Background Information about the data:
Students were randomly divided into two groups (maths skills and confidence building) and asked to complete a number of scales. These were the Fear of Statistics Test (fear of stats time 1), Confidence in coping with Statistics Scale (confidence scale score time 1) and Anxiety Scale (anxiety scale score time 1). One group (group 1 – maths skills) was given sessions designed to improve maths skills. The other group (group 2 – confidence building) was given sessions designed to build confidence in the ability to cope with statistics. After the program, the subjects were asked to complete the scales again (fear of stats test score time2, confidence scale score time2 and anxiety scale score time2). Their performance on the stats exam was also measured.
Scales used to collect data:
Fear of Statistics test:
• 10 questions measured on a 5-point Likert scale.
• Scores range between 10 and 50
• High scores indicate high fear
Confidence in coping with Statistics Scale:
• 5 questions measured on a 5-point Likert scale
• Scores range between 5 and 25
• High scores indicate high confidence
Anxiety Scale:
• 10 questions measures on a 5-point Likert scale.
• Scores range between 10 and 50
• High scores indicate high anxiety
Exam:
• Score out of 100
Grade:
• 70 or above is considered a pass grade
Effort
• Students were given a rating of “poor, average or excellent” at the end of the intervention. This was how much effort the subject coordinator thought the students gave throughout the class.
Some supplementary content before beginning to use SPSS:
Before beginning to use SPSS to undertake inferential statistical tests, it is vital that you understand the content provide in Box 1 below.
Decisions…..decisions….Which statistical test/analysis should I use?
It is essential that you choose the right test/analysis to answer your research question. Your choice of test depends on:
Type of variables: We have already learnt about research questions in previous units, so let’s talk about the type of variable. You need to decide if you have numerical or categorical variables. To run inferential statistical analysis, you need 2 or more variables, this means you will have either…
1 numerical, 1 categorical
2 categorical
2 numerical
For numerical variables: When numerical variables are involved, you will need to determine if the test is parametric or non-parametric and also determine if you have paired or unpaired data.
Parametric and non-parametric tests:
Parametric tests assume that the data is normally distributed.
Non-parametric tests do not rely on any normal distribution of data (data NOT normally distributed).
So, how do I know if my data is normally distributed or not?
This can be determined by:
1. Application of the Central Limit Theorem
2. Visual inspection and statistical tests
1. The Central Limit Theorem (CLT)
• The CLT states that if you have a population with a mean and standard deviation and take sufficiently large samples from the population, the distribution of the sample means will be approximately normally distributed.
• This will hold true when the population is initially normal distributed or skewed, providing that the sample size is 30 or more (n ≥ 30).
• Therefore, we can assume our data is normally distributed if you have 30 or more cases/participants/respondents etc.
Note: If you have multiple groups (for example, splitting the sample into male and female), data for EACH group must fit these criteria.
2. Visual inspection and statistical tests can be viewed together as follows:
• 2A The histogram of your data represents an approximately symmetrical distribution (this is a visual inspection only and cannot infer normal distribution alone)
• 2B We can use skewness value to compare to 0 and to describe our data (this is for descriptive purposes only and cannot infer normal distribution alone)
A value of 0 = perfect normal distribution
A value of >0 = positive skew
A value of <0 = negative skew
• 2C We can look at the Shapiro-Wilk test of normality (this is our value of interest when determining our data distribution)
For normal distributions, the significance value (Sig) will be > 0.05 (non-significant).
For non-normally distributed data, the significance value (Sig) will be < 0.05 (significant). Therefore, data is considered to follow a normal distribution (and therefore be parametric) if the following applies:
• The histogram looks symmetrical AND the statistical tests are non-significant.
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