6.review of statistical methods---misiri.ppt
TRANSCRIPT
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REVIEW OF STATISTICAL METHODS
HE MISIRICOMMUNITY HEALTH DEPARTMENT
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• Describe how you will conduct descriptive statistical analysis in your study
• Describe how you will conduct hypothesis testing in your study (when applicable)
• Describe the statistical tests you will use to analyse data from your proposed study
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Random Error
• Research is usually conducted on samples.• It is expensive, time-consuming and
logistically difficult to conduct a census.• Sample estimates will always be unexact
because of sampling error also known as random variation.
• The smaller the sample the greater the variation.
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Types of Data
• Categorical data-from categorical variables like eye colour,sex, marital status, level of education etc
• A categorical variable has categories. Eg Sex is categorised as Male or Female.
• Continuous variables assume any value on the real line.
• Continuous data is from continuous variables
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Scales of measurement
• Nominal: Sex• Ordinal: Severity of pain• Interval/Ratio: Weight, Speed
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Describing data
Data can be described by using:• Charts• Tables• Numerical summary values• Shapes of distributions
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1. Charts-Histogram
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Pie Chart
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2. Tables-Frequency distributionAge group Number of patients
< 30 30
31-40 102
41-50 162
51-60 96
61-70 22
71-80 4
Total 416
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Percentage distributionSatisfaction with nursing care
No of patients Percentage
Very satisfied 121 25.5
Satisfied 161 33.9
Neutral 90 18.9
Dissatisfied 51 10.7
Very dissatisfied 52 10.9
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TableSex Mean Age(SD)
Males 20.3(1.2)
Females 18.2(1.6)
All 19.3(1.8)
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Table from Misiri et al(2012b)
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HIV Rates-Misiri et al(2012a)
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4. Shapes of distributions:Symmetry and kurtosis
The degree of “peakedness”(Chris Caple,1991) is called kurtosis
• Positively skewed
• Negatively skewed
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Positively skewed
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Symmetric
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Kurtosis
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Variation in sample data
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Numerical summaries
• For categorical data one uses numbers/frequencies ,percentages or proportions, rates to describe data.
• For continuous data one uses measures of central tendency and variation
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3. Numerical values- Summary statistics
Examples of summary statistics are:A. Measures of central tendency:
Mean,Median,Mode
B. Measures of variation:Variance,standard deviation,range,interquartile range
C. Other statistics: Proportion, Percentiles, etc
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Examples-categorical data
• In a class of 200 students, 51 are males and 149 are females.-Numbers.
• 25.5% of patients were very satisfied with nursing care
• The prevalence of Chlamydia in young women in England in 1996 was 3.1%.
• The incidence rate of cancer is 90 cases per 100,000 person years of time
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Moe examples:et al(2012b)
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Ze & Misiri(2009)
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Descriptive statistics-Categorical data
• Proportions
• Percentages
• Each proportion should have a CI
• Better summarized in a percentage distribution or frequency distribution
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Appropriate average to use
• Use the mean and standard deviation for symmetric data.
• Use the median and range or quartiles for skewed data.
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Misiri et al(2012c)
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Standard deviation
• SD=sqrt(44.8/4) =3.3
• This is the average variation in the data.
• That means the difference between individual data points and the sample mean is on average 3.3.
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• A normal distribution is a distribution that is symmetric and looks similar to a bell in shape. If distribution of the data in a population follows a normal distribution (the measure of spread around the mean) then:
• The range covered by 1 SD below and 1 above the mean includes 68% of the distribution.
• The range covered by 2 SDs below and 2 above the mean includes 95% of the distribution.
• The range covered by 3 SDs below and 3 above the mean includes 99.7% of the distribution.
• The standard deviation is not used for the scatter around the median. The measure for the scatter around the median is the INTER-QUARTILE RANGE. There are three quartiles: at 25%, 50% and 75%. They divide the data into four quarters in a similar way to the median (the 50%-ile) dividing it into two halves. The inter-quartile range is the range of values between the 25%-ile and the 75%-ile. These values are used in producing a box (and whisker)-plot.
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Bell-shaped distribution
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• The standard deviation is not used for the scatter around the median. The measure for the scatter around the median is the INTER-QUARTILE RANGE.
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• There are three quartiles: at 25%, 50% and 75%. They divide the data into four quarters in a similar way to the median (the 50%-ile) dividing it into two halves. The inter-quartile range is the range of values between the 25%-ile and the 75%-ile. These values are used in producing a box (and whisker)-plot.
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Example:Plasma glucose
• 4.67• 4.97• 5.11• 5.17• 5.33• 6.22• 6.50• 7.00
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Hypothesis Testing
• Null• Alternative• Type I Error• Type II Error• Level of significance
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Example
• Null hypothesis: mothers attending ANC at clinic A are as likely to be attended by a skilled birth attendant as mothers attending ANC at clinic B
• Alternative hypothesis: mothers attending ANC at clinic A are either more likely or less likely to be attended by a skilled birth attendant as mothers attending ANC at clinic B.
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Paired samples t-test
• See example
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Independent sample t-test
• See example
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• P-value is the probability that the statistic is as observed from your sample or even more extreme.
Example:• If Ho: Mean Difference=0• Ha: Mean Difference >0• The test statistic is Z• Given that the level of significance is 5%:
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• We will reject Ho if p-value < 5%• This is so because this implies that our
findings are less likely to have happened by chance.
• We will accept Ho if the p-value > 5%• This is so because this implies that our
findings are more likely to happen as stated in the Ho.
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WARNING!
• Do not abuse p-values• P-values should always be accompanied by
confidence intervals.• Confidence intervals give the magnitude of
the effect as well as the precision of estimation.
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Example:Zverev & Misiri(2009)
• One-way analysis of variance revealed a significant effect of shift phase on total sleep duration (F = 36.8, d.f. = 8, P < 0.000).
• Ho:The mean total sleep duration of the three shift phases are equal.Ha:The mean total sleep duration for the three shift phases are different.
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Summary of methods
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