Exam 3 Flashcards
1
Q
Uses of statistics in research
A
- Provide a description of the research sample (descriptive statistics)
- Perform statistical tests of significance on research hypotheses (inferential statistics)
2
Q
Descriptive Statistics characterize
A
- shape
- central tendency (average)
- variability
3
Q
When providing a description (picture) of the data set what should you include?
A
- frequency distributions
- measures of central tendency
- measures of variability
4
Q
What do illustrations of statistics allow
A
- comparison of the sample to other samples
5
Q
Frequency Distribution
A
- table of rank ordered scores
- shows how many times each value occurred (frequency)
6
Q
Histogram
A
- bar graph
- composed of a series of columns
- each representing a score or class interval
7
Q
Normal Distribution
A
- bell-shaped
- most scores fall in middle
- fewer scores found at the extremes
- symmetrical
- mean, median, and mode represent the same value
- important assumption for parametric statistics
8
Q
When have a predictable spread of scores with normal distribution
A
- 68.2% of population within 1SD above and below the mean
- 95.44% of the population within 2SD above and below the mean
9
Q
Skewed data
A
- asymmetrical
- to right or left
- distribution of scores above and below the mean are not equivalent
- there are specific stats appropriate to non-normal distributions
10
Q
Data that is skewed positively
A
- skewed to the right (tail points to right)
- most scores cluster at low end
- few at high end
11
Q
Data that is skewed negatively
A
- skewed to the left (tail points to left)
- most scores at high end
- few at low end
12
Q
Measures of Central Tendency
A
- mode: most frequent score
- median: value in middle
- mean: average. sum divided by #
13
Q
Measures of Variability
A
- dispersion/spread of scores
- range
- percentile
- variance
- standard deviation
- coefficient of variation
14
Q
Range
A
- difference between highest and lowest values in distribution
15
Q
Percentiles
A
- percentage of a distribution that is below a specified value
16
Q
Variance
A
- measure of variability in a distribution
- equal to the square of the standard deviation
17
Q
Standard deviation
A
- descriptive statistic reflecting the variability or dispersion of scores around the mean
- square root of the variance
18
Q
Coefficient of Variation
A
- measure of relative variation as a %
- (SD/mean)*100
19
Q
Standardized scores
A
- z scores
- expresses scores in terms of standard deviation units
- z = (score - mean)/SD
- if mean is 30, SD is 2….score of 32, z-score would be +1, if score was 34, z-score would be +2, if it was 28 it would be -1
20
Q
Inferential statistics
A
- decision making process
- estimate population characteristics from data from a sample
21
Q
Draw valid conclusions from research data
A
- does the sample represent the population?
22
Q
Probability
A
- likelihood an event will occur given all possible outcomes
- p represents probability (i.e. p=0.50 that a coin flip will be heads)…probability of being within a single standard deviation of the mean is….26%
- p=0.95 corresponds to z of 1.96 (within 2 SD of mean)
23
Q
Probability used in research
A
- helps make decisions about how well sample data estimates characteristics of a population
- did differences we see between treatment groups occur by chance or are we likely to see these in the larger population?
- estimating what would happen to others based on what we observe in our sample
24
Q
Sampling Error
A
- estimating population characteristics (parameters) from sample data
- assumes that samples are random (i.e. individuals randomly drawn from the population), and that samples represent the population
- i.e. if 1,000,000 people over age of 55 in the population with mean age of 67 and SD of 5.2 years
25
Q
Sampling error of the mean for a single sample
A
- sample mean (Xbar) minus population mean (u)
- if drew many (infinite) samples would see varying degrees of sampling error
26
Q
Normal curve when plot sample means
A
- mean of all sample means will equal population mean
27
Q
Sampling distribution of means
A
- the distribution of sample means
- all plotted
28
Q
Do you use the entire population with sampling error?
