Chapter 15 Flashcards
What are statistics?
a summary value that describes the sample.
mean of a sample and mean of a population
sample: x bar
population: mu
two general categories of statistical techniques:
descriptive and inferential statistics
Descriptive statistics are…
techniques that help describe a set of data.
The goal of descriptive statistics is to organize, summarize, and simplify data.
Inferential statistics are…
Inferential statistics help researchers determine when it is appropriate to generalize from a sample to a population.
-help determine if group/condition differences are from chance
organizing a set of scores into a graph or a table and calculating a single value, such as an average score, that describes the entire set is an example of what category of statistical techniques?
descriptive statistics
Summary values computed for a sample are called ___. The corresponding summary values for a population are called ____.
Summary values computed for a sample are called STATISTICS. The corresponding summary values for a population are called PARAMETERS.
What do frequency distributions demonstrate?
they demonstrate the number of instances a variable takes each possible value
What does each column in a frequency distribution table display?
The first column presents the SCALE OF MEASUREMENT, or simply lists the SET OF CATEGORIES INTO WHICH INDIVIDUALS HAVE BEEN ASSIGNED.
The second column lists the FREQUENCY, or the NUMBER OF INDIVIDUALS, located in each category.
In a frequency distribution graph, the ___ ___ _____ is along the horizontal axis and the _____ is on the vertical axis
In a frequency distribution graph, the SCALE OF MEASUREMENT is along the horizontal axis and the FREQUENCIES is on the vertical axis
2 options of graphing the frequency distribution
- HISTOGRAM: bar graph in which height of bars= frequency of occurrence of particular score. Adjacent bars touch eachother.
- POLYGON: scatterplot in which points are joined by straight lines. Height of dot above each score = frequency
When the categories on the scale of measurement are not numerical values ( NOMINAL or ORDINAL scales), the frequency distribution is presented as a ___ ___
bar graph
bar graph vs histogram
bar graph has spaces between bars.
Define “central tendency”
Statistical measure that identifies a single score that defines the center of distribution.
Its goal is to identify the value that is most typical or most representative of the entire group (single score that represents entire set)
What values measures central tendency?
mean, median, mode
What is the mean?
- measure of central tendency obtained by adding the individual scores, then dividing the sum by the number of scores.
- arithmetic average
What is the median?
-measure of central tendency which identifies the score that divides the distribution in half.
What is the mode?
measure of central tendency by identifying the most frequently occurring score in the distribution
The standard deviation uses the ___ of the distribution as a reference point and describes the _____ of the scores by measuring the distance between each ___ and the ____
The standard deviation uses the MEAN of the distribution as a reference point and describes the VARIABILITY of the scores by measuring the distance between each SCORE and the MEAN
When scores are clustered close to the mean, the standard deviation is ____
small
As a general rule, what percentage of the scores in a distribution are within a distance of 1 standard deviation of the mean? How many are 2 SDs from the mean? 3?
68% usually 1 SD from the mean, 95% usually 2 SDs from the mean, 99.7% is 3 SDs from the mean
The average squared distance from the mean is called ____
variance
How do you find the median in a distribution?
order scores from smallest to largest and find the middle value
In a negatively skewed distribution, where is the “tail” and “peak” of the graph?
the tail is pulled towards the left (negative). More scores are concentrated on the right (positive peak). Visa versa for positive skew
2 measures of error
- VARIANCE: how large is the spread of the data?
2. STANDARD DEVIATION: What is the average difference from the mean?
square root of variance is the
standard deviation
a. What kind of hypothesis states that “nothing is there?”
b. Which hypothesis aligns with prediction?
a. Null hypothesis
b. Alternate hypothesis
In the Capilano Bridge Experiment, why is a hypothesis test needed?
A hypothesis test is needed ti determine how likely it is for the results (ie. more men giving their numbers to research assistant on suspense bridge vs regular bridge) to be due to CHANCE. Helps to ensure INTERNAL VALIDITY
What would the null hypothesis (Ho) be in the capilano bridge experiment?
Ho: u1=u2
in other words: the average number of calls in group one is equal to the average number of calls in group 2.
