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When conducting statistical analyses, many numbers, charts and graphs are outputted. These can be confusing, and it can be challenging to determine what exactly they mean and how we can identify if these figures support or disprove our hypothesis. The two crucial statistical values to determine this are observed values and critical values.First, we will delve into the observed value…
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Jetzt kostenlos anmeldenWhen conducting statistical analyses, many numbers, charts and graphs are outputted. These can be confusing, and it can be challenging to determine what exactly they mean and how we can identify if these figures support or disprove our hypothesis. The two crucial statistical values to determine this are observed values and critical values.
In statistical analyses, the observed value is one of the most important figures as it allows researchers to identify if their data follows the trend predicted in their hypothesis.
A hypothesis is a predictive statement that states what the researcher expects to find in their study.
The observed value is found when carrying out statistical tests called inferential tests.
Some examples of inferential tests are the chisquared test, MannWhitney U test, Wilcoxon, and Spearman's Rho test.
Now that we've figured out the use of the observed value let's explore the observed value meaning.
The observed value meaning is the statistical figure that calculates/ measures the trend/ pattern investigated in the research.
The observed value differs depending on what inferential test is used. For instance, a correlation measures the association/ relationship between variables; using the figure r. In contrast, a ttest compares the mean of two groups; using the figure t.
But how do we know if the observed value we found is significant? And this is where the critical value comes in.
The critical value is a set value that we look at to see if what we have found (the observed value) is due to the variables investigated or chance.
The process involves comparing the observed value to the critical value provided by the statistical test we decide to use (this is why it's essential to ensure you're using the proper test).
First, we need a significance level (pvalue) to do this. Usually, the significance level is p = 0.05, although this value can change.
The 'p' stands for probability.
A pscore of .05 suggests there is a 5% probability the results we found are due to chance. And p = .01 means there is a 1% probability of the results being due to chance.
The 0 before the decimal point in critical values is not reported per APA standards.
There are different rules regarding the critical value in the tests we mentioned above, the chisquared test, Mann Whitney U test, Wilcoxon, and Spearman's Rho test.
Chisquared test: significant if the observed value (χ^{2}) is equal to or larger than the critical value
MannWhitney U test: significant if the observed value (U) is equal to or smaller than the critical value
Wilcoxon test: significant if the observed value (T) is equal to or smaller than the critical value
Spearman's Rho test: significant if the observed value (r) is equal to or larger than the critical value
When using a critical values table, the observed value can be compared to the critical value to see if the results are statistically significant. Each statistical test will have its own critical values table. The critical value we need also depends on if our hypothesis is one or twotailed.
A onetailed hypothesis is when the researcher predicts that the findings will go in a particular direction, e.g. getting more sleep will lead to better exam grades.
A twotailed hypothesis is a predictive statement that suggests there will be an effect, but the direction is unsure, e.g. if there will be an increase or decrease.
We need to know two essential things for the critical values table: the 'N' number (number of participants) and the 'df' (degrees of freedom). Each critical table will have a column of N values or df values depending on what test it is.
We need to look at the N or df column in critical tables provided by statistical tests to find a comparable critical value. Then we can compare the observed value to the critical value and decide on significance based on the test parameters we covered above.
Let's look at an example to help you make sense of this.
The MannWhitney U test compares the scores between two groups (independent groups design), focusing on ranks and ordinal data. Let's look at the steps involved to see if our results are significant.
As we see in this table, ten participants are in each group.
Group A scores  Group B scores 
3  24 
5  6 
8  4 
12  22 
2  10 
9  18 
11  20 
15  1 
14  7 
17  19 
We need to work out the observed value, 'U'. To do this, we need to calculate scores for the two groups (Ua and Ub). The U score will be the lower score of the two.
First, we need to rank each score; this is done for both groups. The highest score is rank 1, the one after that is rank 2, and so on.
