One-tailed test (directional hypothesis) A test of the null hypothesis ...

One-tailed test (directional hypothesis) A test of the null hypothesis where the alternative hypothesis is expressed directionally eg m > M Two-tailed test (non-directional hypothesis) A test of the null hypothesis where the alternative hypothesis is not expressed directionally eg m does not equal M Degrees of Freedom df= (n-1) Number of observations that are completely free to vary Type I Error Occurs when the null hypothesis is rejected, it is called the level of significance. The probability is controlled by the researched Type II Error Occurs when null hypothesis is not rejected. The power of a statistical test is found by (1 - β) Confidence Interval Values 95% of the scores will fall between ± 1.96 standard deviations above and below the mean. 99% of the scores will fall between ± 2.58 standard deviations above and below the mean. Functions of data reduction 1. Summarisation - condenses the raw data into a few meaningful numbers. 2. Conceptualisation - helps you visualise how the calculated statistic is describing the data. 3. Communication - the translation of statistical analysis into a form that is understandable and useful. Normal Distribution Bell shaped curve, symmetric about the mean Measure of Central Locations Statistics which describe the centre of the distribution. Common Measures 1. Mean- average of the responses- interval scaled 2. Mode- value that occurs most often- nominal scaled3. Median- middle value of the data- ordinal scale Measures of Variability Gives additional information to judge the representation and reliability of the measure of central tendency. Able to compare dispersions of different samples. Common Measures 1. Rangedifference between largest and smallest values 2. Variance= Standard deviation squared, =(N-m)^2 3. Standard Deviation: Root of the variance 4. Z Score/Normal Score/ Standard Score: Shows how many units of the standard deviation a raw score is above or below the mean. Zi = ( Xi - μ ) / σ Measures of Shape Statistic which describes the shape of the frequency distribution curve - how far it departs from normal curve, Common Measures 1. Skew: Skewed to the right, Positive skew, Skew to the left, negative skew. No skew, is normal distribution. One hill is unimodal, 2 hills is bimodal 2. Kurtosis: describes the relative peakedness or flatness of the curve described by the frequency distribution. 0= normal distribution, positive= more peaked than normal, negative= less peaked than normal Tabulating Cross tabulation: Examines relationships between two or more variables (chisquared) Simple tabulation: Involves counting single variable (frequency distribution) Nominal scale Level of Measurement Example Please indicate your current martial status. _Married __ Single __ Single, never married __ Widowed Ordinal scale Level of measurement Example! Rank your favourite cola in order from most preferred (1) to least preferred (4). __ Coke __ Pepsi __ Home brand __ Dr Pepper Interval scale Level of Measurement ExamplesTemperature scale - Year date Ordinally-Interval Scales Example I could not survive financially without a credit card. (Strongly Agree, Agree, Neutral, Disagree Strongly Disagree.)Ratio Scales Example How many children under 18 years of age are currently living in !your household? Comparative Scales A direct comparison of stimulus objects is elicited. e.g, two brands may be compared along a dimension such as quality. Non-comparative scales Only one object is evaluated at a time. The respondent provides whatever standard seems appropriate. e.g, one brand is rated on a scale independent of other brands. Summated Scales Examples Rank each brand from 1 to 10. Add all score then divide by 10, Likert Scale-Example Non comparative I could not survive financially without a credit card. (Strongly Agree, Agree, Neutral, Disagree , Strongly Disagree Semantic differential scale-Example! Indicate how you feel about Brand X. (bad 1 2 3 4 5 6 7 good)Face validity- Face validity occurs where something appears to be valid. This of course depends very much on the judgment of the observer. In any case, it is never sufficient and

requires more solid validity to enable acceptable conclusions to be drawn. Measures often start out with face validity as the researcher selects those which seem likely prove the point