SAMPLE vs SAMPLING distribution
Sample distribution: all scores from the sample. Demonstrates frequency of occurrence of each variable.
Sampling distribution: THEORETICAL. All possible values of a statistic for an infinite number of samples of a given size.
Name the Ho and H1 for the following:
Are artists more likely to be left-handed than people found in the general population?
Ho: artists are equally likely to be left or right handed.
H1: artists are more likely to be left-handed
Name the Ho and H1 for the following: Does our class have a higher than average IQ?
Ho: the class IQ = the IQ of the population H1: the class has a higher than average IQ
What is sampling error?
the naturally occurring difference between a sample statistic and the corresponding population parameter.
This is because a sample does not provide a perfectly accurate picture of its population.
Recall: internal validity is threatened whenever…
there is an alternative explanation for results obtained in the research study
The statement which is the exact opposite of the research hypothesis is called the ___ ____
null hypothesis. This states that there is no effect, no change, or no relationship.
define “standard error”
measure of the average, or standard, distance between the sample statistic and the corresponding population parameter
A test statistic is a mathematical technique for comparing the ____ ____ with the ___ ____, using the ___ ____ as a baseline
A test statistic is a mathematical technique for comparing the SAMPLE STATISTIC with the NULL HYPOTHESIS, using the STANDARD ERROR as a baseline
Types of test statistics
For interval/ratio data: -t tests -ANOVAs (F tests) For nominal/ordinal data: -Chi-squared test
the alpha level is the level of ____
significance
What does a test statistic with a value grater than 1 usually indicate?
that the obtained result is GREATER THAN would be expected from chance. An alpha level provides the criterion for the significance of this difference
What is the alpha level?
- level of significance
- the maximum probability that the result was obtained simply by chance
What does it mean if a hypothesis test has an alpha level of 0.01?
This means that the test demands that there is less than a 1% probability that the results are caused only by chance
The probability of flipping a coin and obtaining more than 60 heads in 100 tosses is 0.0228. If the null hypothesis states that you should get 50 heads in a sample of 100 tosses, what decision could be made about the null hypothesis if over 60 heads were obtained (alpha level = 0.05)?
The null hypothesis can be REJECTED and conclude that coin is not perfectly balanced.
This is because the PROBABILITY IS LESS THAN THE ALPHA LEVEL.
A smaller level of significance means that you have ___ confidence in the result
more
In literature, significance levels are reported as ___ values
p values
What does p < 0.05 mean?
that the probability of the result being caused simply by chance is less than 0.05
What does it mean when the researcher rejects the null hypothesis?
This means that they reject chance as a plausible explanation for the research results
What does it mean if a researcher writes p > 0.05?
That the researcher would accept chance as a plausible explanation for the research results.
This is a way of reporting that the RESULT IS NOT SIGNIFICANT.
A significant result is always accompanied by an alpha level that defines the ___ ____ that the result is caused only by chance
maximum probability
What kind of a process is hypothesis testing?
Inferential. ie. using limited info to reach a general conclusion
what two types of errors can be made in hypothesis testing?
TYPE I ERRORS:
-evidence for significant result is found when, in fact, THERE IS NO EFFECT.
-Null is TRUE, but was rejected
TYPE II ERRORS:
-evidence shows no evidence for significant result when, in fact, A REAL EFFECT DOES EXIST WITHIN POPULATION.
-fail to reject the null
Consequence of a type I error is a ___ ___
false report
The ___ ___ or the __ ___ identifies the probability of a Type I error
The ALPHA LEVEL or the P VALUE identifies the probability of a Type I error.
In other words, the chance that a type I error will occur is equal to alpha
Consequence of a type II error?
- researcher fails to detect a real effect.
- study may be abandoned
The chance that a type II error will occur is equal to:
p = 1 - B
two important factors in a hypothesis test that involves numerical scores that have been used to compute means or correlations:
- the number of scores in the sample
2. the variability of the scores (sample variance)
Which is the worst form of error in research? type i or ii?
type I is worse.