Group A scores  Rank  Group B scores  Rank 
3  18  24  1 
5  16  6  15 
8  13  4  17 
12  9  22  2 
2  19  10  11 
9  12  18  5 
11  10  20  3 
15  7  1  20 
14  8  7  14 
17  6  19  4 
Now let's work out at Ua. We need to know Na and Nb, the total number of scores in each group. There were 10 participants in each group, so a total of 10 scores for each group, Na = 10 and Nb = 10.
First, multiply Na and Nb (10 x 10 = 100)
Then multiply Na by (Na + 1) and then divide by 2 (10 x 11/2 = 110/2 = 55) and add the two scores together (100 + 55 = 155). Afterwards, Group A's ranks should be added together (18 + 16 + 13 + 9 + 19 + 12 + 10 + 7 + 8 +6 = 118). And finally, subtract this from the number in the last step (155  118 = 37).
Thus, Ua = 37
Then, repeat for Ub; we won't go over the steps again. In this case Ub = 63.
The U value is the lower of the two, so here, U = 37.
Next, we need to note if our hypothesis is one or twotailed and the pvalue. Let's suppose our hypothesis is onetailed with a pvalue of 0.05.
Then we must consult our critical values table for the MannWhitney U test.
How we do calculations depends on the test used because the various inferential tests measure/ calculate different things.
The critical values table for the MannWhitney U test, p ≤ 0.05 (onetailed), p ≤ 0.10 (twotailed).
 Nb  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20 
Na 

















5 
 4  5  6  8  9  11  12  13  15  16  18  19  20  22  23  25 
6 
 5  7  8  10  12  14  16  17  19  21  23  25  26  28  30  32 
7 
 6  8  11  13  15  17  19  21  24  26  28  30  33  35  37  39 
8 
 8  10  13  15  18  20  23  26  28  31  33  36  39  41  44  47 
9 
 9  12  15  18  21  24  27  30  33  36  39  42  45  48  51  54 
10 
 11  14  17  20  24  27  31  34  37  41  44  48  51  55  58  62 
11 
 12  16  19  23  27  31  34  38  42  46  50  54  57  61  65  69 
12 
 13  17  21  26  30  34  38  42  47  51  55  60  64  68  72  77 
13 
 15  19  24  28  33  37  42  47  51  56  61  65  70  75  82  84 
14 
 16  21  26  31  36  41  46  51  56  61  66  71  77  82  87  92 
15 
 18  23  28  33  39  44  50  55  61  66  72  77  83  88  94  100 
16 
 19  25  30  36  42  48  54  60  65  71  77  83  89  95  101  107 
17 
 20  26  33  39  45  51  57  64  70  77  83  89  96  102  109  115 
18 
 22  28  35  41  48  55  61  68  75  82  88  95  102  109  116  123 
19 
 23  30  37  44  51  58  65  72  80  87  94  101  109  116  123  130 
20 
 25  32  39  47  54  62  69  77  84  92  100  107  115  123  130  138 
The values we need have been highlighted. First, we find Na, which in our case is 10. Then we find Nb, which is 10 too. We find the value where these two meet, which is the critical value. Here it is, 27.
Our observed value is 37, which is larger than the critical value of 27.
Therefore, our results are not significant, so we can accept the null hypothesis and reject the alternative hypothesis.
From this critical and observed psychology example, we can infer there is no statistical difference between the scores of the two groups. i.e. the null hypothesis is accepted.
Critical values psychology is a statistical figure used to identify if the results from inferential tests are significant or if they occurred due to chance.
The observed value is the result obtained from a statistical test. We can compare the observed value to the critical value to see if it is significant or not.
Finding the observed value depends on the statistical test used and can be found using calculations and the corresponding critical values table.
Hypothesis testing critical values is when we look to see if what we have found is due to the variables proposed in the hypothesis or chance. For some tests, the observed value needs to be the same or lower than the critical value to be significant. It needs to be the same or higher than the critical value for other tests to be significant.
The observed value meaning is the statistical figure that calculates/ measures the trend/ pattern investigated in the research.
Critical values psychology is a statistical figure used to identify if the results from inferential tests are significant or if they occurred due to chance.
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