Research Class 9 Part 2

Which of the following are categories of statistical analysis?

descriptive and inferential

Which of the following refer to the purpose of descriptive analysis?

1. Organize the data and its distribution

2. Synthesize the data and its distribution

3. Describe the characteristics of the data and its distribution

Which of the following are descriptive statistical categories?

1. Univariate

2. Bivariate

for each of the questions, answer with which level of measure you can use for the following

frequency counts

Nominal, categorical, interval, ratio

Measures of central tendency

interval, ratio

Measures of variability

interval, ratio

bar charts

Nominal, categorical

Histograms

interval, ratio

pivot table

nominal, categorical

correlation

interval, ratio

Inferential statistics advance data analysis, beyond describing each variable or variables in association with each other, to ___ relationships between or among variables with the goal to generalize the findings from the sample population back to the larger target population.

predict

Inferential statistics involve the calculation of probability to make reasonable ___ of the population parameters from the sample.

estimates

In inferential statistics, the objective of ___ is to determine the probability of getting the calculated study findings from the sample data out of 100% all probabilities.

hypothesis testing

When an outcome (DV) from the data occurs with ___, then that is considered to be common or frequent and therefore likely due to chance alone, and NOT likely due to the IV

high probability

In other words, it happened so frequently that by chance alone it would occur on its own, and the IV had ___ with the outcome (DV).

nothing to do

When an outcome (DV) from the data occurs with ___, then that is rare, and is considered not likely due to chance alone, but likely due to the IV.

low probability

This principle of probability is essential to test a ___ statistically.

hypothesis

___ is an expression of the chance that a certain outcome will occur.

Probability

The probability of the occurrence of one outcome can be expressed as a ___ of all possible outcomes.

proportion

Proportions, and therefore probabilities, can be written as ___, decimals, or percentages.

fractions

Simple random sampling or independent random sampling satisfies two requirements

1. Each element has an equal chance of being selected.

2. There is a constant probability of being selected.

Simple random sampling does not guarantee the sample is ___ of population

representative

Simple random sampling does ensure that any difference between the sample’s attributes and the population’s attributes happened by ___ alone and not by researcher or participant bias.

chance

Both the research samples and the target populations can be presented as ___

frequency distributions

Frequency polygons (smoothed to curved) are the models of those distributions. The area ___ the curve represents 100% of all cases.

under

___ of the area under the curve represent the proportions (out of 100%) of all cases under the curve.

sections

Those proportions provide us with ___

probabilities

The normal distribution is a theoretically perfect ___ and as such, the exact probabilities of sections or proportions of the area under the curve have been calculated.

bell-shaped curve

The normal distribution of ___ proportions under the curve for sections are determined by the number of standard deviations from the mean.

z-score

What is the percent probability of scores within 1 SD above and below the mean?

68.26%.

What is the percent probability of scores within 2 SDs above and below the mean?

95.44%.

What scores are considered extreme scores in descriptive statistics for continuous levels of measure?

Scores that are +/– s SDs from the mean.

The X-axis of the normal curve is measured in ___ (where z = +1 is one standard deviation from the mean).

z-score values

All z-score values are associated with ___ or sections of area under the curve. These proportions are presented as probabilities in the unit normal table.

proportions

We can use the ___ to find probabilities between two z-scores. We commonly want to find probabilities between two X-scores.

unit normal table

Raw X scores can be ___ to z-scores so that we can find the probabilities of any X-score occurring.

converted

We can rarely measure all members of a population for anything. Therefore, we take a ___ of the population.

sample

The sample is rarely normally distributed on any variable because samples cannot be ___ representations of a population.

perfect

___ is the discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.

Sampling error

If we take numerous samples from the same population, the distribution of scores on a curve will all be ___

different

Imagine taking numerous samples from a known population. Each sample would have its own ___, which would be different from the population mean, due to chance error alone.

mean

Imagine making a new distribution from all those sample means.

The ___ is the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.

distribution of sample means

A ___ is a distribution of statistics obtained by selecting all possible samples of a specific size from a population. 

sampling distribution

A sampling distribution is the ___ of the sample means.

distribution

The distribution of sample means will approach the shape of a ___ curve.

normal

what is the central limit theorem

Any shape of a population distribution (even flat shapes) can generate samples with means that (in their own distribution) form a normal distribution

This is so ___ to hypothesis testing that a mathematical theory was established to describe it for all populations.

fundamental

The theory proposes that for any population, ___ of size (N) will result in a distribution of sample means that approaches a normal distribution (which provides a link to the probabilities needed for inference)!

repeated samples

Because the distribution of the sample means takes on the shape of the normal curve, we now have a connection between any ___ sample and the normal distribution.

random

From the normal distribution, we can ___ the probabilities for any specific sample.

determine

On the normal curve below, with a universal mean of 500 and 1 SD = 20, how many SDs away from the mean is the score 560?

