Presenting Data

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# Presenting Data - PowerPoint PPT Presentation

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

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## Presenting Data

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### 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.
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.
• 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.