Statistics as a Tool. A set of tools for collecting, organizing, presenting and analyzing numerical facts or observations.

Transcription

1 Statistics as a Tool A set of tools for collecting, organizing, presenting and analyzing numerical facts or observations.

2 Descriptive Statistics Numerical facts or observations that are organized describe the frequencies, measures of central tendency, and degree of dispersion of variables in a sample of a larger population.

3 Levels of Measurement Reflects type of information measured and helps determine what descriptive statistics and which statistical test can be used.

4 Four Levels of Measurement NOIR -- no one is ready Nominal lowest level, categories, no rank Ordinal second lowest, ranked categories Interval next to highest, ranked categories with known units between rankings Ratio highest level, ranked categories with known intervals and an absolute zero

5 Descriptives for nominal and ordinal data Frequencies and percentages Frequencies absolute number of cases Percentages relative number of cases

6 Frequencies for a nominal variable Reason for referral Valid mental illness sexual abuse physical abuse neglect parentreturn Total Cumulative Frequency Percent Valid Percent Percent

7 Descriptives for ordinal data Quality of outcome Valid Positive Neutral Negative Total Cumulative Frequency Percent Valid Percent Percent

8 Descriptives for interval/ratio (scale) variables Measures of central tendency Mean -- sum of all cases divided by number of cases Median case for which half of all other cases are above and half of all other cases are below. Mode most frequently occurring case

9 Descriptives for scale variables Measures of dispersion Range Value of cases from minimum to maximum Standard Deviation number which when added or taken away from each case adds up to zero. Variance Standard deviation squared

10 Descriptives for a ratio variable MONTHS Valid Total Cumulative Frequency Percent Valid Percent Percent

11 More descriptives for a ratio variable Statistics MONTHS N Mean Median Mode Std. Deviation Variance Range Minimum Maximum Valid Missing

12 Inferential statistics Procedures used to make inferences from sample data and generalize findings to the population

13 Probability Statistical significance the probability that the difference or the association found in the sample would be present in the population. Three common probabilities used <.05 <.01 <.001

14 Sampling bias The systematic differences between sample in study and the larger population of interest. The use of inferential statistics allows us to calculate the odds that what is found in the sample is due to sampling bias.

15 Statistical significance (p-levels) When p <.05, the degree of difference or association being tested would only occur by chance alone five times out of a hundred. When p <.01, the difference or association being observed would only occur by chance alone one time out of a hundred. When p <.001

16 Testing for statistically significant differences When you want to see if there is a difference in outcome by group membership, or by treatment approach. SPSS Analyze Compare means Independent t-test

17 Is there a significant difference in months of service and type of outcome? Group Statistics MONTHS Was outcome positive? yes no Std. Error N Mean Std. Deviation Mean Independent Samples Test MONTHS Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. t df Sig. (2-tailed) t-test for Equality of Means Mean Difference 95% Confidence Interval of the Std. Error Difference Difference Lower Upper

18 Statistically significant differences i.v. nominal and d.v. interval/ratio Analyze Univariate (One d.v.; multiple predictors) Multivariate (Multiple d.v.; multiple predictors) Repeated measures (time series of dependent measures; one predictor.

19 Statistically significant associations at higher levels of measurement Analyze Correlate Bi-variate Pearson s (two interval/ratio variables) Kendall s tau (two ordinal variables) Spearman s rho (two ordinal variables)

20 Test of Pearson Correlation Coefficient (r) Correlations MONTHS Percent of positive cases for each referral reasons Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Percent of positive cases for each referral MONTHS reasons

21 Independent t-test to determine statistical significance Independent Samples Test MONTHS Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. t df Sig. (2-tailed) t-test for Equality of Means Mean Difference 95% Confidence Interval of the Std. Error Difference Difference Lower Upper

22 Differences between groups at lower levels of measurement Analyze Descriptives Crosstabs Identify variable in row and column Select statistics Two nominal (dichotomized) Chi-Square Nominal by ordinal Kendal s tau-b Nominal by interval Eta

23 Difference in LOS by referral Group Statistics MONTHS Reason for referral mental illness sexual abuse Std. Error N Mean Std. Deviation Mean

24 Crosstabs to determine difference between groups Reason for referral * Was outcome positive? Crosstabulation Reason for referral Total mental illness sexual abuse physical abuse neglect parentreturn Count % within Reason for referral Count % within Reason for referral Count % within Reason for referral Count % within Reason for referral Count % within Reason for referral Count % within Reason for referral Was outcome positive? yes no Total % 14.3% 100.0% % 28.6% 100.0% % 37.5% 100.0% % 50.0% 100.0% % 55.6% 100.0% % 37.8% 100.0%

25 Chi-Square tests Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases a. Chi-Square Tests Asymp. Sig. Value df (2-sided) a cells (90.0%) have expected count less than 5. The minimum expected count is 2.27.

26 Which test to use when? Decision is made by what the question is, the level of measurement of the variable and the extent to which assumptions of parametric statistics are met. Question: Difference or Association? Level of measurement: NOIR? Sample size and distribution (normal?)

27 Tests comparing difference between 2 or more groups Test Paired (dependent) t-test Unpaired (independent t- test Dependent variable Interval/ratio pre and post tests Interval/ratio Independent variable Nominal Nominal (2 grps) ANOVA F-test Interval/ratio Nominal (>2 grps) Chi-Square (Nonparametric) Nominal (Dichotomous) Nominal

28 Tests demonstrating association between two groups Test Dependent var. Independent var. Spearman rho Ordinal Ordinal Mann-Whitney U Ordinal Nominal Non-parametric Pearson s r Interval/ratio Interval/ratio

29 Tests demonstrating association between two groups, controlling for third variable Test Dependent Independent Logistic Nominal Nominal regression Linear regression Interval/ratio Interval/ratio Pearson partial r Interval/ratio Interval/ratio Kendall s partial r Ordinal Ordinal

30 Posted with Permission from: Bernie S. Newman, Ph.D., L.C.S.W. Associate Professor MSW Program Director Temple University School of Social Administration 1301 Cecil B. Moore Ave. 505 Ritter Annex Philadelphia, PA