Statistical Methods For Health Research

History Blaise Pascl: tossing ……probability William Gossett: standard error of mean “ how large the sample should be for a given degree of precision, to extrapolate accuracy

Why statistics? 1.You will be able to read research (read, understand, and evaluate) 2.You will be able to do you own research ( you know what you do, you defend what you do, you are able to make changes if changes is in your side)

Levels of measurement Need to understand levels of measurement to be able to evaluate the appropriateness of the analysis

Nominal –classifying objects into mutually exclusive categories (various independent categories) e.g. gender, marital status Ordinal – sorting of objects on the basis of their standing, relative to each other Two rules: 1.Equality – on equality rule 2.Greater than or less than rule. E.g. dependency 1=completely dependent on others 2=needs another’s assistance 3=needs mechanical assistance 4=complete independence

Interval – specifies the rank order and the distance between objects; theoretically, never an absolute zero “How much greater or how much less” “ the distance between the categories are equal” E.g. temperature (scale does not have an absolute zero) Interval is probably the most commonly used level of measurement used in nursing research Ratio – equal intervals and an absolute zero starting point. Many physical characteristics; e.g. length, weight, volume

Levels and analysis The levels of measurement are the determining factor in deciding on the type of statistics to be used in the analysis [ the choice as to which statistical test can be legitimately used]

Statistics Descriptive Inferential Univariate Bivariate Parametric Nonparametric

Planning for data analysis Descriptive statistics provides description of the data from your particular sample [ a technique used to describe large amount of data in abbreviated symbolic form] Inferential analysis, on the other hand, allows you to draw inferences about the larger population from your sample date. [ technique used to measure a sample (subgroups) and then genralize these measures to the population (entire group]

Descriptive statistics A: univariate Frequency distribution – number of time each event occurs is counted; e.g. bar charts Measures of central tendency -Mode (most frequent) -Median (mid point) -Mean (average)

Measures of variability refers to the spread or dispersion of the data Range – difference between the highest and lowest scores Standard deviation (SD) – the most frequently used measure of variability

Descriptive statistics B: Bivariate: degree and magnitude of relationship between two variables Contingency table Correlation – Pearson r for interval level data – Spearman’s rho and Kendall’s tau for ordinal level data

Inferential statistics Parametric statistics – used to describe inferential statistics that assume a normal distribution of the variables and the use of interval or ratio measures. - t tests; analysis of variance; analysis of covariance Nonparametric – do not require the same rigorous assumptions as parametric statistics. Often used when the sample size is small and data are nominal or ordinal - chi-square

Statistical Significance or p value (alpha level) Statistical significant means that the obtained results are not likely to be the results of chance fluctuations at the specified level of probability.

p <.05 There are 5 chances out of 100 that the results are due to chance, and 95 chances that the results are due to the intervention!!! P = in 100 P = in 100 P = in 1000

Steps 1.Hypothesis stated 2.P value setp=.05 p=.01 p= Analysis completed 4. Is results are as predicted in the hypothesis and the p value the same or smaller, results supported.

Interpretation of findings Results – the results of the analysis The information from each Research Question/s or Hypothesis should be presented Then the “So what” question Discussion - must address all results and flow clearly from results

Practical vs statistical significance The discussion section may include a discussion of practical or clinical significance vs statistical significance. The former relates to the importance of the findings to the clinical population, even if statistical significance not found

The normal curve (distribution) Major characteristics 1.most of the scores cluster around the middle of the distribution 2.symmetrical 3.mean = median = mode 4.constant relationship (percentage) with SD 5.Asymptotic

Skewness and kurtosis of D n Neg Skewness: Q2 – Q1 > Q3 – Q2 Pos Skewness: Q2 – Q1 < Q3 – Q2 Nor distribution: Q2 – Q1 = Q3 – Q2 Skewness: -1 to + 1 Kurtosis: +ve leyptikurtic (peaked) - ve platykutric (flat)

S -2S -1S X +1S +2S +3S

NORMAL POSITIVE NEGATIVE BIMODAL

Area of the normal curve + 1 s = = 68% + 2 s = = 95% + 3 s = = 99% Z scores: is says how much above and below the mean a given score is in S units Z score is translation of raw scores into units of SD

FOR RAW SCORE FOR SAMPLE

Z scores are helpful for comparing performances try ? 1. x = 85, M = 65, s = x = 60, M = 55, s = 10

Frequency And Visual Displays

Range ( X MAX – X MIN width of interval = range / number of intervals GRAPHS: – Histogram – Polygon – Ogive curve

Histogram

Polygon

OUTLIERS = 1.5 IQR (Q3-Q1)

hinges OUTLIERS = 1.5 IQR (Q3-Q1) Q3 Q1 see page 55

STEM AND LEAF DISPLAYS

Significance & Testing Hypothesis H 0 : the event in question is only due to chance Significance: excluding chances as one of the explanation Significance = rejecting the null hypothesis

Testing hypothesis For example: T test H 0 : µ 1 = µ 2 H a : µ 1 ≠ µ 2

Types of Error Sampling error: error in selecting the sample Error of inference: error in drawing the conclusion. Type I, type II

The main principle is that the H 0 is true and we are trying to test whether it is true or false The researcher has to make the H a that support his perspective Therefore, we are testing the H 0

Factor affect type II error 1.Sample size 2.The difference between the H 0 and H a 3.Heterogeneity of the sample as the population suppose to be The researcher should avoid falling in type II error.

Confidence interval The area in which the mean of the population falls. Using the standardized scores Therefore, t scores are mainly used for that purpose. 95% = M ± 1.96 (SE) 99% = M ± 2.58 (SE)

Data Preparation

Checking the Data For Accuracy – are the responses legible/readable? – are all important questions answered? – are the responses complete? – is all relevant contextual information included (e.g., data, time, place, researcher)?

Developing a Database Structure – variable name – variable description – variable format (number, data, text) – instrument/method of collection – date collected – respondent or group – variable location (in database) – notes

Entering the Data into the Computer Data Transformations Once the data have been entered it is almost always necessary to transform the raw data into variables that are usable in the analyses. There are a wide variety of transformations that you might perform. Some of the more common are: missing values item reversals

scale totals categories For many variables you will want to collapse them into categories. For instance, you may want to collapse income estimates (in dollar amounts) into income ranges.

Outliers Steps on SPSS 1.Analyze 2.Descriptive 3.Explore 4.Statistics ……plots 5.Outliers

OUTLIRIES SRESID: Studentized residual. ZRESID: Normalized residual.: Residual divided by the square root of the product of PRED and 1–PRED COOK: Analog of Cook’s influence statistic (Cook's distance may be considered "large" if substantially larger than 1).