Statistics as a Tool

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

Similar Concepts Across Cultures

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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.

Environmental Studies: Air/Water

Levels of Measurement

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

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

Descriptives for nominal and ordinal data

Frequencies and percentages Frequencies – absolute number of cases Percentages – relative number of cases

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

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

Inferential statistics

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

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

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.

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……

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

Planned Parenthood

Earth is in need of another one/third earth addition: 8 billion

Is there a significant difference in months of service and type of outcome?

Group Statistics

23 11.2174 5.11643 1.06685

14 10.3571 4.73298 1.26494

Was outcome positive?yes

no

MONTHSN Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

.123 .728 .510 35 .613 .8602 1.68725 -2.56506 4.28556

.520 29.309 .607 .8602 1.65476 -2.52258 4.24307

Equal variancesassumed

Equal variancesnot assumed

MONTHSF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

The Need for Pure Water

What cvan be done? Ans: wells/solar heat

Emerging

Common Vectors

39

• Mosquitoes serve as vectors for Malaria, Dengue fever, Yellow fever, and Chikungunya

• Ticks can serve as vectors for Lyme disease, Rickettsia, and Babesiosis

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.

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)

Test of Pearson Correlation Coefficient (r)

Correlations

1 .069

. .685

37 37

.069 1

.685 .

37 37

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

MONTHS

Percent of positive casesfor each referral reasons

MONTHS

Percent of positive

cases foreach referral

reasons

Person-Doctor==Public Health Group===Population==Mamny

Independent t-test to determine statistical significance

Independent Samples Test

.464 .509 -13.516 12 .000 -13.0000 .96186 -15.09571 -10.90429

-13.516 10.955 .000 -13.0000 .96186 -15.11809 -10.88191

Equal variancesassumed

Equal variancesnot assumed

MONTHSF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

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

Difference in LOS by referral

Group Statistics

7 5.2857 2.05866 .77810

7 18.2857 1.49603 .56544

Reason for referralmental illness

sexual abuse

MONTHSN Mean Std. Deviation

Std. ErrorMean

Crosstabs to determine difference between groups

Reason for referral * Was outcome positive? Crosstabulation

6 1 7

85.7% 14.3% 100.0%

5 2 7

71.4% 28.6% 100.0%

5 3 8

62.5% 37.5% 100.0%

3 3 6

50.0% 50.0% 100.0%

4 5 9

44.4% 55.6% 100.0%

23 14 37

62.2% 37.8% 100.0%

Count

% within Reasonfor referral

Count

% within Reasonfor referral

Count

% within Reasonfor referral

Count

% within Reasonfor referral

Count

% within Reasonfor referral

Count

% within Reasonfor referral

mental illness

sexual abuse

physical abuse

neglect

parentreturn

Reasonfor referral

Total

yes no

Was outcomepositive?

Total

Chi-Square tests

Chi-Square Tests

3.485a 4 .480

3.696 4 .449

3.334 1 .068

37

Pearson Chi-Square

Likelihood Ratio

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)

9 cells (90.0%) have expected count less than 5. Theminimum expected count is 2.27.

a.

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?)

Tests comparing difference between 2 or more groups

Test Dependent variable

Independent variable

Paired (dependent) t-test

Interval/ratio pre and post tests

Nominal

Unpaired (independent t-test

Interval/ratio Nominal (2 grps)

ANOVA F-test Interval/ratio Nominal (>2 grps)

Chi-Square

(Nonparametric)

Nominal (Dichotomous)

Nominal

Tests demonstrating association between two groups

Test Dependent var. Independent var.

Spearman rho Ordinal Ordinal

Mann-Whitney U

Non-parametric

Ordinal Nominal

Pearson’s r Interval/ratio Interval/ratio

Tests demonstrating association between two groups, controlling for third variable

Test Dependent Independent

Logistic regression

Nominal Nominal

Linear regression Interval/ratio Interval/ratio

Pearson partial r Interval/ratio Interval/ratio

Kendall’s partial r Ordinal Ordinal

Mission,Manpower,Math,Maintain

How do you handle malnutrition?

Many healthcare task forces

How do you handle AIDS?

Different Theories About HIV/AIDS

Is Health a Right or is Health a Commodity?

USA Health Care Business Barriers

Some countries will lose

What can be done?