Statistical Analysis and Results Section Flashcards
The results section should contain…
Narrative description of statistical outcomes
Tables and figures that summarize findings
Statements of support of the hypotheses or rejection of the hypotheses
What are results?
Measurement of outcomes using numerical data and statistical data
Concerned with relationship between variables
Variables are the building blocks of the research question
What should be reported in the results section?
The results should be reported in relation to the research problem
Data distributions
Measurement data
Interval or ratio measurement data may be described in terms of…
Central tendency
Variability
Skewness
Kurtosis
What is central tendency?
The average score for a group
3 measures of central tendency:
- Mean
- Median
- Mode
What is variability?
How much the scores vary from the average
3 measures of variability
- Range
- Variance
- Standard deviation
What is skewness?
the lack of symmetry of the distribution of scores
What is kurtosis?
the general shape of the distribution of scores
What is normal distribution?
The normal distribution of the data happens when the middle scores occur most often and the lower and higher scores do not occur often.
If there is a normal distribution of data, then parametric statistics can be used
What happens if the data is not normally distributed?
If the data is not normally distributed and not based on a normal curve model, then nonparametric statistical procedures are used
What are parametric statistical procedures?
Normal distribution of the data
Interval or ratio level of measurement
If 2 or more data distributions are analyzed, their variances should be similar
Large sample size
What are nonparametric statistics?
Nonparametric statistics are used when one or more of the parametric statistical procedures are not met
Statistical significance testing involves…
involves testing the null hypothesis in the context of the data
What happens when the level of statistical significance is small?
When the level of significance is small, then the researcher decides to reject the null hypothesis and therefore decides that the hypothesis is probably true
Statistical significance indicates…
Statistical significance indicates that the results of an analysis are unlikely to be the result of chance at a specified probability level; rejection of the null hypothesis
What is probability?
Probability is the likelihood that one event will occur, given all the possible outcomes. We always use a lowercase italicized p to signify probability.
What is a p value?
The p value just means the probability of the findings.
A level of significance of .05 or less (p < .05) indicates that the difference between X and Y (from our example) could have resulted from chance only 5 times in 100
This number is usually small enough to reject the null hypothesis
p < .05 means the null hypothesis is rejected
p > .05 mean the null hypothesis is not rejected
What is a data analysis?
Data analysis can be correlational or inferential
Correlational statistics evaluate relationships among data
Data analysis relationships are often described using correlation coefficients such as:
Pearson product-moment coefficient of correlation (r)
Spearman’s rank-order correlation coefficient
Describe data analysis relationships.
A perfect positive relationship between two variables is indicated by 1.0
A perfect negative relationship is indicated by -1.0
The absence of a relationship is indicated by zero
A small number indicates a weak relationship between two variables
A large number indicates a strong relationship between two variable
The square of a correlation coefficient is used to assess…
its practical meaning
How do you present the results of correlational statistics?
Regression analysis
Bivariate analysis
Multivariate analysis
Contingency table
What is regression analysis?
Degree to which the values of one variable can be predicted by another one
What is bivariate analysis?
analyzing relationship between two variables
What is multivariate analysis?
analyzing relationship between more than two variables
What is a contingency table?
displays frequencies for combinations of two categorical variables
What is a chi square?
Examines the level of significance of any relationship among the nominal variables
Chi-square is a nonparametric test applied to nominal data, comparing observed frequencies within categories to frequencies expected by chance
Chi-square does not indicate the strength of the relationship
Inferential statistics evaluate…
differences among data, either between-subjects or within-subjects
Inferential statistics is concerned with…
testing hypotheses and using sample data to make generalizations concerning populations
What are parametric procedures of inferential statistics?
z-ratio: when samples are 30 or more
t-test: when samples are less than 30
What is an independent t-test?
used to compare two different groups
What is a dependent t-test?
used for within group comparisons
What are nonparametric procedures for inferential statistics?
Mann-Whitney U Test
Wilcoxon signed rank test
What are nonparametric methods?
Kruskal-Wallis one-way ANOVA- between subjects comparison (ordinal data)
Cochran Q test – from related samples (nominal data)
Friedman two-way ANOVA – within-subjects comparison (ordinal data)
Chi-square – from independent samples (nominal data)
What are parametric methods?
ANOVA- analysis of variance – simultaneous comparison of several means
One-way ANOVA – only one independent variable
Two-way ANOVA – two independent variables
When there is more than one dependent variable and one or more independent variables the analysis procedures used include:
MANOVA- multivariate analysis of variance
ANCOVA – analysis of covariance
Multiple t-test (Bonferroni correction)
Rather than reflecting whether the null hypothesis is false, the effect size estimates…
the degree to which it is false
What is used to compare the means of two or more groups?
Cohen’s d - effect size estimator
What is effect size?
Effect size is a quantitative measure of the difference between two groups
Estimates from individual studies are combined to reflect the overall size of the effect of the independent variable. The larger the difference, the greater the “effect” of the intervention
