HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Topics 43-50: Experimental Design
Isabel Cabrera
EDCI-6300.61 Foundations of Research in Education
Dr. Alberto Jose Herrera
The University of Texas at Brownsville
April 8, 2012
HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Exercise on Topic 43: Descriptive and Inferential Statistics
1. Which branch of statistics (“inferential” or “descriptive”) helps researchers
to summarize data so they can be easily comprehended?
Descriptive statistics summarize the data so they can easily be comprehended.
2. According to Table 1 in this topic, how many participants had a score of 19?
Only one participant had a score of 19.
3. What is the name of the statistic that describes how many participants per
100 have a certain characteristic?
Percentages describe how many students per one hundred had each score.
4. Which branch of statistics helps researchers to draw inferences about the
effects of sampling errors on their results?
Inferential statistics help researchers draw inferences about the effects of
sampling errors on the results that are described with descriptive statistics.
5. If a researcher tests a random sample instead of all members of a population,
is it likely that the sample results will be the same as the results the
researcher would have obtained by testing the population?
The answer is, in all likelihood, no. The results would not be the same.
6. Is a margin of error a “descriptive” or an “inferential” statistics?
The margin or error is an inferential statistic.
7. Are significance tests associated with “descriptive” or “inferential” statistics?
Significant tests are associated with inferential statistics.
8. By studying populations, do researchers obtain “statistics “ or
“parameters”?
Populations yield parameters.
9. By studying samples, do researchers obtain “statistics” or “parameters”?
Samples yield statistics.
HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Exercise Topic 44: Introduction to the Null Hypothesis
1. How many explanations were there for the difference between psychologists
and engineers in the example in this topic?
There were three explanations.
2. What does the null hypothesis say about sampling error?
Sampling error refers only to random errors, not errors created by the bias.
3. Does the term sampling error refer to “random errors” or to “bias”?
It refers to random errors.
4. The null hypothesis says the true difference equals what numerical value?
The true difference between the two groups is zero.
5. Significance tests are designed to determine the probabilities regarding the
truth of what hypothesis?
Significance test determine the probability that the null hypothesis is true.
6. The expression p < .05 stands for what words?
Probability is less than 5 in 100.
7. Do researchers reject the null hypothesis when the probability of its truth is
“high” or when the probability is “low”?
They reject the null hypothesis when the probability is low.
8. What do researchers do if the probability is greater than .05?
Researchers fail to reject the null hypothesis because the probability is greater
than .05.
9. What is an alternative way of saying a researcher has rejected the null
hypothesis?
The researcher will state that the difference is statistically significant.
10. Are null hypotheses more likely to be explicitly stated in a “journal article”
or in a “dissertation”?
Null hypotheses are more likely stated in theses or dissertations.
HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Exercise on Topic 45: Scales of Measurement
1. If a researcher asks participants to name the country in which they were
born, the researcher is using which scale of measurement?
The researcher is using a nominal scale.
2. Which two scales of measurement have equal distances among the scores
they yield?
Measurements at the interval and ratio levels have equal distances among the
scores they yield.
3. If a researcher assigns a teacher to rank students according to their orallanguage skills, the researchers is using which scale of measurement?
The teacher is using an ordinal scale, ranking them from high to low.
4. Which scale of measurement has an absolute zero?
The ratio scale has an absolute zero.
5. While scale of measurement is at the lowest level?
The lowest level is the nominal scale.
6. Objective, multiple-choice achievement tests are usually assumed to measure
at what level?
They measure at interval scales, which is the third level, second to the highest.
7. If a researcher measures in such a way that he or she finds out which
participants is more honest, which is the next most honest, and so on (without
measuring to determine how much honest each on has), the researchers is
measuring with what scale of measurement?
The researcher is using the ordinal scale because he/she is ranking the participants
from the highest to the lowest in honesty.
8. The number of minutes of overtime work that employees perform is an
example of which scale of measurement?
The interval scale is used to measure the minutes of overtime an employee has.
9. Weight measured in pounds is an example of which scale of measurement?
The ratio scale is used when weight is measured in pounds.
HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Exercise on Topic 46: Descriptions of Nominal Data
1. If 600 individual in a population of 1,000 are Democrats, what is the
corresponding percentage of Democrats?
Percentage is found by the following formula: 600 divided by 1000 = .60 or 60%
2. When reporting a percentage, is it a good idea to also report the underlying
number of cases?
Yes, it is important to report the underlying number of cases.
3. Do researchers use “univariate” or “bivariate” analyses to examine
relationships between two nominal variables?
Researchers use bivariate analyses to examine two nominal variables.
4. Percentages for different groups are expressed on a common scale with what
base?
Percentages convert numbers of cases to a common scale, with a base of 100.
5. What is the base for a proportion?
Proportion has a base of 1.
