Transcript Done in Class - Basic Statistics - week 5

Understanding
Your Results
By David Kilgour
1
Statistics: What’s the point?
• Observations researchers make are DATA
• STATISTICS are a set of mathematical
procedures for summarizing and interpreting
data
• To be a good methodologist you need a
CONCEPTUAL skills
2
Statistics: What’s the point?
• 2 types of stats:
• Descriptive Statistics (“the easy ones”)
• Summarize the data in numbers
• Inferential Statistics
Make inferences about the meaning of the
data (infer that the results from the sample
apply to the population)
3
Descriptive Statistics
• Measures of Central Tendency
(the typical response)
• Mean: The sum of all scores divided by
the total number of scores (M)
• Median: The midpoint (Mdn)
• Mode: The most frequent score
4
Descriptive Statistics
Variability
(the amount by which subjects vary from
one another)
• Variance and Standard Deviation: The
“standard” amount by which all of the
scores deviate from the mean
• SD = √Σ (x – M)^2/N
• (x = each score; M = mean; N = number
of scores)
5
Descriptive Statistics in a
Nutshell
• Central tendency tells you about the
“average” person
• Variability tells you how much people
differ from the “average” person
• Great for organizing and summarizing data
but they are only 1/2 the picture…
6
• How do you deicide if the group
differences are reliable and not
due to chance alone?
7
Inferential Statistics
• It is not possible to study an entire population so
we use a sample of the population
• Inferences are made about the likelihood that
differences in the sample reflect differences in the
population
• Inferential statistics tell us if differences in
the
sample are large enough to conclude that there
are differences in the population
(“moving from the sample to the population”)
8
Inferential Statistics
• Inferential statistics establish a
probability
that the results are real (not due to error)
• Data with a probability (alpha level) less
than 5% (p = .05) are regarded as
statistically significant
• This means 5 times out of 100 the
results are going to be due to random
error
9
Points to Ponder
• Statistical significance allows us to say
that our results are probably not due to
chance
• ‘Significance’ only refers to statistical
probability, not to the theoretical or
practical importance
10
Choosing a Statistic
My research Question is about …
Differences
Frequencies
between means
Relationships
Between
variables
t test, ANOVA
Chi-Square
Correlation
Coefficients
Interval / Ratio
Nominal
Ordinal
Interval/Ratio
11
Chi-Square Test
• Nominal data → frequency count
• Observations can only belong to one
category (e.g., male OR female)
• Total # of observations = total # of
participants
• χ2 = Σ(O – E)^2/ E
• O= Observed frequencies (your data)
• E = Expected frequencies (null
hypothesis)
12
Qualitative Data
• Code observations to identify the main
categories/themes/trends/patterns in the data
• The goal of qualitative research is to provide a
description of the context
• Specific examples (snapshots) help to clarify the
patterns
• Use subheadings in the Results to identify the
main trends (method or pattern based)
13
Qualitative Data
• Open-Ended Interviews
The data from the open-ended interviews with students and
teachers are consistent with the questionnaire data.
Specifically, students commonly reported that teachers
controlled and directed their work to a much lesser
degree when students worked on-line than otherwise. As
one high-school student put it: It’s really like she [the
teacher] acts different, because when she is teaching the
class, it’s sort of stuff we have to do – you know,
assignments we have to do. But on the internet, we have
a lot more freedom to do almost whatever we want as
long as we’re getting the work done…
14
15