Descriptive and Inferential Statistics - intro
- 1. Descriptive & Inferential Descriptive & Inferential Statistics Statistics Descriptive Statistics Descriptive Statistics • Organize Organize • Summarize Summarize • Simplify Simplify • Presentation of data Presentation of data Inferential Statistics Inferential Statistics •Generalize from Generalize from samples to pops samples to pops •Hypothesis testing Hypothesis testing •Relationships Relationships among variables among variables Describing data Make predictions Make predictions
- 2. Descriptive Descriptive Statistics Statistics 3 Types 1. Frequency Distributions 3. Summary Stats 2. Graphical Representations # of Ss that fall in a particular category Describe data in just one number Graphs & Tables
- 3. Altman, D. G et al. BMJ 1995;310:298 Central Limit Theorem: the larger the sample size, the closer a distribution will approximate the normal distribution or A distribution of scores taken at random from any distribution will tend to form a normal curve jagged smooth
- 4. 2.5% 2.5% 5% region of rejection of null hypothesis Non directional Two Tail body temperature, shoe sizes, diameters of trees, Wt, height etc… IQ 68% 95% 13.5% 13.5% Normal Distribution: half the scores above mean…half below (symmetrical)
- 6. Summary Statistics describe data in just 2 numbers Measures of central tendency • typical average score Measures of variability • typical average variation
- 7. Measures of Central Tendency • Quantitative data: – Mode – the most frequently occurring observation – Median – the middle value in the data (50 50 ) – Mean – arithmetic average • Qualitative data: – Mode – always appropriate – Mean – never appropriate
- 8. Mean • The most common and most useful average • Mean = sum of all observations number of all observations • Observations can be added in any order. • Sample vs population • Sample mean = X • Population mean = • Summation sign = • Sample size = n • Population size = N Notation
- 9. Special Property of the Mean Balance Point • The sum of all observations expressed as positive and negative deviations from the mean always equals zero!!!! – The mean is the single point of equilibrium (balance) in a data set • The mean is affected by all values in the data set – If you change a single value, the mean changes.
- 10. Summary Statistics describe data in just 2 numbers Measures of central tendency • typical average score Measures of variability • typical average variation 1. range: distance from the lowest to the highest (use 2 data points) 2. Variance: (use all data points) 3. Standard Deviation 4. Standard Error of the Mean
- 11. Measures of Variability 2. Variance: (use all data points): average of the distance that each score is from the mean (Squared deviation from the mean) otation for variance s2 3. Standard Deviation= SD= s2 4. Standard Error of the mean = SEM = SD/ n
- 12. Inferential Statistics Population Sample Draw inferences about the larger group Sample Sample Sample
- 13. Sampling Error: variability among samples due to chance vs population Or true differences? Are just due to sampling error? Probability….. Error…misleading…not a mistake
- 14. Probability • Numerical indication of how likely it is that a given event will occur (General Definition)“hum…what’s the probability it will rain?” • Statistical probability: the odds that what we observed in the sample did not occur because of error (random and/or systematic)“hum…what’s the probability that my results are not just due to chance” • In other words, the probability associated with a statistic is the level of confidence we have that the sample group that we measured actually represents the total population
- 15. Chain of Reasoning for Inferential Statistics Population Sample Inference Selection Measure Probability data Are our inferences valid?…Best we can do is to calculate probability about inferences
- 16. Inferential Statistics: uses sample data to evaluate the credibility of a hypothesis about a population NULL Hypothesis: NULL (nullus - latin): “not any” no differences between means H0 : 1 = 2 “H- Naught” Always testing the null hypothesis
- 17. Inferential statistics: uses sample data to evaluate the credibility of a hypothesis about a population Hypothesis: Scientific or alternative hypothesis Predicts that there are differences between the groups H1 : 1 = 2
- 18. Hypothesis A statement about what findings are expected null hypothesis "the two groups will not differ“ alternative hypothesis "group A will do better than group B" "group A and B will not perform the same"
- 19. Inferential Statistics When making comparisons btw 2 sample means there are 2 possibilities Null hypothesis is true Null hypothesis is false Not reject the Null Hypothesis Reject the Null hypothesis
- 20. Hypothesis Testing - Decision Decision Right or Wrong? But we can know the probability of being right or wrong Can specify and control the probability of making TYPE I of TYPE II Error Try to keep it small…
- 21. 2.5% 2.5% 5% region of rejection of null hypothesis Non directional Two Tail
- 22. 5% 5% region of rejection of null hypothesis Directional One Tail
- 23. Error in Testing
- 24. Take medical testing—a type 1 error (false positive) in this field might lead to unnecessary treatment, while a type 2 error (false negative) could result in a missed diagnosis.
- 25. Reducing Errors •Increase Sample Size •Use Multiple Tests •Continuously monitor and feedback •Conduct root cause analysis
- 26. Inferential statistics Used for Testing for Mean Differences T-test: when experiments include only 2 groups a. Independent b. Correlated i. Within-subjects ii. Matched Based on the t statistic (critical values) based on df & alpha level
- 27. Inferential statistics Used for Testing for Mean Differences Analysis of Variance (ANOVA): used when comparing more than 2 groups 1. Between Subjects 2. Within Subjects – repeated measures Based on the f statistic (critical values) based on df & alpha level More than one IV = factorial (iv=factors) Only one IV=one-way anova
- 28. Inferential statistics Meta-Analysis: Allows for statistical averaging of results From independent studies of the same phenomenon