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Introduction to Statistical Analysis and Hypothesis Testing

STAT1201 Lecture 1 20/02 · Weekly quiz Friday 3pm Lecture 2 23/02 · Sources of variability o Natural variability - students heights are different to each other o Measurement variability - due to measurement errors · Variable o A characteristic or an attribute that you are observing, measuring and recording data Variable Observational Study The researcher observes part of population and measures the characteristics of interest. Make conclusions based on the observations but does not influence to change the existing conditions or does not try to affect them. Example: Examine the effect of smoking on lung cancer Experimental Study The researcher assigns subjects to groups and apply some treatment(s) to group(s) and the other group does not receive the treatment. Can be designed as a blind or a double-blind study. When an experiment involves both comparison and randomization then we call it as a randomized comparative experiment. Example: Examine the effect of caffeinated drinks on blood pressure · Observational and Experimental studies · Hypothesis testing o Used to make conclusions about the population using sample data · Null hypothesis (Ho) o Usually a statement of "no effect" o Refer to the status quo (no change from the past, the old standard still correct) o Either reject or do not reject H0 · Alternative hypothesis (H1) Usually a statement of "an effect" o Also refers challenges to the status quo (something new is now occurring compared to the past) o If we reject H0 we conclude there is sufficient evidence to accept the alternative hypothesis. p-value o We use the concept of p-value to reject or do not reject the null hypothesis o If p-value small, reject the null hypothesis and conclude that we have evidence to accept alternative hypothesis o If p-value large, do not reject the null hypothesis and conclude that we do not have evidence to accept alternative hypothesis o p < 0.01 - strong evidence against Ho o 0.01 ? p < 0.05 - moderate evidence against Ho o 0.05 ? p < 0.1 - weak evidence against Ho o p ? 0.1 - no evidence against Ho o If p < 0.05, results are significant at 5% level of significance Lecture 3 + Tutorial 27/02 · Variables in RStudio o Continuous = height o Discrete = pulse rate o Nominal = eye colour o Ordinal = grade · 138 students . Part C o Variable of interest = maximal load (N) o Maximal load (N) = continuous o Experimental study - randomised comparative o Null hyp - the dietary fat of rats does not affect the average maximal load of their tibia o There is moderate evidence to suggest that high fat diets in rats reduce their average bone max load Lecture 4 02/03 · Measures of Central Tendency o Mode - the most frequently occurring value in a set of data o Median - middle value in the ordered (or ranked) data and can be used to measure the centre of the distribution. 50% of