Better to have Type II than Type I errors in research
In general, a mean difference or a correlation found in a ___ sample is more likely to be significant than the result found with a ___ sample
In general, a mean difference or a correlation found in a LARGE sample is more likely to be significant than the result found with a SMALL sample
Which means that a result is more likely significant? a higher or lower variability?
lower variability = more likely significant
Why does higher variance mean that the scores are more unreliable?
Because large variance means that the scores are widely scattered with large differences between individual scores and the overall mean. In a sample with high variance, it is easy to select an individual whose scores are extreme and NOT REPRESENTATIVE.
-With high variance, adding one or more people to a sample can drastically chance the value of the mean
extreme scores are common when the variance is ___
high
What do test statistics measure?
the proportion of EFFECT to ERROR
How is Cohen’s d computed?
d = sample mean difference / sample standard deviation
A value of d = 2.00 means what? (Cohen’s d)
d = 2.00 indicates that the mean difference is twice as big as the standard deviation.
Cohen’s d corresponds to the amount of separation between the two distributions in terms of standard deviations.
The appropriate test for comparing two means from two separate samples is the:
independent-measures t test
When the percentage of variance is measured for t tests or for correlations, it is typically called ____
r^2
t tests compare two ___ ____
sample means
ANOVA tests compare ___ ___ ____
multiple sample means
What is a “confidence interval?”
a technique for estimating the magnitude of an unknown POPULATION value, such as mean difference or a correlation.
The value of the parameter should be located in an interval, or in a range of values, centered around the sample statistic.
-based on sample statistics
-RANGE WITHIN WHICH POPULATION SHOULD BE
Confidence intervals provide a good indication of what?
a good indication of how large a treatment effect actually is.
In general, larger samples lead to ____ standard errors, which ____ the likelihood of finding a significant result and ____ the width of confidence intervals
In general, larger samples lead to SMALLER standard errors, which INCREASE the likelihood of finding a significant result and DECREASE the width of confidence intervals
height in inches is an example of what scale?
ratio/interval
classifying cups as small, medium, and large are an example of what scale?
ordinal scale
naming academic majors is an example of what scale?
nominal scale
What is defined as the number of scores in a sample that are free to vary for a given statistic
degrees of freedom
There are four balloons: blue, red, yellow, and green. How many degrees of freedom?
3
what is the tcrit?
the value that test stat must be larger than
is tcrit smaller in nondirectional or direction t test
tcrit is smaller in directional test, because the alpha level is split between both tails. (e.g., a=5 in directional test, but 2.5 on each side in nondirectional test)
Why do we need hypothesis tests?
-to determine whether something happened by chance
The level of chance we are willing to accept in a hypothesis test is the ___ value
alpha
How would a researcher officially write whether or not their test is significant using the following example:
Does the faculty of parents influence the faculty choice of students?
N = 200
56 students doing their B.A. had parents who did B.A.
44 students doing their B.A. had parents who did B.Sc.
36 students doing their B.Sc. had parents who did B.A.
64 students doing their B.Sc. had parents who did B.Sc.
X^2 = 8.05
-First calculate df: df = (#rows - 1)(#columns - 1) df = (2-1)(2-1) = 1 -Then, look at table to find tcrit: at alpha level of 0.005, tcrit is 7.88 -Since x^2 is greater than tcrit (8.05>7.88), results are significant and null hypothesis can be rejected.
x^2 (1, N = 200) = 8.05, p < 0.005. Students were more likely to have selected the same faculty as their parents.
After solving a word scramble, researchers asked participants to walk down the hallway to a different room and they measured how quickly they walked down the hall.
Results: people who were primed with “old people” words walked slowly
Problem: other researchers tried to replicate the study and did not find the same effect.
What type of error was committed?
Type I error
r-squared measures the proportion of ___ in ___ accounted for by ___
r-squared measures the proportion of VARIANCE in DV accounted for by IV
How can the chance of committing type I or II errors be reduced?
by having more than one way to test error
4 elements of an experiment:
- MANIPULATION: changing the IV
- CONTROL: ensuring the difference is due to the IV
- MEASUREMENT: measuring the DV
- COMPARISON: determining the difference
