Statistics Midterm Study

Front 1

Descriptive Statistics

Back 1

Used to describe summarize, and communicate data (the results of research).

Front 2

Measures of Central Tendency (3)

Back 2

Mean = average = sum/N
Median = middle value
Mode = most common value

Front 3

Measures of Variability (3)

Back 3

Range = highest score - lowest score in data
Variance = average squared deviation from the mean
Standard Deviation = square root of variance

Front 4

We use to statistics to make an inference about a ______ on the basis of data from a ______ taken from that population.

Back 4

Population, Sample

Front 5

A ______ is based on a sample's data; a ______ is based on all individuals in the population.

Back 5

Statistic, Parameter

Front 6

What type of relationship is it when one variable increases and so does the other?

Back 6

Positive Relationship

Front 7

What type of relationship is it when one variable increases and the other decreases?

Back 7

Negative Relationship

Front 8

Hypotheses are stated in terms of _____ or _____?

Back 8

Differences or Relationships

Front 9

When are groups are being compared, you state the hypothesis in terms of _____?

Back 9

Differences

Front 10

When are variables are being compared, you state the hypothesis in terms of _____?

Back 10

Relationships

Front 11

Variables are conceptualized as _____ and ______ variables?

Back 11

Independent and Dependent

Front 12

The _____ variable is the one conceptualized as the cause (or manipulated)?

Back 12

Independent

Front 13

The _____ variable is the one conceptualized as the effect?

Back 13

Dependent

Front 14

One cannot conclude _____ from correlational research?

Back 14

Causation

Front 15

Levels of Measurement

Back 15

Nominal, Ordinal, Interval/Ratio

Front 16

Can change levels of measurement going from ____ to ____, but not from ____ to ____?

Back 16

Right to Left; Left to Right

Front 17

Examples of Nominal levels of measurement:

Back 17

Categorical variables/labels: gender, race, religion, marital status, linguistic group

Front 18

Examples of Ordinal levels of measurement:

Back 18

Rank Ordered Data: rankings, grades, social class, evaluations (i.e., high, medium, low)

Front 19

Examples of Interval/Ratio levels of measurement:

Back 19

Interval: Celsius scale, age, income, SAT scores
(Ratio: absence of the thing being measured)

Front 20

What are the two types of validity?

Back 20

Internal: rule out alternative explanations of results when high. i.e., How valid is your measurement?
External: how well the results can be generalized beyond the participants in the study. i.e., How valid is your research?

Front 21

What does a Frequency Distribution show?

Back 21

It shows how often each value (or scores) occurs.

Front 22

Areas under the Normal Distribution Curve:

Back 22

50% of scores are > 100
16% of scores are > 116
2% of scores are > 132

Front 23

Percentages under the Normal Distribution Curve at Standard Deviations:

Back 23

1 SD = 34%
2 SD = 14%
3 SD = .02%

Front 24

How do you measure/find a value for a standard score?

Back 24

Finding the z-score converts from score to standard score.

Front 25

If a straight line best fits the points, the relationship is what type?

Back 25

Linear

Front 26

If a curved line best fits the points the relationship is what type?

Back 26

curvilinear

Front 27

Correlation (r)

Back 27

Pearson product-moment correlation: assesses how much two variables have a linear relationship. Has a magnitude and sign.

Front 28

Magnitude indicates the ____ of the relationship; sign indicates the ____ of the relationship (positive or negative).

Back 28

Strength, Direction

Front 29

r-squared = ?

Back 29

Proportion of the variability in Y that is accounted for by X (or predictable from X)

Front 30

r-squared formula

Back 30

shared variability/total variability

Front 31

If X and Y are independent, r = ?

Back 31

Zero

Front 32

X is usually the _____ variable and Y is usually the _____ variable.

Back 32

Independent, Dependent

Front 33

Can not use r when?

Back 33

X and Y are not interval data.

Front 34

What type of correlation coefficient requires ordinal data and is appropriate when the relationship between X and Y are monotonic?

Back 34

Spearman rank correlation coefficient

Front 35

Monotonically increasing

Back 35

Increase in X is accompanied by an increase in Y.

Front 36

Monotonically decreasing

Back 36

Increase in X is accompanied by an decrease in Y.

