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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

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presenting data

Presenting Data

Descriptive Statistics

nominal level
Nominal Level
  • No order, just a name
  • Can report
    • Mode
    • Bar Graph
    • Pie Chart
ordinal level
Ordinal Level
  • Rank order only
  • Can Report
    • Mode
    • Median
    • Percentiles
    • Histograms and Pie Charts
interval ratio level
Interval/Ratio Level
  • Equidistant
  • Can Report
    • Mode, Median, Mean
    • Standard Deviation
    • Percentiles
    • Frequency curves, Histograms
univariate data
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
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
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
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 curve9
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
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
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
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
  • Statistical Hypotheses are statements about population parameters.
  • Hypotheses are not necessarily true.
in statistics we test one hypothesis against another
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
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
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
Statistical Significance
  • Statistically significant: if the probability of obtaining a statistic by chance is less than the set alpha level (usually 5%)
p value19
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
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
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.