General Lectures 1-4 What is statistics? Discipline: collecting, classifying, summarizing, organizing, analyzing and interpreting numerical information. -A means to answer research questions (and to test hypothesis). -No scientific proof: make plausible through empirical data with an empirical observed result. Shape and skewness:  Negatively skewed: mean < median  Symmetry: mean = median  Positively skewed: mean > median Mode = the score that occurs most frequently. Median = middle score when scores are ranked in order. Mean = the average score, the media. Interpreting the standard deviation: -the empirical rule (frequency distribution is bell shaped and symmetric)  68% values: -1 - +1  95% values: -1 - +1  99.7 % values: -3 - +3 -Chebyshev’s rule (applies to all distributions, regardless their shape)  ?% values: -1 - +1  75% values: -2 - +2  88.9% values: -3 - +3 o Choice of numerical measures depends on the measurement level of the variable. o Measurement levels are hierarchical and so are the numerical measures. o ‘Higher’ level measures are generally preferred. o Some measures are sensitive to extreme values. Less sensitive measures are preferred when a distribution is too skewed. o Use the Z-score to determine the relative position of an observation. ( Z = X -  / ) Central Limit Theorem: When the sample is sufficiently large (n30) the sampling distribution will be approximately a normal distribution. Confidence interval: Probability that the random selected interval encloses the unknown parameter. Typical values 99%, 95%, and 90%. Z-values  large samples, t-values  small samples,  unknown. 90% : -1.65 95% : -1.96 99%: -2.58 +1.65 +1.96 +2.58 =SEM (std. error of the mean)

Hypothesis: An assumption or belief concerning the answer to a research question about one variable or the relation between two or