Front 37

A correlation coefficient can be misleading if: (5)

Back 37

1. Range is restricted on either X or Y
(Effect: r seems smaller than it is.)
2. Extreme scores on X or Y
(Effect: r seems larger than it is.
3. Combining groups
(Effect: r can appear smaller or larger than it really is.)
4. A small # of extreme scores.
(Effect: r can appear smaller or larger than it really is.)
5. Curvilinearlity
There appears to be no relationship, but there is a curvilinear relationship.

Front 38

Statistics computed from the data are used to estimate population ______.

Back 38

Parameters

Front 39

Case I Research:

Back 39

Does a particular sample of observations (data) belong to a hypothesized population of observations?

Front 40

Example of Case I Research:

Back 40

Is the sample mean equal to a norm?

Front 41

Steps to answer a Case I Research question: (4)

Back 41

1. Make a hypothesis
2. Take a random sample and collect the data
3. Compute the sample mean
4, Make an inference about whether the people belong to the hyp pop or some other pop.

Front 42

Case II Research:

Back 42

Do two groups differ in some way (e.g., their means)?

Front 43

Steps to answer a Case II Research question: (4)

Back 43

1. Make a hypothesis
2. Make two sets of observations
3. Compute the two means
4, Make an inference: either the populations differ or they do not.

Front 44

The two groups compared in Case II Research can be:

Back 44

1. Pre-existing groups, like men and women
2. Created groups, like experiment and control

Front 45

Hypothesis Testing:
Null is the hypothesis of __ _____.
The alternative expresses _____ _____.

Back 45

No difference, Expected Results (prediction)

Front 46

Hypothesis Testing con't:
Decisions can be correct or incorrect. Possible errors are:

Back 46

Type I Error: Reject the Null Hyp when it is true. (alpha - acceptable error rate)
Type II Error: Accept the null hyp when it is false. (beta)

Front 47

The sampling distribution of means provides what?

Back 47

A model of what is likely to happen of the null hyp is true.

Front 48

Characteristics of the sampling distribution of means: (3)

Back 48

1. Even when scores are not normally distributed, the sampling distribution of means will be approx. normally distributed.
2. Its mean = population mean (sigma = mu)
3. Its SD is called the Standard Error of the Mean

Front 49

Formula for the Standard Error of the Mean (sigma sub X bar):

Back 49

Sigma sub X bar = sigma/square root of N (the SD of the sample divided by the square root of N)

Front 50

How do you make inferences about a population mean: (2 types of problems to solve)

Back 50

Compute the probability of:
1. Observing a particular value of the sample mean.
2. A more extreme value if the pop. mean is a specified value.

Front 51

Compute the probability of observing a particular value of the sample mean:

Back 51

Use formula:
Z sub x bar = Xbar - Mu/Sigma sub Xbar

Front 52

What is a Significance Level?

Back 52

Defines means that would be unlikely to occur of the null hyp were true.

Front 53

What is a Critical Value?

Back 53

The value of Z beyond which ?% of the means fall.

Front 54

Reject null hyp if z is:

Back 54

> then the critical value

Front 55

If z(critical) corresponds to p=.05, ___-tail test.
If z(critical) corresponds to p=.025, ___-tail test.

Back 55

1-tail (directional), 2-tail (nondirectional)

Front 56

If reject null hyp, conclude that the mean from the sample is _____ from the mean of in alt hyp.

Back 56

different

Front 57

Confidence Intervals
The 95% CI is that interval for which the probability is .95 that the:

Back 57

population mean falls within the interval.

Front 58

When the CI around Xbar (mean of the sample) does not include the mean in the null hyp, the null hyp would be:

Back 58

rejected

Front 59

Tests for Correlation Coefficients: what are the two kinds?

Back 59

1. Are the variables related in a population?
Null hyp: p = 0
requires 2 interval levels
only picks up linear relationships
2. Is the correlation between two variables the same in two different populations?
Null hyp: psub1 = psub2, or,
Null hyp: psub1 - psub2 = 0

Front 60

What is Power?

Back 60

The ability to know the probability that you will know whether the experiment is really working.

Front 61

What is alpha?

Back 61

Alpha is your acceptable error level (i.e., the significance level of the hyp test).

Front 62

How to read a correlation matrix:

Back 62

Look at the intersection of the two variables to find their correlation coefficient.

