1. Basic statistical methods in psychiatric research
Abiodun O. Adewuya
MBChB, FWACP, FMCPsych
Mental Health in Africa: Time for Action
Addis ba; 8.30am, 25th April 2006

2. Warning!!!!
I AM NO STATISTICIAN ! ! !

3. Day 1 Definitions and language of statistics
The meaning and classification of variables
Introduction to descriptive and inferential statistics
Univariate analysis
the distribution
the central tendency
the dispersion
Basic multivariate analysis –
chi square,
t-test,
ANOVA,
correlation co-efficient

4. Day 2 Regression analysis Odds Ratio
Data reduction and Factor analysis
Screening and diagnostic tests
Reliabitility, ROC curve
Meta analysis
Sample size calculations

5. Statistics
The science of collecting, summarizing, presenting and interpreting data, and of using them to estimate the magnitude of associations and test hypothesis

6. Language of statistics
Population: everyone/everything you wish to study
Sample: a piece of the population
Variable: Xtics of each member of the pop
Census: study of the entire population
Parameter: no describing xtic of a pop
Statistics : no describing xtics of a sample
Sampling error: Diff btw the xtics of the population and the sample of that pop

7. Sampling error Size of sampling error determined by
size of sample – the more the size of sample, the less the error
variation – how different members of the population are from one another with regards to the variables being studied – the higher the variability, the more the sampling error
Non sampling errors
Respondents lying
Measurement errors
Errors due to non-respondents

8. variables
The raw data of a study consist of observations made on individual
May be people but may be RBC, urine specimen, rats, hospitals etc
Any aspect of an indiv measured like BP, or recorded like age, sex is called variable
There may be only one variable in a study or there may be many

9. Classification of variables
Categorical
Nominal – binary or multiple
Ordinal (ordered)
Numerical
Discrete
Continous

10. Nominal variables
Allow for only qualitative classification. That is, they can be measured only in terms of whether the individual items belong to some distinctively different categories, but we cannot quantify or even rank order those categories.
For example, all we can say is that 2 individuals are different in terms of variable A (e.g., they are of different race), but we cannot say which one "has more" of the quality represented by the variable.
Typical examples of nominal variables are gender, race, color, city, etc.

11. Ordinal variables
Allow us to rank order the items we measure in terms of which has less and which has more of the quality represented by the variable, but still they do not allow us to say "how much more."
A typical example of an ordinal variable is the socioeconomic status of families. For example, we know that upper-middle is higher than middle but we cannot say that it is, for example, 18% higher.
Likert scales – to collect info on attitude, degrees of agreement, frequency of use etc

12. numerical variables……
discrete
numerical but limited number of
discreet values which are usually whole
numbers e.g episodes of diarrhea, relapse
in schizophrenia
Continous
A measurement on a Continous scale e.g
temp, weight, height

13. Derived variables
Often we derive variables for our analysis from those originally recorded
Categorized or calculated from recorded variables e.g
age from “Todays date – DOB”;
age groups
BMI from weight and height
Based on threshold or cut-off e.g
LBW (Yes if <2.5kg, No if =/> 2.5Kg)
Transformed variables e.g
scoring WHOQOL-Bref

14. Outcome & exposure variables
Outcome: variable that is the focus of attention, whose variation we are seeking to understand
Exposure: we are mainly interested n identifying factors or exposures that may influence the size or the occurrence of outcome variables
Outcome = Dependent variable
Exposure = Independent variable

15. Descriptive & inferential statistics
Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures.
Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.
Inferential statistics: making deductions or conclusions

16. Univariate Analysis
Univariate analysis involves the examination across cases of one variable at a time.
There are three major characteristics of a single variable that we tend to look at:
the distribution
the central tendency
the dispersion

17. The distribution
Summary of the frequency of individual values or ranges of values for a variable.
Can be number (percentage) or a range of numbers (percentage)
One of the most common ways to describe a single variable is with a frequency distribution.
Frequency distributions can be depicted in two ways, as a table or as a graph (bar chart, pie chart, histogram etc)

18. The normal distribution
Called Gaussian distribution after its discoverer Gauss
The frequency distribution is symmetrical about the mean and bell-shaped;
The bell is narrow for small SD and wide for large SD
Normally dtb variables include BP, temp, Hb level etc
Dtbs not normally distributed are income, etc

19. The central tendency
The central tendency of a distribution is an estimate of the "center" of a distribution of values. There are three major types of estimates of central tendency:
Mean
Median
Mode

20. The mean
The Mean or average is probably the most commonly used method of describing central tendency.
To compute the mean all you do is add up all the values and divide by the number of values.
For example, the mean or average quiz score is determined by summing all the scores and dividing by the number of students taking the exam. For example, consider the test score values:
15, 20, 21, 20, 36, 15, 25, 15
The sum of these 8 values is 167, so the mean is 167/8 =

21. The median
The Median is the score found at the exact middle of the set of values.
One way to compute the median is to list all scores in numerical order, and then locate the score in the center of the sample.
For example, if there are 500 scores in the list, score #250 would be the median. If we order the 8 scores shown above, we would get:
15,15,15,20,20,21,25,36
There are 8 scores and score #4 and #5 represent the halfway point. Since both of these scores are 20, the median is 20. If the two middle scores had different values, you would have to interpolate to determine the median.

22. The mode
The mode is the most frequently occurring value in the set of scores.
To determine the mode, you might again order the scores as shown above, and then count each one. The most frequently occurring value is the mode.
In our example, the value 15 occurs three times and is the mode.
In some distributions there is more than one modal value. For instance, in a bimodal distribution there are two values that occur most frequently.
Notice that for the same set of 8 scores we got three different values , 20, and for the mean, median and mode respectively.
If the distribution is truly normal (i.e., bell-shaped), the mean, median and mode are all equal to each other.

