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
Sampling error of the mean for a single sample
- sample mean (Xbar) minus population mean (u)
| - if drew many (infinite) samples would see varying degrees of sampling error
26
Normal curve when plot sample means
- mean of all sample means will equal population mean
27
Sampling distribution of means
- the distribution of sample means
| - all plotted
28
Do you use the entire population with sampling error?
- no
| - in practice we only select a single sample and make inferences about populations from that sample
29
Predictable properties of normal curve
- use the concept of the sampling distribution to draw inferences from sample data
30
Standard error of the mean
- 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
Confidence Intervals
- 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
Interval estimate of mean
- interval which contains the population mean
| - range of values which contain the population mean (confidence interval CI)
33
Confidence Intervals
- 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
for a 95% confidence interval, what is the z-score?
- z=1.96
| - we are 95% confident that the population mean falls within this range of values
35
Null Hypothesis
- no differences
| - H0: uA = uB
36
Alternative hypothesis
- difference
| - H1: uA does NOT equal uB
37
Research Hypothesis
- 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
Non-directional hypothesis
- do not specify which group will be greater in value than the other
- i.e. H1: uA does not equal uB
39
Directional hypothesis
- specifies which group will be greater than the other
| - i.e. H1: uA > uB
40
Type 1 Error
- 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
Type 2 Error
- 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
p-value amount
- 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
Statistical Power
- 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
Significane criterion (a=p value)
- 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
Variance within a set of data
- 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
Sample Size differences
- 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
Effect Size (ES)
- 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
Why do power analysis?
- 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
When results are not significant, may want to determine the probability that a type II error was committed
- 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
Parametric vs. Non-parametric statistics
- 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
Testing the normality of SPSS by viewing the histogram
- 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
Testing normality SPSS
- 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
Problem for normality
- 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
Other parametric assumptions
- variances in the samples being compared are approximately equal (homogenous)
- data must be measured on interval or ratio scale
55
Violating assumptions of parametric tests requires what?
- non-parametric testing
56
Nonparametric tests are not based on population assumptions
- 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
examples of comparing 2 means only
- 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
Purpose of Parametric T-Test
- to compare 2 means of independent samples or between 2 means obtained with repeated measures
59
T-Test assumption
- assumption of normality
60
Are t-tests independent or paired samples?
- T-tests can be either independent or paired samples
61
Independent samples t-test
- 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
Independent T-test SPSS
- 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
Output of Independent T-tests
- 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
Independent t-test SPSS (age in males vs females)
- 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
Output 2nd
- 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
Paired samples t-tests
- 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
Paired T-test SPSS
- 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)
Critical Inquiry
flashcards
Decks in class (3)
# Cards