3

The central limit theorem describes ___ of the distribution of the sample.

characteristics

The distribution of the sample means characteristics are:

1. The shape of the curve approaches a ___ distribution.

2. The “mean of the means” (grand mean) is equal to the population mean from which they were drawn.

3. The variation has the standard deviation of the distribution of the sample means which is called the standard error.

4. The standard error measures exactly how much difference should be expected, on average, between a sample mean and the population mean. 

normal

Standard error is directly related to the population standard deviation and ___ related to sample size.

inversely

N is in the denominator, therefore as sample size increases, standard error ___.

decreases

This is because if the population standard deviation is ___ (in the numerator) standard error will be large. 

large

recall: Inferential statistics make ___ about the target population from the sample population.

predictions

Recall: In quantitative research, we test a prediction about the sample population to make a ___ from the sample population back to the target population with any random sample and the normal distribution.

generalization

From the ___ we can determine the probabilities of scores for any specific sample.

normal distribution

A ___ makes an inference about the target population based upon the test on a sample population, hence the term “inferential statistics.”

hypothesis

A ___ is a statistical method that uses sample data to evaluate a hypothesis about a population parameter.

hypothesis test

A researcher begins with a ___ population (as they exist before treatment).

known

The ___ is to determine what happens (DV) to the population after treatment (IV) is administered it is the change in the mean that is the research question

goal

STARTING FROM TEXT

The most basic way to illustrate data is through the creation of a ___

frequency distribution

A frequency distribution is a method of ___, and representing, how often certain scores occur.

tallying

In the creation of a frequency distribution, scores are usually grouped into ___, or ranges of numbers.

class intervals

As you can see from the above table, a class interval is a ___ of numbers, and the first step in the creation of a frequency distribution is to define how large each interval will be.

range

A ___ is a visual representation of the frequency distribution in which the frequencies are represented by bars.

histogram

A ___ is a continuous line that represents the frequencies of

scores within a class interval,

frequency polygon

Once you have created a frequency distribution and have visually represented those data using a histogram or a frequency polygon, another option is to create a visual representation of the cumulative frequency of occurrences by class intervals. This is called a ___

cumulative frequency distribution

A cumulative frequency distribution is based on the same data as a frequency distribution, but it has an added column ___

Cumulative Frequency

A ___ is identical to a column chart, but in this chart, categories are orga- nized on the y-axis and the range of scores is shown horizontally on the x-axis.

bar chart

A ___ should be used when you want to show a trend in the data at equal intervals.

line chart

Excel offers one other correlation tool, the ___ function, which calculates the correlation coefficient

PEARSON

Example of Hypothesis Testing

First, state the null and research hypothesis

The null hypothesis states that there is no relationship between the quality of the marriage and the quality of the relationship between parents and children.

The research hypothesis is a two-tailed, nondirectional research hypothesis because it posits that a relationship exists between the two variables but not the direction of that relationship.

Remember that correlations can be positive (or direct) or negative (or indirect), and the most important characteristic of a correlation coefficient is its absolute ___ and not its sign (positive or negative).

value or size

The null hypothesis is H(0) : p(xy) = 0

The Greek letter p, or rho, represents the ___ estimate of the correlation

coefficient.

population

The research hypothesis states that there is a relationship between the two values and that the relationship differs from a value of zero.

The equation is….

H1 = r(xy) ≠ 0

The second step is to set the level of ___ (or the level of significance or Type I error) associated with the null hypothesis.

risk

The level of risk or probability of a ___ or level of significance is .05 (STEP 2)

Type I error

next, select the appropriate ___

test statistic

We determined that the appropriate test is the ___

correlation coefficient

In this instance, we do not need to compute a test statistic because the sample ___ (r(xy) = .44) is the test statistic

r value

In step five, determine the value needed for ___ of the null hypothesis using the appropriate table of critical values for the particular statistic.

rejection

Our first task here is to determine the ___, which approximates the sample size.

degrees of freedom (df)

Using this number (df = 28), the level of risk you are willing to take (.05), and a two-tailed test (because there is no direction to the research hypothesis), the ___ is .381 (using df= 25 because 28 isn’t shown in the table).

critical value

So, at the .05 level, with 28 degrees of freedom for a two- tailed test, the value needed for rejection of the null hypothesis is ___

.381

In step six, ___ the obtained value and the critical value.

compare

The ___ value is .44, and the critical value for rejection of the null hypothesis that the two variables are not related is .381.

obtained

in 7 you make a decision

If the obtained value (or the value of the test statistic) is more extreme than the critical value (or the tabled value), the null hypothesis cannot be ___

accepted

If the obtained value does not exceed the critical value, the ___ is the most attractive explanation.

null hypothesis

In this case, the obtained value (.44) does ___ the critical value (.381)—it is extreme enough for us to say that the relationship between the two variables (quality of marriage and quality of parent-child relationships) did occur in our sample due to something other than chance.

exceed