23. Dispersion
Dispersion refers to the spread of the values around the central tendency.
There are two common measures of dispersion,
the range
the standard deviation.

24. The range
The range is simply the highest value minus the lowest value.
In our example distribution, the high value is 36 and the low is 15, so the range is = 21.

25. The standard deviation…
The Standard Deviation is a more accurate and detailed estimate of dispersion because an outlier can greatly exaggerate the range (as was true in this example where the single outlier value of 36 stands apart from the rest of the values.
The Standard Deviation shows the relation that set of scores has to the mean of the sample.
the square root of the sum of the squared deviations from the mean divided by the number of scores minus one

26. Inferential Statistics
With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone.
For instance, we use inferential statistics to try to infer from the sample data what the population might think.
Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study.
we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data.

27. Pearson Chi-square
The Pearson Chi-square is the most common test for significance of the relationship between categorical variables.
This measure is based on the fact that we can compute the expected frequencies in a two-way table (i.e., frequencies that we would expect if there was no relationship between the variables).

28. The only assumption underlying the use of the Chi-square (other than random selection of the sample) is that the expected frequencies are not very small.
The reason for this is that, actually, the Chi-square inherently tests the underlying probabilities in each cell; and when the expected cell frequencies fall, for example, below 5, those probabilities cannot be estimated with sufficient precision

29. The value of the Chi-square and its significance level depends on the overall number of observations and the number of cells in the table.
relatively small deviations of the relative frequencies across cells from the expected pattern will prove significant if the number of observations is large

30. Yates Correction.
The approximation of the Chi-square statistic in small 2 x 2 tables can be improved by reducing the absolute value of differences between expected and observed frequencies by 0.5 before squaring (Yates' correction).
This correction, which makes the estimation more conservative, is usually applied when the table contains only small observed frequencies, so that some expected frequencies become less than 5

31. Fisher Exact Test This test is only available for 2x2 tables; For when
Overall total of the table is less than 20 or
Overall total is between 20 and 40 and the smallest of the four expected number is less than 5

32. One-Sample T Test
tests whether the mean of a single variable differs from a specified constant.
whether the average IQ score for a group of students differs from 100 (supposed normal).

33. The Paired-Samples T Test
procedure compares the means of two variables for a single group.
It computes the differences between values of the two variables for each case and tests whether the average differs from 0.
Normally a “BEFORE” and “AFTER” means for the same group e.g mean BPRS score before Antipsychotic and mean BPRS score after 2 weeks of haloperidol treatment

34. The Independent-Samples T Test
procedure compares 2 means for 2 grps of cases. E.g. a YES or NO grp of cases
Ideally, for this test, the subjects should be randomly assigned to two groups, so that any difference in response is due to the YES/NO differences and not to other factors. E.g are the BPRS score differences due to Atypical (YES) or Conventional (NO) antipsycotics?

35. The One-Way ANOVA
ANOVA is used to test the hypothesis that several means are equal.
This technique is an extension of the two-sample t test.
for a quantitative dependent variable by a single factor (independent) variable.
In addition to determining that differences exist among the means, you may want to know which means differ.

36. The One-Way ANOVA There are two types of tests for comparing means:
a priori contrasts - are tests set up before running the experiment
post hoc tests - run after the experiment has been conducted
Once you have determined that differences exist among the means, post hoc range tests and pairwise multiple comparisons can determine which means differ.
Post hoc Range tests identify homogeneous subsets of means that are not different from each other.
Pairwise multiple comparisons test the difference between each pair of means,
Pairwise
Equal distribution= Bonferoni
Unequal distribution + Dunnet

37. Correlations
Correlation is a measure of the relation between two or more variables. The measurement scales used should be at least interval scales
Correlation coefficients can range from to
The value of represents a perfect negative correlation while a value of represents a perfect positive correlation .
A value of 0.00 represents a lack of correlation.
Normal dtb: Pearson
Not normal Spearman

38. The Partial Correlations
procedure computes partial correlation coefficients that describe the linear relationship between two variables while controlling for the effects of one or more additional variables.
Very like regression

39. Basic inferential statistics
Nominal Vs Nominal – Chi- square
Nominal vs Ordinal – Chi-square
Ordinal Vs Ordinal – Chi-square

40. Bi-Nominal (yes/no, male/fem) Vs Continous – Independent sample T-test
Multi-nomial / Ordinal Vs Continous - ANOVA
Continous Vs Continous – Correlation coefficient
Normally dtb – Pearson
Not normally dtb - Spearman

41. Statistical significance (P- value)
the probability that the observed relationship (e.g., between variables) or a difference (e.g., between means) in a sample occurred by pure chance ("luck of the draw"), and that in the population from which the sample was drawn, no such relationship or differences exist.
tells us something about the degree to which the result is "true" (in the sense of being "representative of the population").
More technically, the value of the p-value represents a decreasing index of the reliability of a result . The higher the p-value, the less we can believe that the observed relation between variables in the sample is a reliable indicator of the relation between the respective variables in the population.

42. Specifically, the p-value represents the probability of error that is involved in accepting our observed result as valid, that is, as "representative of the population."
For example, a p-value of .05 (i.e.,1/20) indicates that there is a 5% probability that the relation between the variables found in our sample is a "fluke."
In other words, assuming that in the population there was no relation between those variables whatsoever, and we were repeating experiments like ours one after another, we could expect that approximately in every 20 replications of the experiment there would be one in which the relation between the variables in question would be equal or stronger than in ours

43. Thank you