Inferential Statistics & Variables Paper This is the first week we’re looking at a specific inferential statistic. Please read the week’s materials and “W

Inferential Statistics & Variables Paper This is the first week we’re looking at a specific inferential statistic.

Please read the week’s materials and “Which Statistical Test Do You Use?” as linked in this week’s materials. This is a road map featuring many of the inferential statistics we’ll cover in the next few weeks.

As you’re reading this document, think about your research question and the variables in your evaluation proposal. Are you looking at relationships between variables or differences between groups? Maybe both for different variables? What test/s do you think you’ll propose using in your evaluation proposal?

In your reflection, remind me of

Your research question
Your variables
And propose the statistical test/s you think you’ll use to answer your research question/s.

It’s okay if you’re not sure. I just want you to start thinking about these things. Week 9 Materials
Contents
• Readings
• An Important Note
• t-tests
o t-test for Independent Groups
o t-test for Dependent Groups
• The t Distribution
o Degrees of Freedom
o Critical Value of t
• The 6 Steps of Hypothesis Testing for a t-test
• Important Statistical Terms
• Tools for Calculating t-tests
1 Readings
Textbook Readings
• Inferential Statistics, t-tests, Chapter 9,Assignment Preparation
• Gender Differences in Searching for Health Information on the Internet and the
Virtual Patient-Physician Relationship in Germany: Exploratory Results on
How
Men
and
Women
Differ
and
Why
(Link:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4526954/)
• Which Statistical Test Do You Use? (PDF)
An Important Note
The remaining weeks of the semester will focus on inferential statistics. If you
recall from chapter 1 (I won’t be offended if you don’t!), inferential statistics are
statistical procedures used to test hypotheses and draw conclusions from data collected
during research studies.
From here on out, we’ll use the text more as a reference. A greater emphasis will
be on the lectures and links within them. Consequently, the lectures will be longer than
in previous weeks but the text reading will be lighter.
Also, know that in a traditional statistics course, you would learn how to calculate
these inferential statistics. You won’t be expected to calculate these statistics by hand,
but you will be directed to links to statistical software programs. Know this course
offers a broad review of inferential statistics and you are encouraged to take additional
statistical courses to master this material.
2
t-tests
This lecture will cover the t-test for independent groups & the t-test for dependent
groups. This material is covered in Chapter 9.
Let’s say a marketing firm asks you to volunteer to help them with product
evaluation. You are randomly assigned to 1 of 2 groups, Group A or Group B (you don’t
3
know there is another group besides the one to which you are assigned). Group A sees
the Big Y brand soup and Group B sees the Progresso brand soup.
You (and everyone else) are then asked to evaluate the aesthetics of the product
labels on a scale from 1 (does not look appealing) to 7 (looks very appealing).
Below are the ratings from the two focus groups.
Question: Looking at these numbers, how do we know which soup is more appealing?
Answer: We compare the group means.
• Group A: x̄ = 22/7 = 3.14
• Group B: x̄ = 36/7 = 5.14
How do we know if 3.14 is statistically different than 5.14? We need to conduct
an independent groups t-test (independent because the two groups were not related in
any way, they had different people in them).
Required Video 1: Independent t-test – Explained Simply (Link:

3.1 t-test for Independent Groups
This test is used when participants are randomly assigned to either an experimental
group or a control group. This type of experiment allows us to assume a cause and effect
relationship between the independent and dependent variable.
Assumptions
• the groups are independent
• the dependent variable is normally distributed
• the variance is homogeneous
Imagine another way of doing things…
Let’s say you’ve been hired to evaluate brownies on a scale of 1 (do not like) to 7
(like very much). You taste Brownie A, rate it, take a sip of water and then taste Brownie
B and rate it. The ratings provided by you and six others are below.
How do we know which brownie tasted better? We compare the means, as we did
before
• Brownie A: x̄ = 28/7 = 4.00
• Brownie B: x̄ = 31/7 = 4.43
But we can’t do an independent samples t-test because the Brownie A ratings are
from the same people as the Brownie B ratings (i.e., they are NOT independent).
3.2 t-test for Dependent Groups
We need to use a t-test for dependent groups for the brownie ratings. Know that
a t-test for dependent groups is also called
• a repeated measures t-test
• a paired samples t-test
• a dependent-samples t-test
• a within-subjects t-test
Required
Video
2:
Paired
t-test
Lecture
(Link:

This test is used when the participants in both groups are related to each other in
some way. The pair of scores are dependent (i.e., linked).
Examples
o Before and after some treatment
▪ Before: How stressed do you feel?
▪ Treatment: Have a massage
▪ After: Now how stressed do you feel?
o Participants are ‘related’ in some way
▪ Twins
▪ Couples
▪ Similar/matched scores
o Participants receive both levels of the variables
▪ For example, both brownie A and brownie B
This test can often be more powerful than a t-test for independent groups because
the variability of the same participant over time is less than the variability between 2
unrelated participants.
Assumptions of the t-test for dependent groups
• the dependent variable is normally distributed
• there must be an equal # of scores in each group
• the scores within a group are independent of one another
The t Distribution
The population variance of this distribution is estimated, so the comparison
distribution is not a normal curve
• It is a t distribution
• It is like a normal curve
o Bell-shaped
o Unimodal
o Symmetrical
• But has more scores at the extremes (i.e., heavier tails) and varies according to
the degrees of freedom
4
4.1 Degrees of Freedom
Degrees of freedom are the number of values free to vary in a calculation.
Example
_ + _ + _ + 2 = 16
•
5 + 3 + 6 + 2 = 16
o 4 + 5 + 5 + 2 = 16
o 1 + 9 + 4 + 2 = 16
Three numbers in each of these equations are free to vary- the last number can only be
one value if the first three vary- so this calculation has 3 degrees of freedom.
The equation for degrees of freedom for a t distribution is:
df = n – 1
Know that as the sample size increases, the t distribution approaches the normal
distribution.
o
4.2 Critical Value of t
The table of critical values of t can be found at the back of your book in Table 3.
You need to know 3 things in order to find the critical value of t:
• the degrees of freedom (n-1)
• the level of significance (researchers usually set this, alpha, at .05)
• whether it is a directional (one-tailed) or non-directional (two-tailed) test
Example 1
You have 21 participants in your sample. You set the probability of making a Type I
error (α) at .05. You have a non-directional hypothesis (a two-tailed test).
Question: What is the corresponding critical t?
Answer: 2.086
Example 2
You have 17 participants in your sample. You set the probability of making a Type I
error (α) at .01. You have a directional (one-tailed) hypothesis.
Question: What is the corresponding critical t?
Answer: 2.583
Example 3
You have 17 participants in your sample. You set the probability of making a Type I
error (α) at .01. You have a directional (one-tailed) hypothesis.
Question: What is the corresponding critical t?
Answer: 2.583
The 6 Steps of Hypothesis Testing for a t-test
1. State the Research Problem
2. State the Statistical Hypotheses
3. Make the Decision Rule
4. Do the Calculations
5. Make the Decision
6. The Interpretation
1. State the Research Problem
“Mean A is different from mean B.”
2. State the Statistical Hypothese
H0: ̅ 1 = ̅ 2
Ha: ̅ 1 ≠ ̅ 2
3. Make the Decision Rule
Determine a one-tailed or a two-tailed (non-directional alternative hypothesis) test
of significance
Determine the level of significance
p =.05 (conventional level)
4. Do the Calculations (or have a statistical software program do them for you!)
Determine the critical values of t at p