Descriptive Stats - Psych 217 (Descriptive Statistics)

PSYCH 217-DESCRIPTIVE STATS The purpose of descriptive stats is to summarize and communicate the data collected. - [Conditions:] not including all data - [Goal:] max info with min space **The purpose of descriptive stat:** 1. Summarize massive data points 2. Calculate within conditions (...

PSYCH 217-DESCRIPTIVE STATS The purpose of descriptive stats is to summarize and communicate the data collected. - [Conditions:] not including all data - [Goal:] max info with min space **The purpose of descriptive stat:** 1. Summarize massive data points 2. Calculate within conditions (ex: mean, standard deviation...) 3. Use in correlation designs (ex: correlation coefficient of variable pairs, central tendency of each variable) Scales of measurement: What: arrangement of data is the suitable way to represent the data. 1. **Nominal:** grouping by category, [no numeric value], no order/direction 2. **Ordinal:** [ranked order], unknown space between levels *Best for: self-reports, competitions (ex: very good/good/neutral/bad. Or 1^st^, 2^nd^, 3^rd^ place)* 3. **Interval:** numerical scales, ordering, space between levels, [no zero point ] *Best for: when zero does not mean anything in the data (ex: zero Celsius does not mean the weather has degree, sleeping hours cannot be 0hrs if alive!)* Measured mean. Median and standard deviation 4. **Ratio:** numerical scales, ordering, space between levels, [there is true zero point reference ] Measured mean. Median and standard deviation **Central tendency:** *What's normal?* Ex: 1 6 6 3 2 7 9 2 8 4 2 1. **Mean:** average of all scores (Arithmetic) How: A. Organize- 1 2 2 2 3 4 6 6 7 8 9 B. Add all: 50 C. Number of scores: 11 D. 50/11 = **4.54 MEAN** 2. **Median:** split ordered scores find the middle and average \*\*even total numbers: take 2 middle most \*\*odd total numbers: take middle most How: A. Organized- 1 2 2 2 3 4 6 6 7 8 9 B. Even/odd? \*\* there are 11 numbers (odd) C. Split in half -- take one out : 5 on each side middle number 4 D. Median = 4 E. **If Even take both numbers, add, divide by 2** 3. **Mode:** most frequent number How: what repeated the most \*\*if two equal include both Mode = 2 **Usefulness:** *Which to use? When?* Outliers=extreme levels - **Mode:** frequency difference is extreme - **Median:** remove extreme scores that are not generalized. (Not for most of population) - **Mean:** maximize data scores information \*\*problem: affected by outliers \*\*solution: sample size increase- reduce influence of outliers Measures of variability: How spaced out are the data scores? 1. Range 2. Variance 3. Standard deviation (most common) \*\*calculation doesn't matter- graph allocation of standard deviation matters A. **Range:** Min and max score How: Max minus min B. **Variance:** compared to the mean value (how far scores are from the mean) square root of SD C. **Standard deviation:** radical of Variance \*\* standardized=unit less and very descriptive! *How to make calculations descriptive?* **Graph-normal distribution:** According to the mean-point of data we can identify the normal distribution of the data, then we could find the standard deviation with any calculations. How? A. **Mean** -use as point of reference B. **Normal distribution**= 50% on each side of mean C. **Percentage**- each 50% divided into portions D. **X-axis**- defines what the data is representing \*\*difference between portions = variance (space between scores)   **[Measures of relationship:]** **Types of correlation:** 1. Regression 2. R and r squared 3. Partial correlation **General info:** Correlation is measurement of how two variables are related. r=0 No linear relationship/ no relationship (may have other form of relationship) r= +/- direction. r- value = strength The greater the value of r (max=1) the greater the impact of variables on each other. *So now what is r2? In depth correlation between the range of two variables.* **R-radical correlation-correlation measures:** [Restriction of range:] correlation insufficient information if full range of two variables not considered. What: variable X is correlated with variable Y at r=... Problem: how the range of variable X correlated with range of variable Y? Why: the space between scores influences the space between the scores of another variable. Procedure: - Squared of r= r2. (\*\*x100% as %) - If r2=1 full overlap r2=0 no overlap - Conclusion= variance of variable X shared with variance of variable Y, variance of variable X is predictable by variance in variable Y or (vice versa)