A
- no
- in practice we only select a single sample and make inferences about populations from that sample
29
Q
Predictable properties of normal curve
A
- use the concept of the sampling distribution to draw inferences from sample data
30
Q
Standard error of the mean
A
- sampling distribution is a normal curve (can establish its variability)
- standard deviation of sampling distribution of means is called standard error of the mean (SEM)
- SEM = SD/root(n), where n is sample size
31
Q
Confidence Intervals
A
- can use sample mean as an estimate of population mean
- point estimate
- single sample value will not be a true estimate of population mean
32
Q
Interval estimate of mean
A
- interval which contains the population mean
- range of values which contain the population mean (confidence interval CI)
33
Q
Confidence Intervals
A
- CI is a range of scores
- boundaries (confidence limits), contains the population mean
- boundaries are based on sample mean and SEM
- expressed as 95% confidence interval
34
Q
for a 95% confidence interval, what is the z-score?
A
- z=1.96
- we are 95% confident that the population mean falls within this range of values
35
Q
Null Hypothesis
A
- no differences
- H0: uA = uB
36
Q
Alternative hypothesis
A
- difference
- H1: uA does NOT equal uB
37
Q
Research Hypothesis
A
- your statistical tests are based on the null hypothesis only: rejecting or failing to reject H0
- if p<0.05, we reject the null hypothesis and accept the alternative hypothesis
- if p>0.05, we fail to reject the null hypothesis
38
Q
Non-directional hypothesis
A
- do not specify which group will be greater in value than the other
- i.e. H1: uA does not equal uB
39
Q
Directional hypothesis
A
- specifies which group will be greater than the other
- i.e. H1: uA > uB
40
Q
Type 1 Error
A
- alpha: 0.05
- when you state there IS a statical difference but there really ISNT
- we reject the null in study but should have accepted
41
Q
Type 2 Error
A
- Beta: 0.20
- when you state that there IS NOT statistical difference but there ACTUALLY IS A DIFFERENCE
- WORSE
- if we fail to reject the null but we should have rejected it
42
Q
p-value amount
A
- less rigorous p value (i.e. 0.05) INCREASES the change of type I error and REDUCES chance of type II error
- more rigorous p value (i.e. 0.01) REDUCES the change of Type I error, INCREASES the chance of type II error
43
Q
Statistical Power
A
- power of a test is the probability that a statistical test will lead to rejection of the null hypothesis (probability of attaining statistical significance i.e. showing diff between groups)
- usually choose 80% power (for test at 80% power, probability is 80% that a test would correctly show a statistical difference if actual differences exist)
- statistical power of a test is the complement of B error, 1-B
- B is probability of a type II error (usually 20%)
44
Q
Significane criterion (a=p value)
A
- if you chose p=0.01 it is more dificult to show statistical differences btwn groups than if you choose p=0.05
- trade-off between type I and II errors: the more you reduce the probability of a type I error, the greater your chance of a type II error
- p=0.05; power=80%; beta=20% (prob. of type II error)
- p=0.01; power=75%; beta=25% (prob of type II error)
45
Q
Variance within a set of data
A
- when variability within individual groups is large in their responses or performance on a test
- then ability to detect differences between groups is reduced (i.e. power is reduced)
46
Q
Sample Size differences
A
- larger the sample (the greater the power)
- small samples are unlikely to accurately reflect population characteristics
- therefore true differences between groups are unlikely to be manifested
47
Q
Effect Size (ES)
A
- is magnitude of the observed difference between group means or magnitude of relationship between 2 variables
- if difference between groups means is MSL is 10 inches, ES is 10
- if we find a correlation of 0.67, ES is 0.67
- greater ES = greater power
48
Q
Why do power analysis?
