Lecture notes on statistics Elspeth Slayter, M.S.W., Ph.D.

Today’s class  Administrative matters Readings  Review of QL data analysis  Take-home message: Match stats to question Purpose, logistics, interpretation! (PLI)  Discussion of Assignment 3

Feedback on Annotated Bibliography  What is QL research?  Populations: Client vs. Study  Moving forward: Using findings, methods  Which interventions “rose up” for you?  Start thinking: What is the best way to evaluate?

Moving to assignment 3 A1 Agency assessment Guiding question A2 Annotated Bibliography A3 Literature review – intervention choice Proposed program evaluation

Critical consumption of research AND skills to evaluate practice Learn to critically consume research Learn to develop practice evaluation plans Consider the process of evidence-based practice beyond evidence- supported interventions Overlapping goals in course:

Starting to think about ProcessOutcome

Remember:

4 basic types of statistical tests: Mean, standard deviation Median, Mode Percentage, frequency Description Pearson’s correlation Correlation Student’s t tests Chi-square tests ANOVA Odds ratios Comparison OLS regression Logit regression Prediction

Univariate & Descriptive  Univariate - describe individual variables  Descriptive – describe, summarize data  Frequency  Range  Percentage  Central tendency (simple mean, median mode)  Standard deviation

Cheat sheet: Descriptive statistics Type:Used for:Variable structure: FrequencyCountingAny Mean/average, median or mode Measure of central tendency Continuous

What is a frequency measure and what do you do with it?  Counts  Numbers of people/places/things with: a certain characteristic a certain set or combination of characteristics  How do you report these results in a way that is accessible to the reader? Percentages Mean (SD), median, mode

Table 1: Demographics of Elders with MR/SA Socio- behavioral model VariableMR/SA (N=350) NoMR/SA (N=48,014) Test Predisposing Characteristics Gender (male)238 (68%)25,064 (52%)OR=1.9*** Mean age (SD)70 (5)73 (7)t=4.5* Race (white)260 (74%)28,741 (59%)OR=1.9*** (SSI/SSDI)199 (57%)29,131 (61%)NS Enabling resources Dually eligible303 (87%)43,226 (90%)OR=0.7* FFS coverage262 (75%)34,283 (71%)NS Low state SA coverage 141 (40%)16,899 (35%)OR= OR= 1.2* Urban location213 (61%)30,027 (63%)NS Need factors SMI diagnosis151 (43%)7,540 (16%)OR= 4.1*** Long-term SA diagnosis 19 (5%)5,549 (12%)OR= 0.4*** ***p<.001 *p<.05

Rodriguez & Murphy: Frequencies? Ranges?

Mean (a.k.a. average, sample mean, arithmetic mean)  Only for continuous (vs. nominal) variables  Add up all scores/divide by total number of scores  Can be misleading for a skewed sample with “outliers”  In the literature often shows up as “x-bar”

Standard deviation:  Most commonly used measure of dispersion around a mean how “spread out” are the values?  Always reported together – otherwise considered to be biased  Can’t be done with nominal variables

Standard deviation in a normally distributed sample Dark blue < 1 “standard deviation” from the mean Accounts for 68.3%

Table 1: Demographics of Elders with MR/SA Socio- behavioral model VariableMR/SA (N=350) NoMR/SA (N=48,014) Test Predisposing Characteristics Gender (male)238 (68%)25,064 (52%)OR=1.9*** Mean age (SD)70 (5)73 (7)t=4.5* Race (white)260 (74%)28,741 (59%)OR=1.9*** (SSI/SSDI)199 (57%)29,131 (61%)NS Enabling resources Dually eligible303 (87%)43,226 (90%)OR=0.7* FFS coverage262 (75%)34,283 (71%)NS Low state SA coverage 141 (40%)16,899 (35%)OR= OR= 1.2* Urban location213 (61%)30,027 (63%)NS Need factors SMI diagnosis151 (43%)7,540 (16%)OR= 4.1*** Long-term SA diagnosis 19 (5%)5,549 (12%)OR= 0.4*** ***p<.001 *p<.05

Example of percentage, mean and standard deviation reporting: AWOL history: Girls in this study were reported to have run away more often (M = 3.6 +/- 5.8) as compared to boys (M = 2.8 +/- 6.6).

