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Statistics (AKA: Sadistics) Made Easy by Donna L. Agan, EdD

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9/14/20102 Show of Hands Who is doing a study that involves statistical analysis of data? What type of (quantitative) data are you collecting? Will there be enough data to achieve statistical significance? (adequate power vs. pilot) If pilot: –Descriptive statistics –Chart/graph

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9/14/20103 Types of data Continuous –Equal increments Ordinal/Rank –In order but not equal (Likert) Categorical –Names

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What type of statistical test do I want to do?

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9/14/20105 Continuous Data If comparing 2 groups (treatment/control) –t-test If comparing > 2 groups –ANOVA (F-test) If measuring association between 2 variables –Pearson r correlation If trying to predict an outcome (crystal ball) –Regression or multiple regression

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9/14/20106 Ordinal Data Beyond the capability of Excel – just FYI If comparing 2 groups –Mann Whitney U (treatment vs. control) –Wilcoxon (matched pre vs. post) If comparing > 2 groups –Kruskal-Wallis (median test) If measuring association between 2 variables –Spearman rho (ρ) Likert-type scales are ordinal data

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9/14/20107 Categorical Data Called a test of frequency – how often something is observed (AKA: Goodness of Fit Test, Test of Homogeneity) Chi-Square (χ 2 ) Examples of burning research questions: –Do negative ads change how people vote? –Is there a relationship between marital status and health insurance coverage? –Do blonds have more fun?

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Words we use to describe statistics

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9/14/20109 Mean ( μ) The arithmetic average (add all of the scores together, then divide by the number of scores) μ = ∑x / n

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9/14/201010 Median The middle number (just like the median strip that divides a highway down the middle; 50/50) Used when data is not normally distributed Often hear about the median price of housing

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9/14/201011 Mode The most frequently occurring number (score, measurement, value, cost) On a frequency distribution, it’s the highest point (like the á la mode on pie)

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Area Under the Curve That’s where the population lives

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9/14/201013 Photo courtesy of Judy Davidson, DNP, RN

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9/14/201014 Standard Deviation (σ) 95% 99%

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9/14/201015 We Make Mistakes! Alpha level Set BEFORE we collect data, run statistics Defines how much of an error we are willing to make to say we made a difference If we’re wrong, it’s an alpha error or Type 1 error p value Calculated AFTER we gather the data The calculated probability of a mistake by saying it works AKA: level of significance Describes the percent of the population/area under the curve (in the tail) that is beyond our statistic

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9/14/201016 2-tailed Test The critical value is the number that separates the “blue zone” from the middle (± 1.96 this example) In a t-test, in order to be statistically significant the t score needs to be in the “blue zone” If α =.05, then 2.5% of the area is in each tail

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9/14/201017 1-tailed Test The critical value is either + or -, but not both. In this case, you would have statistical significance (p <.05) if t ≥ 1.645.

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9/14/201018 Chi-Square (χ 2 ) Any number squared is a positive number Therefore, area under the curve starts at 0 and goes to infinity To be statistically significant, needs to be in the upper 5% (α =.05) Compares observed frequency to what we expected

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So, what’s your data? And what are you going to do about it?

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9/14/201020

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