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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

Presenting Data

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Presenting Data

Descriptive Statistics

- No order, just a name
- Can report
- Mode
- Bar Graph
- Pie Chart

- Rank order only
- Can Report
- Mode
- Median
- Percentiles
- Histograms and Pie Charts

- Equidistant
- Can Report
- Mode, Median, Mean
- Standard Deviation
- Percentiles
- Frequency curves, Histograms

- Good to start at the univariate level
- Univariate: one variable at a time
- Investigate the responses
- Assess usability for the rest of the analysis

- 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

- 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)

- 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

- To get a statistical summary, including an imposed normal curve in Minitab:
- Select: Stat > Basic Statistics > Display Descriptive Statistics > Graph > Graphical Summary

- 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

- 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

- 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 are statements about population parameters.
- Hypotheses are not necessarily true.

- 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.

- 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.

- 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%.

- Statistically significant: if the probability of obtaining a statistic by chance is less than the set alpha level (usually 5%)

- 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.

- 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.

- 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.