Transcript Powerpoint
Presenting Data Descriptive Statistics Nominal Level No order, just a name Can report – Mode – Bar Graph – Pie Chart Ordinal Level Rank order only Can Report – Mode – Median – Percentiles – Histograms and Pie Charts Interval/Ratio Level Equidistant Can Report – Mode, Median, Mean – Standard Deviation – Percentiles – Frequency curves, Histograms Univariate Data Good to start at the univariate level Univariate: one variable at a time – Investigate the responses – Assess usability for the rest of the analysis Frequency Table Shows how often each response was given by the respondents Most useful with nominal or ordinal – Interval/ratio has too many categories In Minitab, Select: Stat>Tables>Tally Charts and Graphs Use a bar graph or pie chart if the variable has a limited number of discrete values – Nominal or ordinal measures Histograms and frequency curves are best for interval/ratio measures In Minitab, Select: Graph > (and then type) Normal Curve The normal curve is critical to assessing normality which is an underlying assumption in inferential statistical procedures – And in reporting of results Kurtosis: related to the bell-shape Skewness: symmetry of the curve – If more scores are bunched together on the left side, positive skew (right) – If most scores are bunched together on the right side, negative skew Normal Curve To get a statistical summary, including an imposed normal curve in Minitab: Select: Stat > Basic Statistics > Display Descriptive Statistics > Graph > Graphical Summary Measures of Central Tendency Mode: most frequently selected – Bimodal = two modes – If more than two modes, either multiple modes or no mode Median: halfway point – Not always an actual response Mean: arithmetic mean Percentiles The median is the 50 percentile A percentile tells you the percentage of responses that fall above and below a particular point Interquartile range = 75th percentile – 25th percentile – Not affected by outliers as the range is Z-scores Standard deviations provide an estimate of variability If scores follow a ‘normal curve’, you can comparing any two scores by standardizing them – Translate scores into z-scores – (Value – mean) / standard deviation Statistical Hypotheses Statistical Hypotheses are statements about population parameters. Hypotheses are not necessarily true. In statistics, we test one hypothesis against another… The hypothesis that we want to prove is called the alternative hypothesis, Ha. Another hypothesis is formed which contradicts Ha. – This hypothesis is called the null hypothesis, Ho. Ho contains an equality statement. Errors Decision Reject Ho Fail to Reject Ho Truth Ho is true Ho is false Type I Error OK OK Type II Error P-value The choice of is subjective. The smaller is, the smaller the critical region. Thus, the harder it is to Reject Ho. The p-value of a hypothesis test is the smallest value of such that Ho would have been rejected. Interval Estimates Statisticians prefer interval estimates. X Something Something depends on amount of variability in data and how certain we want to be that we are correct. The degree of certainty that we are correct is known as the level of confidence. – Common levels are 90%, 95%, and 99%. Statistical Significance Statistically significant: if the probability of obtaining a statistic by chance is less than the set alpha level (usually 5%) P-value The probability, computed assuming that Ho is true, that the test statistic would take a value as extreme or more extreme than that actually observed is called the p-value of the test. The smaller the p-value, the stronger the evidence against Ho provided by the data. If the p-value is as small or smaller than alpha, we say that the data are statistically significant at level alpha. Power The probability that a fixed level alpha significance test will reject Ho when a particular alternative value of the parameter is true is called the power of the test to detect that alternative. One way to increase power is to increase sample size. Use and Abuse P-values are more informative than the results of a fixed level alpha test. Beware of placing too much weight on traditional values of alpha. Very small effects can be highly significant, especially when a test is based on a large sample. Lack of significance does not imply that Ho is true, especially when the test has low power. Significance tests are not always valid.