Front 63

Effect Size
4 characteristics of Power:

Back 63

1. Power increases as alpha increases.
2. Power is greater the larger the treatment effect or difference between means.
3. Power increases as the SD increases.
4. Power increases with sample size.

Front 64

Inferences about differences between means:
Can use this sampling distribution to test hypotheses about differences between means. How?

Back 64

Using z test
If reject null hyp, conclude that the two groups compared have different means.
Use when you are comparing 2 independent groups and you know sigma (SD of population).

Front 65

What kind of test do you use for Between-Subjects Designs?

Back 65

t-test, when sigma (pop SD) is not known.

Front 66

t-test Case I research:

Back 66

Compare observed mean to a specific value of mu (pop mean).
Conclusion: if reject null hyp, mean of the pop is not equal to the mean specified in null hyp. (not used often, usually z-test)

Front 67

t-test Case II research:

Back 67

Compare means of 2 independent groups.
Have 2 groups with the same IV
Conclusion: if reject null hyp, means of the 2 pop sampled are not equal.

Front 68

In Within Subjects Designs and Mixed Designs, the DV is what?

Back 68

Measured more than once for each participant (i.e., repeated measures)

Front 69

Within Subjects Designs and Mixed Designs are used when? (3 situations)

Back 69

1. The individual is observed under all treatment conditions.
2. The individual is observed before and after a treatment (could be pre, post, follow-up)
3. Matched individuals are assigned to treatments.

Front 70

What is advantage of Within Subjects Designs and Mixed Designs?

Back 70

It removes differences between individuals in initial level of the DV as a source of error, which makes for a more powerful hyp test. You are more likely to get a significant result when there is actually a difference in the pop.

Front 71

What is a Mixed Design test?

Back 71

1+ between-subjects variable(s) and 1 + within-subject variable(s).
Think of each variable in a design as between-subjects or within-subjects variable.

Front 72

What is a t-test for dependent samples?

Back 72

you observe a group of people twice (e.g., pre/post). You want to know if the means of the two observations (DV) are equal. Useful when the 2 sets of observations are positively correlated. Also called a "t-test for correlated observations."

Front 73

95% CI:
99% CI:

Back 73

95% CI: -1.96, +1.96
99% CI: -2.58, +2.58

Front 74

Steps to draw a normal distribution when given scores:

Back 74

Solving for SD to be able to draw normal distribution curve:
1. Find mean of scores (sum of scores/# of scores)
2. Subtract the mean from each score.
3. Square each difference.
4. Sum differences and divide by N-1.
5. Square root of result. is SD.
6. Draw the curve with mean at center.

Front 75

If an author does a good job of writing the method section of the research report, what should the reader be able to do?

Back 75

Replicate the investigation

Front 76

If a researcher compares the IQ scores of 100 boys with the IQ scores of 100 girls, what would the DV be?

Back 76

IQ/intelligence

Front 77

Symbols:
Q(3)
Q(2)
Q(1)

Back 77

Q(3): Upper quartile point - separates the top 25% of scores from the bottom 25% of scores
Q(2): Middle quartile point or median
Q(1): Lower quartile point

Front 78

Symbols:
N
M
s
Mdn
SD

Back 78

N: Sample size
M: Mean
s: Standard Deviation of the sample
Mdn: Median
SD: Standard Deviation

Front 79

Symbols:
R
Sigma
s-squared
sigma-squared
Mu

Back 79

R: Range
Sigma: Mean of the population
s-squared: Variance of the sample
sigma-squared: Variance of the pop
Mu: Mean of the pop

Front 80

Cumulative Frequency Distribution:
Ex. What would be the CF for women in age group 41-50?

Back 80

Answer: the scores of the group in question plus all the scores in the table before/above it.
Ex. age range 41-50 (345) + age range 31-40 (61) + age range < 31 (14) = (420)

Front 81

When data are summarized using a picture containing vertical columns to indicate how many scores there are for a particular thing, what is the name for this kind of of picture technique for summarizing data?

Back 81

Bar Graph

Front 82

T or F: in any set of data, the median is equal to the score value that lies halfway between the high and low scores?

Back 82

False. The mean separates the higher half from the lower half of the sample or pop. The median is used primarily for skewed distributions because it is a better indication of central tendency.