Median and mode  Sometimes the mean is skewed  If so, using one of these makes more sense:  Median the value below which 50% of the scores fall, or the middle score Median age at which people first had a counseling experience  Mode the most frequent score Most common age at which people first had a counseling experience

Rodriquez & Murphy

Rodriguez & Murphy

4 basic types of statistical tests: Mean, standard deviation Median, Mode Percentage, frequency Description Pearson’s correlation Correlation Student’s t tests Chi-square tests ANOVA Odds ratios Comparison OLS regression Logit regression Prediction

What you need to know: I. Purpose of test Match question to test II. Logistics for test Structure of variable needed for test ○ Continuous ○ Nominal Number of variables needed for test III. Interpret test findings Basic knowledge of the “squigglies” in reporting statistical results

Review: Variable structure  Continuous (a.k.a. numeric) Examples?  Nominal (a.k.a. dummy variable, categorical variables) Examples?

I

Correlation tests  Measures association/relationship between 2 continuous variables  Does not measure causation  Distinguish vernacular usage of the term from statistical usage  Requires a logic model/theory/research- based idea

Correlation test: A measure of association The longer you work at the agency…...the more likely you are to experience “burnout” 0-5 years Burnout score variable This is a positive correlation, when one variable increases, so does the other Years of employment variable 6-10 years years 30 (Low) 60 (Mid) 90 (High)

Correlation test: A measure of association The lower your caseload…..the less likely you are to experience “burnout” 0-18 Burnout score variable This is a positive correlation too, when one variable decreases, so does the other Caseload variable (Low) 60 (Mid) 90 (High)

Correlation test: A measure of association  With higher scores on job satisfaction….and lower scores on burnout This is an inverse/negative correlation, when one variable increases, the other decreases

Correlation tests: Interpretation  Magnitude/stregnth.9 to 1 very high correlation.7 to.9 high correlation.5 to.7 moderate correlation.3 to.5 low correlation.0 to.3 little if any correlation

Correlation tests: Interpretation Value of rInterpretation r= 0The two variables do not vary together at all PositiveThe two variables tend to increase or decrease together r = 1.0Perfect correlation – something is wrong Negative/InverseOne variable increases as the other decreases r = -1.0Perfect negative or inverse correlation

Look for the “r” and “p” values  Statistically significant association between variables  p-level should be between p<.05* p<.01** p<.001

Correlation: You tell me  Is there a relationship between… Age and number of MD visits per year among 0-3 year olds? Gender and number of MD visits per year? High vs. low levels of burnout scores and working at DMH for over 20 years? Burnout scores and number of years with DOC?

I

4 basic types of statistical tests: Mean, standard deviation Median, Mode Percentage, frequency Description Pearson’s correlation Correlation Student’s t tests Chi-square tests ANOVA Odds ratios Comparison OLS regression Logit regression Prediction

Χ 2 or Chi-Square Tests  AKA: Chi-square goodness-of-fit test, commonly referred to as the chi-square test Pearson’s chi-square test Yates’ chi-square test, also known as Yates' correction for continuity Mantel-Haenszel chi-square test Linear-by-linear association chi-square test

Χ 2 or Chi-Square Tests  Compare 2 or more groups (2 is easiest)  Compare those groups on a nominal variable only  Way to tell if there is a difference between groups of observations

t-tests  AKA: Independent samples t-test Paired samples t-test Students’ t-test  When these tests can’t be conducted due to small N, similar tests can be used: (Independent) Mann-Whitney U test (Paired) Binomial test or Wilcoxon signed-rank test

Students’ t-test: Why use it?  Assesses whether the means of 2 groups are statistically different from each other  Appropriate whenever you want to compare the means of 2 groups

“Student’s t” test: Choices Independent samples  Groups are independent of each other  Individuals randomly assigned into two groups Paired samples  Groups are paired  Each group member has a unique relationship with a particular member of the other sample

“Student’s t” test: What are you looking for?

Odds ratios:  A way of comparing whether the probability of a certain event is the same for two groups  Requires two groups  Comparison of groups on a nominal variable Intuitive: Easy to interpret Easy for your audience to interpret!

Odds ratios: What does it tell you?  What are the odds that one group is more likely than another to experience one condition Male vs. Female ex-offenders on post- incarceration employment retention for a year or more (Y/N)? People with and without disabilities: Who is more likely to access substance abuse treatment (Y/N)?

Odds ratios: What you are looking for  OR = 1 Condition equally likely in both groups  OR > 1 Looks like this: OR=2.34* Condition is more likely in the first group  OR < 1 Looks like this: OR=0.34* Condition is less likely in the first group

Odds ratios: How to interpret them OR=1.5***1.5 times more likely… OR=12.5***Almost 13 times more likely… OR=0.50***Fifty percent less likely… OR=O.89***11 percent less likely…

ANOVA tests  AKA: Fisher’s test of variance Fisher’s ANOVA Fisher’s analysis of variance One-way ANOVA  Compare 2 or more groups (usually used with 3 or more)  Compare groups on a continuous variable

Do all three social work units have the same average caseload?  Unit A  Unit B  Unit C