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  • Introduction to Statistical Concepts and Research Design

Introduction to Statistical Concepts and Research Design

Population = The set of all objects/people/events that we are interested in knowing about. Experimental = IV is manipulated, can make causal conclusions Observational = Observe both IV and DV, IV free to vary, can't make causal conclusions Nuisance variables = Variable related to the DV, never the IV Confounding variables = Masks the ef f ect of the IV on the DV Research designs: Repeated measures, Matched pairs, Independent groups Theory behind signif i cance When we compare a reference proportion to a sample estimate, we are checking to see whether the reference proportion falls within the conf i dence interval that we have generated using the sample estimate. If it does fall within this range, then we can't conclude that our sample comes from a population with a dif f erent proportion. If it does not fall within this conf i dence interval, then we can conclude this! So, to recap, we can calculate the interval within which the population proportion is likely to lie by calculating the sampling distribution, and f i nding the values within 2SDs of the mean. This interval is called the 95% conf i dence interval. It is the interval within which the population proportion is likely to lie. Proportion = Frequency /Total number, ie 70/100=0.07 X100 =7% Standardized value or z score = data value-mean/standard deviation. Example: z=(70-60)/5 =(10)/5=2. Check if they are positive or negative. Correlation coef f i cient = looks at strength, form and direction of the relationship b/w metric variables. Value b/w -1 and +1, where -1 to 0 indicates -ve correlation where one variable increases the other decreases and vice versa. The co ef f i cient of determination = Tells us how much of the variation in xyz can be explained by the relationship. R 2 =. 65 X.65 ==. 42 or 42% (example: In this sample of 30 participants, 42% of the variation in salary can be explained by the linear relationship between experience and salary). Reporting t values: When reporting t values, you don't need to put the sign in front. When reporting negative CI you just need to mention if the values represents are lower or higher than the reference (no need for negative) however for correlation coef f i cients you need to mention the direction of the relationship and if that is negative. One Sample t-test (comparing known mean to a reference mean) It was hypothesised that the age of tourists in Katatonia has increased since 1995. In a random sample of 250 tourists in Katatonia, the average age was 44.84 years (s = 9.96 years). While this is lower than the average age of 45 years recorded in 1995, a one-sample t-test shows that this dif f erence in mean age is not signif i cant, t(249) = 0.25, p = . 805. The 95% confi dence interval indicates that the average age of tourists is between 1.40 years less and 1.08 years more than in 1995. There is insuf