Front 83

Which one of these terms means the same as negatively skewed:
A) Skewed left
B) Skewed right

Back 83

A

Front 84

If the variance of a set of scores = 9, how large is the SD?

Back 84

3

Front 85

Indicate whether the following variables are measured on a nominal, ordinal or interval scale:
a) Score on a measure of introversion-extroversion
b) Annual income in dollars
c) Ranking of teachers on enthusiasm
d) Score on a low school test
e) Type of counseling technique

Back 85

a) Score on a measure of introversion-extroversion - Interval
b) Annual income in dollars - Interval
c) Ranking of teachers on enthusiasm - Ordinal
d) Score on a low school test - Interval
e) Type of counseling technique - Nominal

Front 86

The mode, median & mean in a normal distribution are?

Back 86

Equal

Front 87

The mode, median & mean in a positively skewed distribution are in what order?

Back 87

Mode, Median, Mean

Front 88

The mode, median & mean in a negatively skewed distribution are in what order?

Back 88

Mean, Median, Mode

Front 89

What is the variability of a distribution?

Back 89

The general term for the spread of scores in it.

Front 90

What is a Class Interval?

Back 90

A range of values of a variable, an interval used in dividing the scale of the variable for the purpose of tabulating the frequency distribution of a sample. In other words, we can define as the individual group of scores in a grouped frequency distribution.

Front 91

What is the name of the correlation procedure used when measuring two sets of raw scores?

Back 91

Pearson's r

Front 92

What is the name of the correlation procedure used when measuring two sets of ranks?

Back 92

Kendal's Tau

Front 93

In what direction does statistical inference move? Pop. to sample or sample to pop.

Back 93

From the sample to the pop.

Front 94

Symbols:
Sample mean
Sample variance
Sample value of Pearson's correlation

Back 94

Symbols:
Sample mean: M
Sample variance: s-squared
Sample value of Pearson's correlation: r

Front 95

Symbols:
Pop. mean
Pop. variance
Pop. value of Pearson's correlation

Back 95

Symbols:
Pop. mean: Mu
Pop. variance: sigma-squared
Pop. value of Pearson's correlation: Rho

Front 96

The SD of the sampling distribution is called the _______?

Back 96

Standard Error

Front 97

T or F: You can have more faith in a researcher's sample data if the standard error is large (rather than small).

Back 97

False

Front 98

The two most popular levels of confidence associated with CI's are:

Back 98

95% and 99%

Front 99

If the 95% CI was 46-56 and was changed to a 99% CI, the upper end of the CI would have been lower, higher, or equal to 56?

Back 99

Higher

Front 100

What is the Coefficient of Determination?

Back 100

It is the Pearson correlation coefficient squared and can be interpreted as the proportion of variability in Y that can be accounted for by knowing X, and vice versa. (r-squared x 100 = the percentage of the variance)

Front 101

What is another way to express the null hyp: mu1 - mu2 = 0?

Back 101

Null hyp: mu1 = mu2

Front 102

If a researcher takes a sample from a pop., computes the correlation between scores and wants to test whether the pop. correlation is different from 0, how would you write the null hyp?

Back 102

H-o: Rho not = to 0

Front 103

Which level of significance offers greatest protection against Type I errors, .05 or .01?

Back 103

.01

Front 104

If a researcher sets alpha = .05 and then finds out that p = .03, reject or not reject the null hyp?

Back 104

Answer: reject
Alpha of .05 (area above z on table) = z of 1.65
Rho (pop correlation) of .03 (area above z on table) = z of 1.88

Front 105

Statistical power equals the probability of not making a Type I or Type II error?

Back 105

Type II

Front 106

Statistical power of a study lies somewhere between ____ and ____?

Back 106

0 and 1

Front 107

When the Bonferroni adjustment is used, what gets adjusted first: null hyp, alt hyp, alpha, rho?

Back 107

Alpha

Front 108

If the researcher's sample size is too ____, the results can yield statistical significance even in the absence of any practical significance.

Back 108

Large

Front 109

If the researcher's sample size is too ____, the results can yield a nonsignificant result even though the null hyp is incorrect by a large margin.

