Concept of Inferential statistics
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Inferential statistics use samples to make generalizations about populations. It allows researchers to test theories designed to apply to entire populations even though samples are used. The goal is to determine if sample characteristics differ enough from the null hypothesis, which states there is no difference or relationship, to justify rejecting the null in favor of the research hypothesis. All inferential tests examine the size of differences or relationships in a sample compared to variability and sample size to evaluate how deviant the results are from what would be expected by chance alone.
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Concept of Inferential statistics
- 2. Inferential statistics use a random sample of data taken from a population to describe and make inferences about the population. Inferential Statistics
- 3. • Inferential statistics are valuable when examination of each member of an entire population is not convenient or possible. For example, To measure the diameter of each nail that is manufactured in a mill is impractical. You can measure the diameters of a representative random sample of nails. You can use the information from the sample to make generalizations about the diameters of all of the nails. Inferential Statistics
- 4. • The Goal of Inferential Statistics Quantitative research in psychology and social science aims to test theories about the nature of the world in general (or some part of it) based on samples of “subjects” taken from the world (or some part of it).
- 5. • The Goal of Inferential Statistics When we perform research on the effect of TV violence on children’s aggression, our intent is to create theories that apply to all children who watch TV, or perhaps to all children in cultures similar to our own who watch TV. Inferential Statistics
- 6. • The Goal of Inferential Statistics We of course cannot study all children, but we can perform research on samples of children that, hopefully, will generalize back to the populations from which the samples were taken. Recall that external validity is the ability of a sample to generalize to the population (and to other operationalizations that are assumed to represent that same constructs). Inferential Statistics
- 7. • The Goal of Inferential Statistics Inferential statistics is the mathematics and logic of how this generalization from sample to population can be made. The fundamental question is: • Can we infer the population’s characteristics from the sample’s characteristics? Inferential Statistics
- 8. • The Goal of Inferential Statistics Descriptive statistics remains local to the sample, describing its central tendency and variability, while inferential statistics focuses on making statements about the population. Inferential Statistics
- 9. Hypothesis Testing • Inferential stats is closely tied to the logic of hypothesis testing. • In hypothesis testing, the goal is usually to reject the null hypothesis. • The null hypothesis is the null condition: “No difference between means or no relationship between variables” Inferential Statistics
- 10. • Data are collected that allow us to decide if we can reject the null hypothesis, and do so with some confidence that we’re not making a mistake. • In psychology, the standard level of confidence, “alpha,” is a probability of .05 that we are rejecting the null hypothesis when we shouldn’t (Type I Error).
- 11. • The null hypothesis is a statement of the null condition in the population, not the sample. For example, H0: mean of males = mean of females is formally expressed in terms of population, not sample, means: H0: μM = μF where μ (mu) signifies the population mean, that is, the mean of all the males or females in the entire population.
- 12. • However, we only have a sample to work with, so we obtain a sample mean, M (or X-bar). • The null hypothesis we are so intent on rejecting concerns the population means. • Our task is to determine if the sample means are sufficiently different to infer that the population means are different.
- 13. Basic Principle of Inferential Statistics At a certain basic level, all inferential statistics procedures are the same: they seek to determine if the observed (sample) characteristics are sufficiently deviant from the null hypothesis to justify rejecting it. How deviant?
- 14. Basic Principle of Inferential Statistics The ingredients for making this calculation are the same for all statistical procedures: 1. the size of the observed difference(s) 2. the variability in the sample 3. the sample size.
- 15. Basic Principle of Inferential Statistics If instead we are looking for relationships (e.g., correlation analysis), the size of the relationship replaces the size of the difference. Therefore, researchers seeks to: 1. find large differences (or relationships) 2. hold down unwanted variability 3. obtain large samples. (Good research must also worry about internal and external validity, and the ultimate goal: building theories.)
- 17. Procedure for Performing an Inferential Test Here is a step-by-step procedure for performing inferential statistics. 1. Start with a theory (TV violence reduces children’s ability to detect violent behavior because it blurs the distinction between real and fantasy violence) 2. Make a research hypothesis (Children who experience TV violence will fail to detect violent behavior in other children)
- 18. Procedure for Performing an Inferential Test 3. Operationalize the variables 4. Identify the population to which the study results should apply (Kids in developed nations) 5. Form a null hypothesis for this population (H0: uH = uL, where uH is mean accurate detection of violence by children with high prior exposure to TV violence; uL is low prior exposure)
- 19. Procedure for Performing an Inferential Test 6. Collect a sample of children from the population and run the study 7. Perform statistical tests to see if the obtained sample characteristics are sufficiently different from what would be expected under the null hypothesis to be able to reject the null hypothesis.