Data Analysis Descriptive

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Data AnalysisDescriptive Inferential Statistics

• N295
• March 22, 2005

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Data Analysis

• Goal provide answers to the research questions
• Gives organization and meaning to the data
• Descriptive
• Inferential
• Consumers of research need to understand its
  meaning, use, and limitations

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Using Statistics to Describe

• Descriptive statistics are also referred to as
  summary statistics.
• In any study in which the data are numerical,
  data analysis begins with descriptive statistics.

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Describing the Sample

• Purpose to obtain as complete a picture of the
  sample as possible
• Determine frequencies of variables related to
  sample
• Age
• Education
• Health status
• Gender
• Ethnicity

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Descriptive Analysis

• Describes data for a particular sample
• Makes data more manageable by summarizing them
  and describing various characteristics

• Includes
• Measures of central tendency
• Mode, median, mean
• Measures of variability
• Range,
• standard deviation (SD)
• percentile

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Descriptive Analysis

• Measures of central tendency describe the
  average member of the sample
• Measures of variability describe how much
  dispersion there is in the sample
• Example ages of students in a class

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Levels of Measurement

• Determine which statistics should be used
• Nominal classification
• Ordinal relative rankings
• Interval rank ordering with equal intervals
• Ratio rank ordering w/absolute zero

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Descriptive Analysis
Content analysis
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Measures of Central Tendency What is a typical
score?

• Mode
• The numerical value or score that occurs with
  greatest frequency
• Median
• Value in the exact center of ungrouped frequency
  distribution
• Obtained by rank ordering the values

• Mean
• The sum of values divided by the number of values
  being summed
• Example
• 11113333334444444455555555555555777777778888889999
  
• 264/50 5.28

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Frequency Distribution

• Presents data in tabular or graphic form and
  allows for the calculation or observations of
  characteristics of the distribution of the data

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Normal Distribution

• A theoretical frequency distribution of all
  possible values in a population
• No real distribution exactly fits the normal
  curve.
• Levels of significance and probability are based
  on the logic of the normal curve.

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Normal Distribution

• Normal curve
• Symmetrical around the mean and unimodal
• Fixed percentage of scores fall within a given
  distance of the mean

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Measures of Variability

• Concerned with the spread of data
• Is the sample similar or different?

• Range difference between highest lowest
  scores
• Semiquartile range range of the middle 50
• Percentile of cases a score exceeds
• Median 50th percentile

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Measures of Variability

• Standard deviation (SD)
• Most frequently used measure of variability
• Based on the concept of the normal curve
• Always reported with the mean

• The square root of the variance
• Just as the mean is the average value, the
  standard deviation is the average difference
  score.

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Correlations

• Used to answer what is the relationship?
  questions
• Scatterplots
• Show strength/magnitude of relationship between 2
  variables
• Strength of the correlation is demonstrated by
  how closely the data points approximate a
  straight line

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Correlations
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Critiquing Descriptive Stats

• Are descriptive statistics appropriate for level
  of measurement reported?
• Appropriate summary statistics for each major
  variable?
• Enough information presented to judge the
  results?
• Results clearly and completely stated?
• Tables/graphs agree with text and extend it or
  merely repeat it?

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Inferential Analysis

• Provides statistical support for the population
  from your sample data
• Requires interval level measurement
• Allow us to
• Test hypotheses about a population using
  probability samples
• Estimate the probability that statistics found in
  the sample accurately reflect the population

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Inferential Analysis Difference Questions
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Inferential Analysis Relationship Questions
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Probability

• Deductive
• Used to explain
• Extent of a relationship
• Probability of an event occurring
• Probability that an event can be accurately
  predicted
• Expressed as lower case p with values expressed
  as percents

• If probability is 0.23, then p 0.23.
• There is a 23 probability that a particular
  event will occur.

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Hypothesis Testing

• Allows researchers to answer questions like
• How much of this effect is a result of chance?
• How strongly are these variables associated with
  each other?
• Research hypothesis
• Null hypothesis
• Can actually be tested by statistical methods

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Null Hypothesis

• Claims no difference between the variables and
  that any observed difference is merely a function
  of chance
• All hypothesis testing is a process of disproof
  or rejection
• To reject the null hypothesis shows support for
  the research hypothesis and is the desired
  outcome of most studies using inferential stats

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Type I and Type II Errors

• Type I error occurs when the researcher rejects
  the null hypothesis when it is true (the results
  indicate that there is a significant difference,
  when in reality, there is not).

• Type II error occurs when the researcher regards
  the null hypothesis as true, but it is false (the
  results indicate there is no significant
  difference, when in reality, there is a
  difference).

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Type I and Type II Errors

• Decision to reject or accept null hypothesis
  based on how probable it is that observed
  differences are a result of chance alone
• Nonsignificant results (negative results)
• Could be a Type II error

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Occurrence of Type I and Type II Errors

• Data Analysis In reality the In reality the
• indicates null hypothesis null hypothesis
• is true is false
• Results
• significant null Type I error Correct decision
  
• Results not
• significant null Correct decision Type II error
• not rejected

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Level of Significance

• Probability of making a Type I error
• Alpha level
• Point at which the results of statistical
  analysis are judged to indicate a statistically
  significant difference between groups
• For most nursing studies, level of significance
  is 0.05.
• Sometimes written as a 0.05

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Tests of Statistical Significance

• Parametric
• Estimation of at least one parameter
• Measurement of interval level or above
• Involve assumptions about variables being studied

• Nonparametric
• Often used on nominal or ordinal level
  measurement
• Not based on estimation of parameters
• Less restrictive assumptions about distribution

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Tests of Differences Between Means
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Tests of Association
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t - Test

• Requires interval level measures
• Tests for significant differences between two
  samples
• Most commonly used test of differences

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Confidence Interval

• How well does your sample statistic predict the
  population parameter?
• Confidence interval gives a range of values
  within which the true value of the population
  parameter is estimated to fall
• Can be obtained from the t test provided that
  data is interval level and data is normally
  distributed

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Judging Statistical Suitability

• Factors that must be considered
• Study purpose
• Hypotheses, questions, or objectives
• Design
• Level of measurement

• Judge whether the procedure was performed
  appropriately and the results interpreted
  correctly.
• Judgments required
• Whether the data for analysis were treated as
  nominal, ordinal, or interval
• The number of groups in the study
• Whether the groups were dependent or independent

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Clinical Significance

• Findings can have statistical significance but
  not clinical significance.
• Related to practical importance of the findings
• No common agreement in nursing about how to judge
  clinical significance
• Effect size?
• Difference sufficiently important to warrant
  changing the patients care?

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Steps in Sorting Through Stats in Research
Articles

• Identify the research question
• What is the difference?
• How can I predict?
• What is the relationship?
• Identify the outcome (dependent) variable(s)

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Steps in Sorting Through Stats in Research
Articles

• Identify the level at which the outcome variable
  is measured.
• Match statistics to
• The research question
• The level at which outcome variable is measured

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