Back 109

Small

Front 110

Null hyp: mu = 0
Alt hyp: mu not = 0
alpha = .05
What is z critical

Back 110

-1.96, 1.96

Front 111

Null hyp: mu = 0
Alt hyp: mu < 0
alpha = .05
What is z critical

Back 111

-1.65

Front 112

Mean hyp testing: Step 1 of 4
(Case I: Does a particular sample belong to a specified population?)

Back 112

1. Null hyp: mu = particular value; Alt hyp: mu < or > particular value
(1-tail test)

Front 113

Mean hyp testing: Step 2 of 4
(Case I)

Back 113

2.Specify the decision rule with a 1-tail test at alpha = .05:
Reject null hyp if z-obs > or = 1.65
Do not reject null hyp if z-obs < 1.65

Front 114

Mean hyp testing: Step 3 of 4
(Case I)

Back 114

Compute z-obs using z formula for sample means

Front 115

Mean hyp testing: Step 4 of 4 - if do not reject
(Case I)

Back 115

Make a decision and reach a conclusion.
Ex. For a 1-tailed test with alpha = .05, z-obs (1.7) < 1.96, Do not reject null hyp.
"We are not able to support the hyp that the mean ability is greater in the principal's school than in the pop. 1.7 is still within the probability that the score happened by chance

Front 116

Mean hyp testing: Step 4 of 4 - if reject
(Case I)

Back 116

Make a decision and reach a conclusion.
Ex. For a 1-tailed test with alpha = .05, z-obs (1.7) > 1.65, Reject null hyp.
"Mean mechanical ability is greater in the principal's school than in throughout the state.

Front 117

Confidence Interval equation: how to solve?

Back 117

If given X-bar (mean) and sigma sub X-bar (SD), plug into CI formula.

Front 118

Level of Significance:

Back 118

Alpha; unlikely sample test result
Reject null hyp if the probability of obatining a sample mean at or beyond a certain value id < or equal to .05 (or .01); otherwise, do not reject the null hyp.

Front 119

Mean hyp testing: difference between population means?

Back 119

Case II: Difference between pop. means; i.e., might the observed difference between the sample means of an experimental and control group be due to chance, or are they due to a systematic treatment effect?

Front 120

When to use the Standard Error of the Difference Between Means?

Back 120

When solving for the difference between means. It is the formula in the denominator when solving for the z-score of the difference between means.

Front 121

What do you need to remember to do when solving the formula for SEDBM?

Back 121

First step: solve for Xbar sub-1 and xbar sub-2 independently

Front 122

Steps for solving for the probability (> or =) of observing a DBSM's:

Back 122

1. Use z-score formula for DBM
2. Convert using table (area above z)
3. Write as P(Z-Xbar sub1 - Xbar sub2) > or = z-score) = area above z

Front 123

Step 1 of 6 for Null Hyp. Testing DBM's:

Back 123

1. Specify Ho and H1:
Ho: mu1 - mu2 = 0
H1: mu1 - mu2 not = 0

Front 124

Step 2 of 6 for Null Hyp. Testing DBM's:

Back 124

2. Specify a decision rule:
2-tail test at alpha = .01, reject Ho if:
Abs value (Z-Xbar sub1 - Xbar sub2obs) >= Z-Xbar sub1 - Xbar sub2crit = 2.58

Front 125

Decision rule Critical Values:
alpha = .01 1-tail
alpha = .01 2-tail
alpha = .05 1-tail
alpha = .05 2-tail

Back 125

Decision rule Critical Values:
alpha = .01 1-tail: 2.33
alpha = .01 2-tail: 2.58
alpha = .05 1-tail: 1.65
alpha = .05 2-tail: 1.96

Front 126

Step 3 of 6 for Null Hyp. Testing DBM's:

Back 126

3. Draw a random sample and randomly assign each subject to 1 of 2 groups. Conduct study and collect data.

Front 127

Step 4 of 6 for Null Hyp. Testing DBM's:

Back 127

4. Compute Standard Error of Diff. Bet. Means: sigma Xbar sub1 minus Xbar sub2
***Need to compute XbarsubE and XbarsubC independently first using SEofMean formula***

Front 128

Step 5 of 6 for Null Hyp. Testing DBM's:

Back 128

5. Compute Z-Xbarsub1 - Xbarsub2obs

Front 129

Step 6 of 6 for Null Hyp. Testing DBM's:

Back 129

6. Make a decision whether or not to reject Ho and draw a conclusion.