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Null Hypothesis Significance
Null Hypothesis Significance Testing
Please analyze the data according to the NHST steps. Show your work and respond to as much of the following as you can.
STUDY 1
STEP 1 Design a study (Make a choice for the items that have a choice/choice below)
a) observation/correlation/experiment?
b) Model variable is IV/predictor/QIV/none?
c) Outcome variable is nominal/ordinal/interval/ratio?
d) Model variable is continuous/discrete?
e) What parametric assumptions still need checking?
Assume representativeness = yes and linearity = yes.
f) RQ: What is the effect/association of _____________ on/to ___________?
STEP 2 State mutually exclusive hypotheses
a) H0:
b) H1:
STEP 3 Calculate test statistic(s), df, and effect size(s). Indicate whether the effect size(s) are small, medium, large.
STEP 4 Compare to alpha level
STEP 5 Invoke a decision rule and draw a conclusion(s)
STEP 6 Interpret and report Write up the results in APA style, include appropriate descriptive statistics, inferential statistics, and effect size. Interpret the results in terms of the research question(s).
Results
STUDY 2
STEP 1 Design a study (Make a choice for the items that have a choice/choice below)
a) observation/correlation/experiment?
b) Model variable is IV/predictor/QIV/none?
c) Outcome variable is nominal/ordinal/interval/ratio?
d) Model variable is continuous/discrete?
e) What parametric assumptions still need checking?
Assume representativeness = yes and linearity = yes.
f) RQ: What is the effect/association of _____________ on/to ___________?
STEP 2 State mutually exclusive hypotheses
a) H0:
b) H1:
STEP 3 Calculate test statistic(s), df, and effect size(s). Indicate whether the effect size(s) are small, medium, large.
STEP 4 Compare to alpha level
STEP 5 Invoke a decision rule and draw a conclusion(s)
STEP 6 Interpret and report Write up the results in APA style, include appropriate descriptive statistics, inferential statistics, and effect size. Interpret the results in terms of the research question(s).
Results
Null Hypothesis Significance Testing
Null Hypothesis Significance Testing
Please analyze the data according to the NHST steps. Show your work and respond to as much of the following as you can.
STUDY 1
STEP 1 Design a study (Make a choice for the items that have a choice/choice below)
a) observation/correlation/experiment?
b) Model variable is IV/predictor/QIV/none?
c) Outcome variable is nominal/ordinal/interval/ratio?
d) Model variable is continuous/discrete?
e) What parametric assumptions still need checking?
Assume representativeness = yes and linearity = yes.
f) RQ: What is the effect/association of the number of hours worked on/to the number of publications?
STEP 2 State mutually exclusive hypotheses
a) H0: There is no association between the number of hours worked and the number of publications by a faculty member
b) H1: There is an association between the number of hours worked and the number of publications by a faculty member
STEP 3 Calculate test statistic(s), df, and effect size(s). Indicate whether the effect size(s) are small, medium, large.
Pearson correlation0.604
Df = 20 – 1 = 19
P-value0.005
STEP 4 Compare to alpha level
A p-value of 0.005 is statistically significant for an alpha level of 0.05
STEP 5 Invoke a decision rule and draw a conclusion(s)
The null hypothesis is rejected if we have a statistically significant p-value. We therefore conclude that there is an association between the number of hours worked and the number of publications by a faculty member
STEP 6 Interpret and report Write up the results in APA style, include appropriate descriptive statistics, inferential statistics, and effect size. Interpret the results in terms of the research question(s).
Results
Correlation: hours, num_pubsCorrelations
Pearson correlation 0.604
P-value 0.005
Descriptive Statistics: num_pubs, hours
Statistics
Variable N N* Mean SE Mean StDevMinimum Q1 Median Q3 Maximum
num_pubs20 0 7.45 2.98 13.31 0.00 0.25 1.00 9.25 49.00
hours 20 0 24.85 3.28 14.65 5.00 13.00 21.50 40.25 50.00
STUDY 2
STEP 1 Design a study (Make a choice for the items that have a choice/choice below)
a) observation/correlation/experiment?
b) Model variable is IV/predictor/QIV/none?
c) Outcome variable is nominal/ordinal/interval/ratio?
d) Model variable is continuous/discrete?
e) What parametric assumptions still need checking?
Assume representativeness = yes and linearity = yes.
f) RQ: What is the effect/association of _____________ on/to ___________?
STEP 2 State mutually exclusive hypotheses
a) H0:
b) H1:
STEP 3 Calculate test statistic(s), df, and effect size(s). Indicate whether the effect size(s) are small, medium, large.
STEP 4 Compare to alpha level
STEP 5 Invoke a decision rule and draw a conclusion(s)
STEP 6 Interpret and report Write up the results in APA style, include appropriate descriptive statistics, inferential statistics, and effect size. Interpret the results in terms of the research question(s).
Results
Null and alternate hypotheses
Null and alternate hypotheses
Week X Y XY XX 1 29 21 609 841 2 35 32 1120 1225 3 41 11 451 1681 4 32 26 832 1024 Total ∑X = 137 ∑Y = 90 ∑ XY = 3012 ∑XX = 4771 Given n = 4, ∑X = 137 Mean = ∑X / n Standard Deviation (s) = √ ∑{(X – x)(X – x)} / n Mean = 137 / 4 Standard Deviation (s) = √ 17689 / 4 Mean = 34.25 Standard Deviation (s) = √ 4422.25 Standard Deviation (s) = 66.5 The null and alternate hypothesis here becomes:
H0: μ ≥ 34.25
H1: μ < 34.25
The hypothesis test statistics is:
Z = (x-μ) / (σ-√n)
= (34.25-35) / (0.05-√100)
= -0.75 / -9.95
= 0.075
Probability (p) value when (σ) = 0.05, and its meaning
p-value = P(Z>0.075) = 0.0001
The probability of getting a sample whose mean is 34.25 or more when H0 is true is 0.0001.
Comparing the p – value to alpha
For a large test statistic, the critical value is large and its p-value is small than even the alpha value.A rejection is made if test statistics is found in the rejection region.