 groups is significant One-Way Analysis of Variance I. Research Questions… Generically-Stated Research Question: What is the difference between Groups 1, 2, & 3 on Variable A? Which, if any, groups are significantly different? Examples of Appropriately-Stated Research Questions: Do preschoolers of low, middle, and high socio-economic status have different literacy test scores? If so, which groups are significantly different? How do teachers’ assessment practices differ based on school district rating? Which of these differences, if any, are statistically significant? Examples of Inappropriately-Stated Research Questions: Similar to those for t-test… II. Sampling & Data… Samples should always be selected randomly (probability samples) Allows for generalization of results to larger population, especially using any inferential statistical test Data must be quantitative Scale of measurement (i.e., nominal, ordinal, interval, ratio) – grouping variable is nominal (categorical); actual measures must be interval or ratio III. Data Analysis & Interpretation… Analysis involves the calculation and interpretation of an F- statistic or F-ratio (& its associated significance) Sample output from SPSS… Descriptive statistics for the five groups Value of F-ratio P-value; p < .05, so there are significant differences…bu t where??? Also, note about the value of .000! These are pairwise comparisons; every pair appears twice in the table Any value < .05 indicates a significant difference between these 2 particular groups One-Way Analysis of Covariance I. Research Questions… Generically-Stated Research Question: What are the differences between Groups 1, 2, & 3 on Variable A, after controlling for the effects of Variable B? Which, if any, groups are significantly different? Examples of Appropriately-Stated Research Questions: Do preschoolers of low, middle, and high socio-economic status have different literacy test scores after adjusting for family type? How do teachers’ assessment practices differ based on school district rating, controlling for years of teaching experience? Which of these differences, if any, are statistically significant? Examples of Inappropriately-Stated Research Questions: Similar to those for t-test… II. Sampling & Data… Samples should always be selected randomly (probability samples) Allows for generalization of results to larger population, especially using any inferential statistical test Data must be quantitative Scale of measurement (i.e., nominal, ordinal, interval, ratio) – grouping variable is nominal (categorical); actual measures must be interval or ratio (including covariate) III. Data Analysis & Interpretation… Analysis involves the calculation and interpretation of an F- statistic or F-ratio (& its associated significance) Sample output from SPSS… Significance “District of Rating” is covariate & the DV of group differences (after controlling “Years of for the Experience covariate) ” is the covariate

DOCUMENT INFO

Shared By:

Categories:

Tags:
data analysis, Biological Applications, descriptive statistics, regression analysis, probability distributions, second year, David Booth, point scales, Marketing Group, work experience

Stats:

views: | 102 |

posted: | 6/25/2011 |

language: | English |

pages: | 5 |

OTHER DOCS BY wanghonghx

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.