A
- to determine sample size needed for a study
- researcher can specify a priori a level of significance and a desired power level
- based on this can estimate (using tables) how many subjects are needed to detect significance for an expected ES
49
Q
When results are not significant, may want to determine the probability that a type II error was committed
A
- this is a POST HOC analysis
- if you know the observed ES, level of significance used, and sample size, the researcher can determine degree of power achieved in the study
- if power was low (high type II error): replicate study with larger sample to increase power
50
Q
Parametric vs. Non-parametric statistics
A
- stats used to estimate population characteristics (parameters) are called parametric statistics
- use of parametric tests assumes that the samples are randomly drawn from population that are normally distributed
- to test this assumption, you test for normality within data
51
Q
Testing the normality of SPSS by viewing the histogram
A
- analyze; descriptive stats, frequencies, charts, check histograms with normal curves, choose appropriate variables
- as histogram is just a visual check, may seem to be normally distributed, however move onto the 1 sample K-S test to confirm
52
Q
Testing normality SPSS
A
- view Kolmogorov-Smirnov test (1 sample K-S) and look for its significance or non-significance (2-tailed) is the p-value
- go to analyze, non-parametric stats, legacy dialog; 1 sample KS; add in variables you want to test normality
- if asymp. sig (2 tailed) p-value is p>0.05 then data are normal
- if p<0.05 then your data is not normal (cannot use parametric stats)
53
Q
Problem for normality
A
- small samples: one or a few outliers may skew the sample i.e. may not be normally distributed due to 1 or a few outliers
- high/low z-score (i.e. greater than 3, -3) may be thrown out of a dataset as an outlier
54
Q
Other parametric assumptions
A
- variances in the samples being compared are approximately equal (homogenous)
- data must be measured on interval or ratio scale
55
Q
Violating assumptions of parametric tests requires what?
A
- non-parametric testing
56
Q
Nonparametric tests are not based on population assumptions
A
- used when NORMALITY or HOMOGENEITY of VARIANCE assumptions are violated
- used with VERY SMALL SAMPLES that are NOT NORMALLY DISTRIBUTED
- used with DATA THAT ARE NOT CONTINUOUS (i.e. nominal or ordinal scales)
57
Q
examples of comparing 2 means only
A
- males vs females
- young vs old
- fallers vs non-fallers
- strength today versus in 7 days time
- sway with eyes open vs eyes closed
58
Q
Purpose of Parametric T-Test
A
- to compare 2 means of independent samples or between 2 means obtained with repeated measures
59
Q
T-Test assumption
A
- assumption of normality
60
Q
Are t-tests independent or paired samples?
A
- T-tests can be either independent or paired samples
61
Q
Independent samples t-test
A
- unpaired t-test
- used when 2 independent groups are compared
- each group is composed of independent sets of subjects (male vs female, fallers vs non-fallers, assistive device users vs. non-users)
62
Q
Independent T-test SPSS
A
- analyze. compare means. independent samples t-test.
- select your grouping variable (i.e. gender is grouped as male or female) and define groups (1=male, 2=female)
- the group coding is determined based on how data was coded in the variable view
- test variables are what you want to compare between the two groups and you can click over as many variables as you want
- once click ok, will take you to output
63
Q
Output of Independent T-tests
A
- first look at the Levene’s test to determine if there is equal or unequal variance for age between M and F
- if Levene’s test is significant then equal variance is not assumed
- if Levene’s test is not significant, then equal variance is assumed
- depending on this value you will use the top or bottom row of the output in the independent samples test box
64
Q
Independent t-test SPSS (age in males vs females)
A
- 1st check equality of variances
- in this case, equal variance for age in M vs F is not assumed because the Levene’s test is significant (i.e. there is a significant difference in the variance for the variable age, between males and females)
65
Q
Output 2nd
A
- to determine if there was an actual difference in mean age between the two groups
- you then look at the Sig (2-tailed) value in the appropriate row
66
Q
Paired samples t-tests
A
- used when there is a definite relationship between each pair of data points
- measurements are taken from the same subject (i.e. each subjects step length for trial one versus trial two)
67
Q
Paired T-test SPSS
A
- analyze; compare means; paired samples t-test
- select the two variables you want to compare
- click ok
- output: look in the table labeled “paired samples test”…do not look at the p-value under the table labeled “paired samples correlations”. to determine if there is a diff between the variables, look at the p-value under sig (2-tailed)
