[Describe the sample; paint a picture; sense the data]
Location
– Central tendency of the data (mean, median, mode)
o
Mean – Average
o
Median – Central Point
Eg. 3
5
2
4
(no one median)
2
3
4
5
(choose 2 in the middle)
o
Mode – Most frequent occurring
Spread
– Variability in the data (range, standard deviation)
o
Range – maximum-minimum (difference between max and
min)
o
Standard Deviation – average deviation; average distance
of the distribution values from the mean
Shape
– Pattern indicated by the data (histogram)
o
Left skewed (highest point on the right)
o
Symmetric (highest point in the middle)
o
Right Skewed (highest point on the left)
o
Bi-model shape (two highest points) not good for data to
have this (either data collected incorrectly or used wrong
scale)
Consistency
– Performance over time
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Inferential Statistics:
to infer form the same data what the population
might think. We use inferential statistics to make judgments of the
probability that an observed difference between groups in a
dependable one or one that might have happened by chance in the
study.
Hypothesis testing
o
Means
o
Variances
o
Proportions
Regression
Examples:
Enables use of one or more samples of observation to infer
values of a population
Test hypothesis to determine if observed differenced between
groups of variables are real or occur simply by chance
Produces new information by making predictions and
generalizations based on samples
Uses data to estimates or influences about population based
upon sample
Parameter estimating – estimating a parameter based on a
sample
Confidence interval
•
Sample size
•
Sample Standard deviation
•
Sample mean
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X- bar: 54
X- bar: 50
•
Confidence level
Statistical Significance:
Definition:
The significance level, also denoted as alpha or α, is the
probability of rejecting the null hypothesis when it is true. For example,
a significance level of 0.05 indicates a 5% risk of concluding that a
difference exists when there is no actual difference.
Why do we look at statistics?
To summarize the information and to form a picture to interpret
the information easily
Why do we look at inferential statistics?
To look at how the probability is linked to a certainty or
confidence
Confidence Interval
=
48 - 52
Sample 1
X=54
X=50
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TEST
Ho
Ha
TEST
Ho
Happy
α
Ha
β
Happy
If
p
<
a→Ha
If
p≥a→ Ho
Y = Output Variable (contribute)
X = Input Variable (attribute)
Mean
o
Anova (3+)
o
T-tests (2 of 1)
Variance (Standard Deviation)
Proportionate
The test of Significance:
Test of statistical significance can be used to determine the
extent to which chance has operated

- Fall '19
- researcher