Hypothesis testing Descriptive statistics Inferential statistics Allow us to make statements about a...
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Hypothesis testing Hypothesis testing Descriptive statistics Inferential statistics Allow us to make statements about a population based on info from samples of population
Hypothesis testing Descriptive statistics Inferential statistics Allow us to make statements about a population based on info from samples of population
Hypothesis testing Descriptive statistics Inferential
statistics Allow us to make statements about a population based on
info from samples of population
Slide 2
Hypothesis testing Systematic model: summarises evidence from
sampling Can now decide between possible hypotheses Null hypothesis
= H O States: no difference between two items Alternate hypothesis
= H A States: the two items are different Null hypothesis = H O
States: no difference between two items Alternate hypothesis = H A
States: the two items are different Hypotheses stated in terms of
population parameters
Slide 3
Hypothesis testing e.g. Is there a difference between the
heights of students at UWC and at Wits? Find: there is a difference
in average height. Two possibilities: populations are indeed
different or difference is due to random error H O : there is no
difference in the average height of the two groups of students H A
: there is a difference in the average height between the two
groups of students. H O : there is no difference in the average
height of the two groups of students H A : there is a difference in
the average height between the two groups of students.
Slide 4
Hypothesis testing Q: how much difference is there in the
sample?
Slide 5
Hypothesis testing What is the probability of obtaining this
much difference just by chance if we have sampled populations that
are not different? i.e., is H O correct? Probability = alpha ()
probability If probability of the statistic is > 0.05, then fail
to reject H O If probability of the statistic is 0.05, then reject
H O.
Slide 6
Hypothesis testing When rejecting, or failing to reject a H O,
we could be making one of two errors: Type I error : conclude there
is a difference when there is not a difference probability Type II
error : fail to find a difference that actually exists probability
Only way to decrease both and is to increase your sample size.
Slide 7
Hypothesis testing Reasoning of hypothesis testing 1. Make a
statement (the null hypothesis) about some unknown population
parameter. 2. Collect some data. 3. Assuming the null hypothesis is
true, what is the probability of obtaining data such as ours? (this
is the p-value). 4. If this probability is small, then reject the
null hypothesis.
Slide 8
Hypothesis testing One-sided H 0 : =110 H A : < 110 Stating
hypotheses Two-sided H 0 : = 110 H A : 110
Slide 9
Hypothesis testing Decide what p-value would be too unlikely
(the alpha level). The retention region. The range of sample mean
values that are likely if H 0 is true. If your sample mean is in
this region, retain the null hypothesis The rejection region. The
range of sample mean values that are unlikely if H 0 is true. If
your sample mean is in this region, reject the null hypothesis
Setting a criterion
Slide 10
Hypothesis testing Setting a criterion
Slide 11
Hypothesis testing Computing sample statistics A test statistic
(e.g. Z test, T test, or F test ) is information we get from the
sample that we use to make the decision to reject or keep the null
hypothesis. A test statistic converts the original measurement
(e.g. a sample mean) into units of the null distribution (e.g. a
z-score), so that we can look up probabilities in a table.
Slide 12
Hypothesis testing Setting a criterion Z crit Accept H 0 Reject
H 0
Slide 13
Hypothesis testing Making a decision
Slide 14
Hypothesis testing
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Progress assessment By now, you should be able to answer the
following questions: Do I understand all the terms dealt with in
the chapter on definitions? What are the different types of data,
and how are they represented? What is the difference between
descriptive and inferential statistics? What is the difference
between a sample and a population? What is the difference between
design structure and treatment structure? What is a measure of
location, and which is the most commonly used? What are the most
commonly used measures of dispersion, and can I use the formulas in
order to calculate them? What is the normal curve, and which
parameters define it?
Slide 21
Progress assessment How is the normal curve used in order to
determine probability? What is a Z score and Z dispersion? What are
we doing when we are hypothesis testing? What is the difference
between Type I and Type II errors? How do we use Z scores in order
to reject or fail to reject the null hypothesis? What is the
difference between a one-tailed and a two-tailed test? Qs
cont.