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Statistics 2
Shira Farby
Parametric statistics
Reading: Field, A. & G. Hole. 2003. How to design and Report Experiments. London: A
Sage Publications Company, 120-139; 141-155
Last time: we looked at models for central tendency (mean, median, mode)
Today: we look at how much the data is spread / varied.
Key terms: Deviation, sun of squared errors, variance, standard deviation
Term
mean
Deviation
sun of squared
errors
variance
formula
Definition in words
∑𝑥
𝑁
𝐷𝑒𝑣 = 𝑥 − 𝑥
𝑥̅ =
𝑆𝑆 = ∑(𝑥 − 𝑥)2
𝑆𝑆
𝑁−1
𝑆𝐷 = √𝑆 2
𝑆2 =
standard deviation
𝑆𝐷 = √
Degrees of
freedom
Standard error
∑(𝑥 − 𝑥)2
𝑁−1
𝑑𝑓 = 𝑁 − 1
𝑆𝐸 =
𝑆𝐷
√𝑁
Sample-population
Key terms: sampling distribution of the mean, standard error, source of variance,
confidence interval
sampling distribution of
the mean
standard error
source of variance
confidence interval
Statistics 2
Shira Farby
Class practice
An experiment compared children with specific language impairment (SLI) and children
who are typically developing (TD). The research hypothesis was that the groups will have
different responses to different word order.
30 Children were tested, each was presented with 10 sentences (5 SVO, 5 VSO).
The task was sentence repetition, and the response measure was whether the verb was
produced correctly (yes/no)

Before we begin:
Which are the independent variables in this design?
Which are the dependent variables? On what scale?
How many conditions? Within subject or between subject?
Describe the findings:
In a _____ design of _____ conditions, the effect of ___________________________ as
the independent variable(s) on _________________________as the dependent
variable(s) was measured in a ___________________task. Mean responses and standard
deviations are presented below:
MEAN
SD
Statistics 2
Shira Farby
Inferential statistics
H0= the experiment has no effect
 The purpose of statistical inference is to reject this hypothesis
H1 = the mean of the population affected by the experiment is different from the general
population
 In order to reject the null hypothesis, we check if our sample belongs to the
population under H1 or H0
 Is the difference between the sample and the population big enough to reject H0?
Key terms: level of significance, critical value, reject the null hypothesis, power of the
effect
Statistical tests

t-tests
Paired t-test
Independent t-test

ANOVA
(Comparing Means of more than two samples)
One way ANOVA
Two-Way Independent ANOVA
Two-Way Repeated Measures ANOVA
Two-Way Mixed ANOVA