USING STATISTICAL TESTS TO MAKE INFERENCES ABOUT POPULATIONS

USING STATISTICAL TESTS TO MAKE INFERENCES ABOUT POPULATIONS

1. Parametric tests

   • tests are used to make inferences about the population when specific conditions have been met
     • 1. use of probability sampling, 2. normal distribution of data, 3. measurement of variables at the interval or ratio level, and 4. reduction of error.
   • high levels of confidence about the conclusions made.

2. Nonparametric tests.

   • are used for interval data that do not have a normal distribution or for data that are nominal or ordinal in nature.

3. degrees of freedom

   • are used to correct for possible underestimation of population parameters when performing mathematical equations

4. sampling distribution

   • an infinite number of samples can be drawn from a population.

5. Testing for Differences Between Groups

   • Pilot studies
     • Imvolve one group
       • Before analyzing data, researchers need to consider whether the groups are dependent or independent to select the correct tests to perform
   • classic experiments and quasi-experiments
     • can include two or more groups
   • The Chi-Square Statistic
     • Calculated when analyzing nominal and ordinal data, it is a nonparametric test.
       • it is very useful for finding differences between the groups on demographic variables at the start of the study
         • debe haber al menos cinco o más frecuencias observadas
   • The t Statistic
     • is used to determine whether there is a statistically significant difference between two groups
       • correlated test
         • Used: there are only two measurements taken on the same person (one group) or when the groups are related
       • independent test
         • Used: when data values vary independently from one another
           • experimental and quasi-experimental designs
             • t test is used to determine whether the means of two groups are statistically different
   • Analysis of Variance (ANOVA)
     • Used: the level of measurement is interval or ratio and there are more than two groups or the variable of interest is measured more than two times

6. Testing for Relationships Among Variables

   • Correlation and Pearson’s r
     • evaluated in terms of magnitude, direction, and sometimes significance.
       • Direction
         • refers to the way the two variables covary
       • Magnitude
         • refers to the strength of the relationship found to exist between two variables
   • Multiple Regression
     • when researchers want to study the relationship of many independent variables on one dependent variable
       • Multiple linearregression is used
         • when the dependent variable is measured at the interval or ratio level
       • multiple logistic regression is used
         • When the dependent variable is dichotomous,

7. EFFECT SIZE

   • is the magnitude (or size) of an effect
   • It could also be the strength of the relation-ship between two variables
   • It can be measured ina number of ways
     • Mean difference (MD)
       • o examine the size of the differencein means between two groups in a study,
     • Standardized mean difference (SMD)
       • number that shows how far apart the meansare in standard deviation units
   • wers thequestion “How well does it work?”

8. RISK STATISTICS

   • risk ratio or relative risk (RR),
     • compares the probability of an out-come in two groups
       • One group is exposed to something (usually a risk factor), and theother group is not.
     • expresses how much more (or less) likely it is for theexposed person to develop an outcome (relative to an unexposed person)
       • If the RR is greater than 1, it suggests an increased risk of that outcome in the exposed group
       • If the RR is less than 1, it suggests a reduced risk in the exposed group
   • odds ratio (OR)
     • the odds of an outcome or event such as a disease
       • An OR of 1.0 means that the odds of an event in the groups are the same
   • hazard ratio (HR)
     • is a ratio of the hazard rate of one group to the hazard rate in another group
     • answer the question, “Does a specific risk factor/treatment cause the event to occur earlier or later than without the risk factor/treatment?”
     • HR is 1, the event rate or risk for each group is the same
     • less than 1, then fewer participants in the treatment/exposed group are having an event proportionally to the comparison group

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