6. Are “percentages” or “proportions” easier for most individuals to
comprehend?
Percentages are easier to comprehend.
7. When consumers of research encounter proportions in research reports, it is
a good idea to do what?
It is a good idea to convert them mentally to percentages.
HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Exercise on Topic 47: Introduction to the Chi-Square Test
1. When researchers study a sample are the results called the “true results” or
the “observed results”?
When researchers study a sample, the results are called observed results.
2. According to the null hypothesis, what created the difference in Table 1 in
this topic?
The null hypothesis asserts that any observed difference was created by random
sampling errors.
3. What is the name of the test of the null hypothesis used in this topic?
The name of the test is also known as the Chi-Square test.
4. According to this topic, should the typical consumer try to interpret the value
of df?
A typical consumer should not try to interpret the value of degrees of freedom(df).
5. What is the symbol for probability?
The symbol for probability is (p).
6. If a researcher found that a chi-square test of a difference yielded a p of less
than 5 in 100, on the basis of conventional wisdom, what should the
researcher conclude about the null hypothesis?
Researchers should reject the null hypothesis.
7. Does “p < .05” or “p > .05” usually lead a researcher to declare to declare a
difference statistically significant or null hypothesis?
The researcher can say that the difference is statistically significant at the .05 level
or “p>.05.”
8. If a researcher fails to reject a null hypothesis, is the difference in question
statistically significant?
No, only when the null hypothesis is .05 or less.
9. If a researcher has a statistically significant result, should the null hypothesis
remain on the list of viable explanations for an observed difference?
No, only when it is statistically insignificant.
HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Exercise on Topic 48: A Closer Look at the Chi-Square Test
1. Which type of analysis classifies participants in terms of two variables in
order examine the relationship between the two variables?
Bivariate analysis classifies participants in terms of two variables.
2. What decision should researchers make about the null hypothesis if a chisquare test leads to the conclusion that the observed difference are unlikely
to be due to random errors?
The researcher should reject the null hypothesis and declare the result to be
significant.
3. If p = .05 for a chi-square test, chances are how many in 100 that the null
hypothesis is true?
There are 5 chances in 100 that the null hypothesis is correct.
4. When a researcher uses the .01 level, what are the odds of making a Type I
Error?
The odds are 1 in 100.
5. What is the name of the error researchers make when they fail to reject the
null hypothesis when, in fact, it is an incorrect hypothesis?
Type II Error is failing to reject the null hypothesis when it is in fact an incorrect
hypothesis.
6. What is the name of the error researchers make when they reject the null
hypothesis when, in fact it is a correct hypothesis?
Type I Error is rejecting the null hypothesis when it is in fact a correct hypothesis.
7. Why is random sampling desirable even though it creates errors?
Sample at random is the desirable way to sample because it is free from bias.
HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Exercise on Topic 49: Shapes of Distributions
1. According to Figure 1, about how many participants had a score of 16?
About 55 participants had a score of 16.
2. In Figure 1, are the frequencies on the “vertical” or the “horizontal” axis?
The frequencies are on the listed on the vertical axis.
3. What is the name of the curve that is symmetrical?
The normal curve is symmetrical.
4. If a distribution has some extreme scores on the right (but not on the left), it
is said to have what type of skew?
It is said to have a positive skew because the tail is to the right.
5. If a distribution is skewed to the left, does it have a “positive” or a “negative”
skew?
If it skews to the left than it is said to have a negative skew.
6. In most populations, income has what type of skew?
Most individuals earn relatively small amounts and so it will have a positive
skew.
7. Does a distribution with a tail to the right have a “positive” or a “negative”
skew?
If it has a tail to the right it has a positive skew.
HOMEWORK TEN: PART F: UNDERSTANDING STATISTICS
Exercise on Topic 50: The Mean, Median, and Mode
1. Which average is defined as the most frequently occurring score?
The mode is the most frequently occurring score.
2. Which average is defined as the balance point in a distribution?
The mean is the balance point in a distribution. You add up all the scores and divide
by the number of scores.
3. Which average is defined as the middle score?
The median is known as the middle score. Put scores in order from low to high
and then count to the middle. Median is also known as the middle score.
4. What is the formal definition of the mean?
Mean is the value around which the deviations sum to zero.
5. How is the mean calculated?
The mean is calculated when you add up all of the scores and divide it by the
number of scores.
6. Should the mean be used for highly skewed distributions?
No, the mean is used most frequently used for averages.
7. Should the median be used for highly skewed distributions?
Yes, the median is used for highly skewed distributions.
8. Which one of the three averages is very seldom used in formal reports of
research?
The mode is sometimes used in informal reporting but is very seldom reported in
formal reports of research.
9. What is a synonym for the term averages?
A synonym for the term averages is measures of central tendency.