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Mean comparison2
- 1. Mean Comparison2 Desmond Ayim-Aboagye,Ph.D. F Ratio
- 2. F Ratio • F= between-group variance • within-group variance • Error variance, which is estimated by within- group variance, refers to the idiosyncratic, uncontrollable, unknown factors or events that create differences among the observations within a group. (e.g., misunderstood directions, equipment problems, it represents the differential behaviour of participants)
- 3. F Ratio • Whencalculating an F ratio, the estimate of within-group variance or error variance is based on the average variance of the observations within each sample.
- 4. TREATMENT VARIANCE • Thebetween-group variance also adopts a particular name in the context of ANOVA– Treatment variance • Independent variable is “treated“ or "manipulated“ in order to elicit some reaction or response from research participants • E.g., drug to experimental group, while pacebo to control group. • Treatment variance is also comprised of error variance, that is, individual differences and experimental error.
- 5. Treatment variance • Treatmentvariance is based on the systematic influence of different levels of an independent variable on a dependent measure, combined with error variance. • As the treatment variance increases, the three samples appear to stand out from one another– the respective levels of the independent variable lead to distinct behaviors and accompanying treatment variance. • F = treatment variance + error variance • error variance
- 6. Describing the FDistribution • F distribution is different, why? • A. it is based on the ratio of two independent estimates of variance. • B. One variance represents an F statistic‘s numerator and the other its denomenator • C. At the population level, F ratio is described • F = 𝜎²between • 𝜎²within • F ratio in terms of sample variance • F = s²between • s²within
- 7. Characteristics of Fratio/Distribution • 1. Because they are based on variance estimates, which in turn are determined by sum of squares, F ratio are always positive numbers. • 2. The logic underlying the Ratio calculation. When the null hypothesis is true, the two variance estimates representing the numerator and the denominator, respectively should be equal to 1.00 • 3. When the F ratio exceeds 1.00 it is clear that the null hypothesis of no difference between or among a set of means may be false.
- 8. ANOVA DISTINCTIVENESS • Howdoes the ANOVA differ from prior statistical tests examined? 3 ways. • 1. It compares means • 2. Protect against Type 1 error • 3. Enables researchers to think about complex causal relationships among variables.
- 9. Omnibus Test: ComparingMore than Two Means Simultaneously • ANOVA is known as Omnibus Statistical Test • It enables the investigator to detect significant differences between two means or among more than two means. • The availability of the ANOVA as an analytic tool invites researchers to theorize more broadly, to tackle more complex questions empirically.
- 10. One-Factor Analysis ofVariance • A one-way analysis of variance (one-way ANOVA) is a statistical technique for analyzing the variation found within the various levels of a single independent or treatment variable. A one-way ANOVA will compare the means of two or more levels with one another in order to determine if any significant difference(s) exist(s) between or among them.
- 11. A factor analysis •A factor is a synonym for a treatment or independent variable within an ANOVA. To be analytically viable, a factor must have two or more levels within in it. • Used example from your work • Ambient light as Independent variable • Aspects of behaviour as dependent measure e.g., work productivity, books read or check out.