Ch. 11 Exam 2 Flashcards
Theory addressing statistical analysis from the perspective of the extent of a relationship or the probability of accurately predicting an event. If probability is 0.23, then p = 0.23. There is a 23% probability that a particular event will occur. Probability is usually expected to be p < 0.05 or p < 0.01.
probability theory
Theory based on assumptions associated with the theoretical normal curve. Used in testing for differences between groups, with the expectation that all the groups are members of the same population. The expectation is expressed as a null hypothesis, and the level of significance (alpha) is often set at 0.05 before data collection.
decision theory
A theoretical frequency distribution of all possible values in a population. In a normal distribution curve, the mode, median, and mean are =. Levels of significance and probability are based on the logic of the normal curve. In research, the probability that any data score will be within a certain range of a mean values is calculated based on the theory of the normal curve.
normal curve
2 tailed test of significance = the analysis of nondirectional hypothesis. One tailed test of significance = the analysis of directional hypothesis. One tailed statistics test are uniformly more powerful than 2 tailed test.
tailedness
the risk of a type II error can be determined using power analysis (1-B).
power
describes or summarize the sample and variables.
descriptive statistics
ungrouped frequency distributions. Grouped frequency distributions. % distributions.
frequency
Grouped Frequency Distributions. Example: data are pre-grouped into categories.
Ages 20 - 39: 14
Ages 40 - 59: 43
Ages 60 - 79: 26
Ages 80 - 100: 4
% distribution. Example:
Salaries: 41.7%
Maintenance: 8.3%
Equipment: 16.7%
Fixed cost: 8.3%
Supplies: 25%
Ungrouped Frequency distributions: Example: data are presented in raw, counted form.
- I
- IIIII
- III
- I
- II
Measures of Central Tendency
Mean
Median
Mode
is the numerical value or score that occurs with greatest frequency.
mode
is the midpoint or the score at the exact center of the ungrouped frequency distribution—the 50th percentile
median
is the sum of the scores divided by the number of scores being summed.
mean
Is obtained by subtracting lowest score from highest score. Uses only the two extreme scores. Very crude measure and sensitive to outliers
ranges
Indicates the spread or dispersion of the scores
Variance
is the square root of the variance. Mean = average value. SD = average difference score.
standard deviation
Raw scores that cannot be compared and are transformed into standardized scores. Common standardized score is a Z-score. Provides a way to compare scores in a similar process. Ex: children’s BMI
standardized scores
Have 2 scales: horizontal axis (X) and vertical axis (Y). Illustrate a relationship between 2 variables.
scatterplots
Frequency:
group freq distributions
% distribution
ungrouped freq distributions
infer or address objectives, ?’s, and hypotheses. Assist in: identifying relationships, examining predictions, and determining group differences in studies.
inferential statistics
inferential statistics:
Examining differences
Predicting outcomes
Examining relations
test for significant differences between 2 samples. Most commonly used test of differences. Example: t = 4.169 (p <0.05)
t-test
test for differences between variance. More flexible than other analyses in that it can examine Data from 3 or more. If there are more than 2 groups under study, it is not possible to determine where the significant differences are. Post hoc test are used to determine the location of differences.
ANOVA
used with nominal or ordinal data. Test for differences between expected frequencies if groups are alike and frequencies if groups are alike and frequencies actually observed in the data. Indicate that there is a significant difference between some of the cells in the table. The difference may be between only 2 of the cells, or there may be differences among all of the cells. Chi-square results will not tell you which cells are different. Ex: x2 = 4.98, df = 2, p = 0.05.
chi-squared test
used when 1 wishes to predict the value of the 1 variable based on the value of 1 or more other variables.
predicting outcomes (regression)
Examining relationships
Test for the presence of a relationship between 2 variables.
Results: nature of the relation (pos or neg), magnitude of the relation (-1 or +1) and testing the significance or a correlation coefficient.
Does not identify direction of a relationship ( 1 variable does not cause the other). They are symmetrical. Test for the presence of a relation between 2 variables.
Pearson product-moment correlation
Results:
R2 = 0.56 (p = 0.03)
R2 = -0.13 (p = 0.2)
R2 = 0.65 (p< 0,002) —> SIGNIFICANT
Using statistics to describe:
Descriptive statistics are also referred to as summary statistics. In any study which the data are numerical, data analysis begins with descriptive statistics. In simple descriptive studies, analysis may be limited to descriptive statistics.
